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Weighing Helps Understanding the Laws of Nature

PhysicsChemistry

Biology

Practical Experiments

in the classroom

1

3

Preface

8

History

Density of solid bodies from volume and weight measurement 6Density of solids (buoyancy method) 7Temperature dependence of the density of water 9Density of air 11Density of gases 12Buoyancy in gases 13Density of liquids 15Force and opposing force 16Deflection force 17Resisting force in an airstream 20Forces on an airfoil 22Dependence of the magnetic field strength of a coil on the current intensity 25Soft iron in a magnetic field 26

Physics

How much sodium bicarbonatedoes an effervescent tablet contain? 28Determination of fat in soya and nuts 29Determination of chalk in rock and soil samples 30Determination of the water of crystallization in salts 31Thermolysis of salts 33Synthesis of copper sulfide 35Molar mass determination of liquified gas 37Rate of evaporation 39Homogeneous catalysis: The decomposition of H2O2 41

Chemistry

Cont

ents

Transpiration in plants 45Intake of water vapor by lichens 47Water intake and loss in mosses 48Water and ash content of different plant organs 49Concerning alcoholic fermentation 51

Biology

Pref

ace

3

Descriptive experiments in the classroom and independent experimentation in practicalcourses: for the natural sciences, these continue to be those components which impart theessential flesh and blood to theoretical studies of natural laws. A concept illustrated byexperiment is not only easier to convert into abstract formulae, but can also be better retainedin the pupil’s memory.

With the aid of an electronic balance, you can demonstrate the meaning of the laws, formulaeand phenomena in physics, chemistry and biology in a most impressive manner.

Our principal concern has been to ensure that the individual experiments can be set up withvery little effort and with simple resources. In addition, we have tested each individual experi-ment a number of times. During demonstration of an experiment, the simple handling of theelectronic balances demands only your occasional attention thus enabling you to concentratefully on the instruction. We would ask you to observe the general safety directions outlinedbelow.

It remains for us to wish you every success and a great deal of enjoyment.

METTLER TOLEDO GmbHCH-8606 Greifensee

This brochure shows examples of how practical experiments may be set up for teachingpurposes. The set-up, materials and substances used, as well as the specified quantities havebeen selected purely for purposes of illustration. All responsibility for the set-up and correctperformance of the experiments is borne solely by the person who carries them out. METTLER TOLEDO disclaims any liability with respect to the above.

The experiments should be carried out only by persons qualified to do so or under the super-vision of such qualified persons.

The operating instructions for all the equipment used (precision scales, Bunsen burners, wind generator etc.) must be observed.

Various substances mentioned in the experiments may be hazardous, toxic or explosive. Use of such substances may also be prohibited or restricted by law or by internal schoolregulations, or be subject to rigorous (safety) specifications. Responsibility for using all thesesubstances and observing the applicable specifications is borne solely by the user. All safetyspecifications and directions must be observed.

General safety directions

His

tory

4

Accurate measuring equipment is not only the basis of scientific research, but also plays avery prominent role in our lives in general. It is important for all of us in day-to-day events. People who can measure length, time and weight accurately are trustworthy. People who areauthorized to determine mass and weight have power.

Whereas time and linear measure could be derived biologically or physically, the establish-ment of weight units was random. Thus countries, princedoms and towns had all their ownweight units well into modern times.

It was not until the Meter Convention in 1875, now signed by over 50 countries, that a stan-dardized mass and weight system became possible.

Our well known base unit of 1 kilogram corresponds to the mass of the international prototype kilogram. This “prototype kilogram” is stored in the InternationalBureau of Weights and Measures in Sèvres near Parisunder extremely strict climatic conditions. It is a cylinderof height 39 mm and diameter 39 mm and is made of an alloy of 90% platinum and 10% iridium thusguaranteeing constant mass. National standards arecompared at regular intervals of 25 years with thisprototype kilogram, but not too frequently to ensure that the prototype kilogram does not become unnecessarilyworn.

The history of the balance or scale goes back a long way. Remains of the oldest knownbalances were discovered in a prehistoric grave in Egypt: they have been dated around 5000 years before our time. Single weight stones are known from even earlier times. It can beassumed that man has been weighing for more than 7000 years.

The best known form of balance (or scale) is the equal-arm beam balance. A weighing sam-ple is compared in proportion 1:1 with standard weights. But simple beam balances with onlyone lever or unequal-arm beam balances with a different transmission ratio can frequently befound in historical drawings. Other important types of balances are, e.g. the weighbridge forvehicles, the familiar postal scale or spring balances in which the weight force dependent ongravity is shown on a scale.

The balance is familiar to man not only as one of the mostcommon and diverse measuring instruments, but also sincetime immemorial as a emblem of equality and fair assessment.The balance or scale thus occupies an equivalent position asthe sword of judgement of the Goddess Justitia as a symbol of a balanced judgement.

Metrology, the art of measurement

Cultural history

5

Another interesting symbolic use of the balance involves the weighing ofsouls of the ancient Egyptians and Greeks. Ancient Egyptian mummycaskets and papyri accompanying the dead contain many representationsof soul weighing, which was used as a means of judgement in the court of the dead. Depending on the outcome, the soul, shown on the balanceas a small vessel, with the person to be judged standing by, passes to agod of damnation for destruction or to a god of light for safekeeping. The soul is weighed with the truth shown in the form of a feather (hiero-glyphic for truth) on the other weighing pan.

A similar portrayal from the Christian veneration ofsaints is that of Saint Michael as the just advocate inthe Last Judgement.

That something light or even immaterial can have a large weight is shown above all whensomeone succeeds in bringing about a weighty decision with a single word. However, a wrong word can also have severe consequences, But that we do not completely lose oursense of balance is ensured by a good friend to whom the scales are tipped in our favor: He may then perhaps give us the following advice “Weigh weighty things up first”. Yet whilepeople who weigh up every word may generally be clever, they must be regarded as pedanticcontemporaries who are uncomfortable to be with.

Colloquialisms

Phys

ics

6

The concepts of mass and density are illustrated with this experiment; it also serves as anintroduction to weighing techniques.

Calculation of the volume from the dimensions of regularly-shaped solid bodies. The mass is determined by weighing. The density is calculated from the volume and mass.

METTLER TOLEDO precision balance (readability 0.01g)Rectangular, spherical, conical or cylindrical bodies (nonporous)Length gauges, sliding calipers, micrometer screw gauges

Each pupil is given a sample and determines the dimensions and calculates the volume. Then the sample is weighed (under supervision ot the teacher) and subsequently the resultsare evaluated.

The density is the quotient of mass and volume

ρ = units: g/cm3, kg/m3

In school experiments, the individual samples can be evaluated in succession by all pupils(or groups of 2 pupils).

The relative uncertainty of the result should be estimated by means of an uncertainty calculation:– Weighing uncertainties neglectable– Accuracy of the geometric shape?– Relative uncertainty of the length measurements?– Relative uncertainty of the weighing?

– The balance only displays the exact mass of the sample, when the sample density is 8000 kg/m3. In the determination of bodies with low density (e.g. styrofoam), a buoyancycorrection must be made according to the formula, otherwise a relative error is incurred.

– With thin wires or sheets of known density, the thickness can be determined by weighing(copper wire, aluminium foil).

– From the known density of cylindrical or spherical bodies, π can be calculated.

mV

Density of solid bodies from volumeand weight measurement

Teaching objective

Assignment

Material

Procedure

Evaluation

Final considerations

Note

7

This experiment is used to illustrate the concepts of mass, buoyancy and density.

For irregularly-shaped solid bodies, determination of the volume from the buoyancy and themass by weighing. These two quantities are used to calculate the mean density of the body.

METTLER TOLEDO precision balance (readability 0.01g) and a METTLER TOLEDO density kitalternativelyBeaker with waterStand with boss and rodThin threadWide-meshed basket of fine wireTweezersBody of any shape (e.g. screw, key, coin)

The empty basket hangsfrom a thread inwater without touchingthe beaker wall.

The balance is tared. The body is placed on the weighing pan next to the beaker and its massm determined. The body is now placed in the basket using tweezers. No water must be lost by splashing or remain on the tweezers. Air bubbles around the basketand the object must be removed. The object experiences the lifting force (buoyancy) FL in anupward direction and exerts an opposing force F of equal magnitude on the water in a down-ward direction. The balance displays m~, and FL = m~ · g holds.

According to Archimedes’ principle FA = Vbody · ρliq · g = m~g

Vbody =

and the density ρbody = = = ρliq ·

Example: Car wheel nutWater temperature 20 °CMass of nut m = 52.74 gBuoyancy m~ = 06.74 g

ρ = 1.00 g/cm3 · = 7.83 g /cm352.74 g6.74 g

mm~

m~

ρliq

mVbody

m~

ρliq

Teaching objective

Assignment

Material

Experimental arrangement

Procedure

Evaluation

Density of solids (buoyancy method)

Thread

Wire basketStand

Phys

ics

8

At 20 °C, the density of water is 0.2% smaller than 1 g/cm3. Even without consideration of thetemperature dependence of the density, the volume and the mean density of even small coinscan be determined to better than 1% uncertainty.With gold and silver coins, the standard can be calculated if the (mean) density of the alloyedmaterial is known.The following applies:

m = mx + mR

V · ρ= Vx · ρx + (V – Vx) · ρR

Vx =ρ – ρR or mx / m = …

V ρx– ρR

Final considerations

mass volume (mean density)

coin m V ρgold, silver mx Vx ρx

residue mR ρR

9

Temperature dependenceof the density of water

The density of water changes with temperature. It attains its greatest density at 4°C (anomaly of water).

The density of water in the temperature range from 0 to 50°C is determined with the aid of aspecific gravity bottle and a balance. The experimental results should be plotted graphically.

METTLER TOLEDO precision balance (readability 0.01 g)Specific gravity bottle 50 or 100 ml, if possible of quartz and with a thermometer equippedwith a taper jointBeaker 1000 mlPossibly thermometer 0 to 50°C, graduated in 1/10 or 1/5 degreeHot plateStyrofoam board for thermal insulationHand towelIce cubes

A styrofoam board is placed on the weighing pan to provide thermal insulation. Make sure thestyrofoam does not overlap the weighing platform for reasons of electrostatic interference.The balance is tared with the empty specific gravity bottle. The specific gravity bottle is filledby immersion in the beaker containing the ice water, and the stopper (or the thermometer withtaper joint) inserted under water. The water temperature ϑ is measured.The specific gravity bottle is then lifted out of the water, dried off and placed on the balance.The mass m of the water is noted down. The remaining ice is removed from the water, whichis then warmed gently. In the range 0 to 10 °C, measurement of ϑ and m is carried outapproximately every two degrees initially and then later at intervals of approximately 10 de-grees. The contents of the specific gravity bottle are poured back in the beaker after eachmeasurement and the water stirred thoroughly.

With a specific gravity bottle made of Jena glass (coefficient of linear expansion α = 3.2 · 10–6/K) that is calibrated to 50 cm3 at 20 °C, the following experimental valuesshould be found:

Teaching objective

Assignment

Material

Procedure

Evaluation

Temperature Mass Densityϑ in ºC m in g ρ in g/cm3

0 49.991 0.999 842 49.996 0.999 944 49.997 0.999 976 49.996 0.999 948 49.992 0.999 85

10 49.984 0.999 7020 49.910 0.998 2130 49.783 0.995 6540 49.612 0.992 2250 49.405 0.988 05

Phys

ics

10

With specific gravity bottle and balance, the density of a wide variety of liquids, e.g. hexane,ethanol, chloroform, etc. can be determined.

– According to the table, in the temperature interval O to 4°C the density of water changes by0.00013 g/cm3, corresponding to 13‰. In the same interval, the volume of Jena glasschanges by 0.04‰, but that of quartz glass seven times less. If the specific gravity bottle isnot made of quartz glass, a volume correction is advisable.

– If the specific gravity bottle is filled with water at about 2°C, a lowering of the water levelin the capillary of the stopper can be observed on warming. If the specific gravity bottle isclasped with a warm hand, the contraction occurs within a few seconds.

– The density of water at 20°C must be measured with particular accuracy as this is thecalibration temperature for burettes, pipettes and measuring cylinders.It is approximately 2‰ less than that at 4°C.

Final considerations

Note

11

Density of air

Even air possesses mass and density!

A flask is evacuated and the density of air determined from the mass and volume of theevacuated air. The density should be converted to standard temperature and pressure.

METTLER TOLEDO precision balance (readability 0.01g)Vacuum pump (water pump)Glass flask with 2 stopcocks approx. 1 liter)Bucket containing waterMeasuring cylinder (1 liter)Thermometer (water temperature)Thermometer (room temperature)Barometer (not adjusted to sea level)

To simplify the calculations, the water should be at room temperature.The dry flask filled with air is tared on the balance. It is then evacuated and weighed. The mass m of the evacuated air is noted.The flask is then held in the bucket of water, the stopcock opened slowly and water allowed to enter until the pressure in the flask is the same as the external pressure. The water level inthe flask is then at the same height as the water level in the bucket. The volume V of the waterwhich entered the flask equals the volume of the evacuated air and can be determined with a measuring cylinder or by weighing.

The density is determined as the quotient of mass and volume

in g/dm3 or kg/m3

Mass of the evacuated air m in gVolume of the evacuated air V in dm3

Room temperature θ in ºCand hence T in K

Air pressure p in mbarFor the density at room temperature

and for the standard density

ρo =

(literature value 1.293 kg/m3)

– If the volume is measured with a measuring cylinder, the best possible uncertainty is 1%.– Atmospheric moisture and CO2 content are difficult to correct for; their influence is also

approx. 1%.

m ·

1013 mbar·

TV p 273.1K

ρ = mV

ρ = mV

Teaching objective

Assignment

Material

Procedure

Evaluation

Note

Phys

ics

12

Density of gases

This experiment illustrates the density of a gaseous substance.

The density of a gaseous substance is determined from its volume and mass and converted to standard temperature and pressure.

METTLER TOLEDO precision balance (readability 0.01g)Conical flask (approx. 1 liter)Measuring cylinder (approx. 1 liter)Vessel containing waterCO2, He, H2 or O2 from a cylinderThermometer (room temperature)Barometer (not adjusted to sea level)

The conical flask is tared filled with air. Gas is passed into the flask for a few seconds viarubber tubing fitted with a glass tube which reaches the bottom of the vessel. When the dis-play of the balance no longer changes, the gas flow is discontinued and the mass ∆ m read.The conical flask is then filled with water and volume V determined with a measuring cylinder.The volume can be found more accurately and just as conveniently with the aid of a balanceand the assumption that the density of water = 1.00 g/cm3.

The gas density is the quotient of the gas and its volume. The gas mass has not beenmeasured directly, but is calculated:

mgas = m(flask with gas) – m(flask with air) + mair

= ∆m + mair

Mass difference between gas and air ∆m in gMass of air (not measured) mair in gVolume of conical flask V in dm3

Room temperature ϑ in ºCand hence T in K

Air pressure p in mbar

Under the experimental conditions, the gas density is

and under standard conditions

with ρo air = 1.293 g/dm3

– The conical flask must be completely dry.– The gas cylinders should be at room temperature.– Gases that are lighter than air (e.g. helium) should be allowed to flow into the inverted

conical flask from below.

ρo gas = · · + ρo air∆m 1013 mbar T

V p 273.1 K

ρgas = =mgas ∆m + mair

V V

Teaching objective

Assignment

Material

Procedure

Evaluation

Note

13

Buoyancy in gases

If a body is weighed in air, the buoyancy force is equal in magnitude to the weight of thedisplaced air.The same applies for other gaseous and liquid media. In the determination of the mass ofbodies of low density, a buoyancy correction must therefore be made.

– Determine the buoyancy difference between air and helium of a litre flask filled with air.– Determine the buoyancy difference between air and helium of a litre flask filled with helium.

METTLER TOLEDO precision balance (readability 0.01 g)1 Round-bottomed flask 1 I with stopper (bored through halfway)1 Small bucket (51)StandHelium or carbon dioxide from a steel cylinder20 cm long metal tube Β 6 mm, on base

The tube is inserted in the stopper with an appropriate bore and then placed on the balance.The round-bottomed flask is now attached to the stopper and the weight read. The next step isto invert a bucket over the flask and allow helium to flow into the bucket from below until theweight is constant. The flask has become “heavier”!The flask is now filled with helium and placed on the scales again. The scales show a lowermass because the mass of the helium in the flask is lower than that of the air. If the flask isagain surrounded by a helium atmosphere, the scales show the same mass as if the air-filledflask were surrounded by air.

Teaching objective

Assignment

Material

Procedure

Risk of explosion

Phys

ics

1414

The mean molar mass of air (28.8 g/mol) is about seven times greater than that of helium.Consequently, quite different forces act on the liter flask:

The forces acting on the litre flask are thus very different: about 1.15 g for air asagainst about 0.16 g for helium.

The forces investigated can be represented schematically as follows:

The relevant experiments may be carried out with carbon dioxide (CO2) instead of helium.Since the specific gravity of CO2 is greater than that of air, the arrangement must be reversed.

– The bucket is at the very bottom.– The round-bottomed flask hangs on the balance and is immersed in the bucket.– The balance is supported by a stand or more simply on a stool with a grip hole. The round-

bottomed flask is hung on the hook on the underside of the balance. First, however, thebalance must be switched on.

The liter flask holds approximately 1.75 g carbon dioxide. Accordingly, the “weight differ-ences” with CO2 are over half as great as with He; this is shown by a comparison of theirmolar masses:

44–28.828.8 –4

= 0.61

Evaluation

Extension

15

Density of liquids

To determine the density of liquids from the measurement of the volume and mass.

Assignment Investigation of the density of various liquids such as water, alcohol, chloroform,hexane and benzine.

METTLER TOLEDO precision balance (readability 0.01g)Measuring cylinders, volumetric flasks, pipettes, specific gravity bottles, beakersVarious liquids, see above

The glass apparatus such as specific gravity bottle, beaker or measuring cylinder is tared andthen filled with the liquid under investigation. The mass is noted down.

The density is determined as the quotient of mass and volume.

ρt = density at temperature tm = massV = volumet,ϑ = temperature of liquid

Since the density of liquids is temperature-dependent, the temperature must be specified.For very accurate measurements, a buoyancy correction is necessary.

The liquid used for school experiments must not be irritant or poisonous.Carbon tetrachloride, benzene and concentrated alkalis and acids must not be used.

ρt =mV

Teaching objective

Assignment

Material

Procedure

Evaluation

Final considerations

Note

15

Measuringcylinder

Specific gravity bottlePipetteVolumetric flask

Phys

ics

16

“Forces always occur in pairs – if a body exerts a force on another body, the second bodyacts on the first with a forcea) of equal magnitudeb) which is oppositely-directed ‘opposing force’, c) which is along the same line of action.”(Newton’s Law of action and reaction)

a) The two balances are operated in the no-load condition (!) in accordance with theinstructions.

b) The body is hung from the upper balance and the lab jack with beaker + liquid placed onthe lower balance.

c) The beaker can now be raised so that the suspended body is gradually immersed in theliquid.

d) As the upper balance shows, the body is forced upwards by the liquid and apparentlybecomes lighter.As the lower balance shows, the liquid (and the beaker and lab jack) is forced downwardsby the immersed body and apparently becomes heavier. Both changes are exactly equalin magnitude.

a) Negative: The use of two electronic balances with projected displays appears veryextravagant.In a school of moderate or large size, it should be easy to find the second balance inanother department.

b) Positive:1) The experimental setup is fully comprehensible without additional explanation.2) The handling of the apparatus is simple and there are no hidden snags.3) The demonstration can be performed without unnecessary loss of time.4) The interest of the pupils is held since by the raising and lowering process as well as

by later retaring, fresh pairs of values are continuously found whose adherence to thelaw can be checked with and even sometimes without mental arithmetic.

5) Other experiments for “action” and “reaction” are mostly less enlightening and demandintricate explanations.

16

Force and opposing force

Theme

Experimental arrangement

Procedure

Critical comment

1 METTLER TOLEDO precision balance(readability 0.01g)

2 Stool, stand or similar3 Suspended body4 Beaker with liquid, e.g. water5 Adjustable lab jack6 METTLER TOLEDO precision balance

(readability 0.01g)

1

2

3

4

5

6

17

Deflection force

To change the direction of a flow, a normalforce is needed (perpendicular to thedirection of velocity).

Investigation of the force which divertsthe water flow

METTLER TOLEDO precision balance (readability 0.01g)Plastic tubing, diameter: external, e.g. 12 mm; internal 8 mm,length according to requirementTubing connector on water tapFirst guide tube approximately 20 cm long, internal diameter slightly greater than the externaldiameter of the tubingNon-slip stand and clamps to hold the tube horizontalPlastic tank, 5 literMETTLER TOLEDO balance, weighing range e.g. 0...6 kg or measuring cylinder1000 mlStop watchSecond guide tube made of wood (to secure the tubing on the balance), e.g.

Teaching objective

Assignment

Material

Experimental arrangement

17

1 Plastic tubing2 First guide tube secured to stand3 Second guide tube made of wood4 Weight to hold 3 firmly in place

on the balance5 Plastic tank6 Sink with water outlet

Phys

ics

18

The first guide tube is secured on the stand at the same height as the second tube on thebalance. The tubing support must be incapable of displacement on the balance; it may benecessary to add an additional weight. While longer tubing can be displaced more easily,when the length is doubled the maximum flow rate is reduced by approximately half and themaximum force by approximately a factor of four!

It is essential in this experiment that the weighing pan of a METTLER TOLEDO compensationbalance remains at exactly the same height above the bench even with changeable loading.This prevents the plastic tubing from twisting and the measurements thus suffer no distur-bance due to deformation forces. The water is diverted by the tubing and consequently exertsan opposing force in an upward direction at the right on the tubing. The vertical force compo-nent F is measured with the balance. It depends on the mean rate of flow v– of the water andthis can be calculated from the throughput volume ∆V during time ∆ t and the internal cross-section of the tubing A:

a) The water is allowed to flow very slowly at a rate which just prevents air bubbles enteringthe tubing via the open end; the balance is tared.

b) The water tap is opened slightly and the force F measured.c) The empty tank is held in the water stream for a suitable time interval ∆ t.

At the same time, a careful watch must be kept on the balance display as the water supplypressure can show short-term fluctuations.

d) The volume of water in the tank is determined either with a measuring cylinder or – quickerand more accurately – by weighing on a second balance.

e) The steps b) to d) are repeated with other flow rates.Table with F, ∆ t, ∆V, v–

With the non-rigorous but simplifying assumption that each water particle has thesame drift velocity.

The volume which flows through the cross-section Ain time δ t is given by:The corresponding masshas the momentum

Initially, it is directed horizontally, but later downwards. Thus, during time δ t, a momentumchange in a downward direction is produced by the force (–F

Ý) of the tubing:

and the reading on the balance18

Theoreticalconsiderations

Procedure

Evaluation

F · δt = δp = ρ · A · v2 · δt

F = ρ · A · v2 = ρ ·(∆V/∆t )2

A

(∆m/∆t )2

ρ · AF =

m~ = Fg

(∆m/∆t )2

ρ · A · g=

(2)

(3)

v– = ∆V / ∆tA

(1)

δV = A · v · δ t.δm = ρ · δVδ p = v · δm = ρ · A · v2 · δ t.

v– = ∆V / ∆tA

v =

19

A line with slope 2 is drawn. The experimental points lie virtually on the line so that the qua-dratic relationship between ∆m/∆t and m~ is confirmed.The values of the above table have naturally not been invented and are actualmeasured values obtained with plastic tubing of 8 mm internal cross-section. How do they fitequation (3)? The fifth measurement, for example, gives with

The agreement appears good; nonetheless, not all water particles move at the same rate.

The experiment is carried out in 20 minutes. It offers the opportunity to review the concepts:“action and reaction”, “momentum change equals impulse” and “log-log graduation”.

Final considerations

19

∆m /∆t = 99.8 g/sρwater = 1.00 g/cm3

A tubing = π · (0.40 cm)2

g = 981 cm/s2 inserted in (3)

m~ calculated = 20.2 g instead offm~ measured = 20.0 g ±0.2 g

The measured relationship between ∆m/∆t and m~ I (F) can best be represented in adouble logarithmic diagram.

Phys

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2020

Resisting force in an airstream

In flowing media, a body experiences a resisting force F, which depends on the size (A) andthe shape (cr) of the body as well as on the density ρ and the relative velocity v of the flowingmedium.

Investigation of the resisting force with various bodies in the airstream of a wind generator.

METTLER TOLEDO precision balance (readability 0.01g)Wind generatorIf possible, Prandtl pitot tube with manometer to measure the air velocityVarious resistance bodies (with support rods)– with an equal as possible flow area against the body (maximum section); e.g. circular

disk, sphere, solid hemisphere, hollow hemisphere, streamlined bodies, model planes– of the same shape, e.g. small, medium and large circular disks or square plates– rod alone, without resistance bodies

Mounting of the resistance bodies, e.g.

1) Weighted base with additional cross hole of 8.2 mm Β2) Aluminium rod 8 mm Β, 400 mm long3) Hole to accept the rod of the resistance body4) M3 screw to prevent twisting5) Possibly a counter weight

To protect the balance against drafts, use a box 60 cm x 60 cm x 40 cm, for example, withthe features:– free access for the users/students– secured to the bench with two clamps– with a cutout in the base to allow the balance

to stand directly on the bench– with a small lateral opening for the aluminium

rod (2) of the mounting.

If a powerful wind generator is used, the protectivebox is an absolute necessity as the airstream isreflected at the ceiling and air vortexes hit thebalance from above (check with a candle flame!)

1. Wind generator2. Box3. Resistance body in mounting

Teaching objective

Assignment

Material

Experimental arrangement

21

wl

Procedure

Evaluation

Final considerations

21

pdyn = · v2ρ2

F = cr · pdyn · A

ρ = density of the flowing mediumcr = resistance parameter (shape factor)A = maximum section (area of the body

projection on a plane vertical to the flowdirection)

a) Preliminary trial: A pitostatic tube is used to determine the region in which the airstreamhas a constant velocity.

b) Note for all further experiments: In what follows, the resisting force F(body) which the bodyalone experiences is desired. The airstream exerts pressure on the mounting, however,and the balance displays the force F(measurement). Consequently, a second measure-ment must be performed without the body, namely with only the rod, to determine the forceF(rod). F(body) is then given by F(measurement) – F(rod).

c) The resisting force F is measured at different air velocities v with one body.Table with v, F(measurement) and F(body).Possibly a different body size or shape can be selected and the experiment repeated.

d) F (body) is determined at constant wind velocity for bodies of different size (A) but thesame shape. Table with A, F(body) and F(body)/A.Possibly repeat with bodies of a different shape.

e) F(body) is determined at constant wind velocity for bodies of different shape but the sameairflow area (maximum section) A.Table with shape sketch and F(body).Possibly repeat with a different wind velocity.

f) The time for a single measurement takes one to two minutes and depends greatly on thedexterity and experience of the user.

For turbulent flow, theory predicts

for the dynamicpressure

and for theresisting force

the following is thus expected:with c) proportionality between v2 and the resisting forces [F(measurement), F(rod),F(body)];

with d) a constant quotient F(body)/A;

with e) cw > cw l >cw • > cw

The experiment is well suited for a demonstration in the lesson since it can be carried outquickly.

Phys

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2222

Forces on an airfoil

An asymmetric body subjected to an airflow experiences a force component perpendicular tothe resisting force (drag) FR in the flow direction. In the case of the airfoil, this normal force isthe lifting force (aerodynamic lift) FA.

Investigation using a flat plate and an airfoil of the dependence of the desired lifting force FL,the undesired resisting force FR as well as their quotient FL/FR on the angle of incidence α.

METTLER TOLEDO precision balance (readability 0.01g)Wind generatorIf possible, Prandtl pitot tube with manometer to measure the air velocityAirfoil model, with very thin parallel fins and revolving mountingSmall board (of wood, plastic or metal) with fins and revolving mountingNon-slip stand base with vertical drill holeMounting for horizontal clamping of the model, e.g. a wooden block

1) Rod, which carries the revolving model2) Wooden block, 180 mm x 100 mm x 30 mm3) Drill hole, suitable for rod 1)4) Possibly a screw; prevents rod 1) from twisting5) Rod, 10 mm ∅, fitting snugly in the block6) Counter weight of approximately 1 kg, e.g. weighted base

To protect the balance against drafts, use a box 60 cm x 60 cm x 40 cm,for example, with the features:– free access for the experimenters– secured to the bench with two clamps– with a cutout in the base to allow the balance to stand directly on the bench– with a small lateral opening for the rod 1)

Teaching abjective

Assignment

Material

23

Measurements of the lifting forceand the resisting force requiredifferent arrangements.

Lifting force

Resisting force

a) The velocity distribution in the airstream in front of the wind generator is investigated with aPrandtl pitot tube.

b) Lifting force FL: This can be calculated theoretically as follows:

Investigate the dependence of the lifting force on the wind velocity.Table with v, FL, graph.Possibly repeat with a different profile or a different angle of incidence.

c) For the following measurements, the air velocity is kept constant; at the profile let it be v *.The dependence of the lifting force on the angle of incidence α is measured first for thesmall board.

Experimental arrangements

Prodecure

23

CA = lifting parameter, shape dependentA = maximum section (area of the body projection

on a plane vertical to the flow direction)ρ = air densityv = wind velocity (relative velocity of the air with respect

to the body)

If a powerful wind generator is used, the protective box is an absolute necessityas the airstream is reflected at the ceilingand air vortexes hit the balance fromabove (check with a candle flame).

FA = cA · A · · v 2ρ2

Phys

ics

2424

d) Resisting force FR: Also this is proportional to the dynamic pressure

This should be checked if time allows.

e) Since the airstream strikes not only the test body but also its mounting, Fw (mounting)must be measured in a preliminary experiment without the body, i.e. with the mountingalone. Subsequent measurements FR (total) must be corrected:

f) For the following measurements, the air velocity at the site of the test body is againadjusted to v = v * as above. The dependence of the resisting force FR (total) on the angleof incidence α is then measured at the board and the airfoil.Table with α, FR (total) and FR (model), graphs.

For the measurements alone, a practised experimenter needs approximately 45 minutes.When the evaluation is included, a school group needs three to four hours.

It is usual to represent FL and FR of theairfoil in a polar diagram after Lilienthal.For further interpretation of the results,consult the specialist literature, e.g.course documentation for glider pilots.

The apparatus is simple to operate, butthe experimental work demands very carefulattention and the evaluation also requirescare. Despite its stringent requirements,the experiment is very popular.

Time required

Evaluation

Final considerations

(pdyn = · v2), hence FR ~ v 2.ρ2

FR (model) = FR (total) – FR (mounting)

25

Dependence of the magnetic fieldstrength of a coil on the current intensity

The magnetic field strength of a coil is proportional to the current intensity.

Measurement of the dependence of the force which a small bar magnet experiences in themagnetic field of a coil on the current intensity in the coil.

METTLER TOLEDO precision balance (readability 0.01g)Air-core coil (e.g. 7 cm long, 4 cm diameter, 250 windings)Direct current source which can supply approximately 5 to 10 ASliding resistor (e.g. 6 Ω) if the voltage of the direct current source cannot beregulatedSwitchAmmeterElectrical cableStandSmall permanent magnet, e.g. cylindrical barNon-magnetic bar (aluminum rod, wood), approx. 15 cm long, in a non-magnetic light base

The magnet is affixed to the upper face of the bar with a little grease. The coil is positioned sothat the magnet is located just below one end of the coil.

An initial test is performed to establish whether the magnetic field of the coil has a directinfluence on the balance causing the display to change when the current is switched on. It willbe seen that METTLER TOLEDO balances are virtually insensitive to external magnetic fields!Further, it should be noted that the magnet must not be displaced relative to the coil during aseries of measurements since the coil field is inhomogeneous. In this respect, no difficultiesarise with a balance which operates according to the compensation principle as the weighingpan remains approximately at the same height above the bench whatever the load.After the balance has been tared, the current intensity l is increased in steps. The associatedvalues of l and F (for the force) are tabulated and later plotted graphically. It is seen that theforce is strictly proportional to the current intensity.Consequently, the magnetic field strength is also proportional to the intensity of the current.

Teaching objective

Assignment

Material

Experimental arrangement

Procedure

25

M MagnetR RodB Base

Q Current sourceSw SwitchR Sliding resistorA Ammeter

Phys

ics

26

Soft iron in a magnetic field

Soft iron is magnetized in an external magnetic field and experiences an attractive force whenthe field is inhomogeneous.

Measurement of the dependence of the force experienced by a piece of soft iron in themagnetic field of a coil on the current intensity in the coil.

Exactly the same material as in the previous experiment on page 25, except the magnet isreplaced by a piece of soft iron, e.g. by an iron screw of approximately the same size.

As for the previous experiment on page 25.

The measurement procedure corresponds exactly to that of the experiment described on page 25. However, the relationship between I and m (for F) is by no means linear.

Example of measurement with Allen key M8,25 mm long:

Teaching objective

Assignment

Material

Experimental arrangement

Procedure and evaluation

Conclusions

The forces for 3 A and 6 A imply a quadraticrelationship:

This can be checked most simply by a graphi-cal plot with double logarithmic axes:

m~ = k · l 2

The drawn line has a slope of exactly 2. Sincethe experimental points fit the line extremelywell, the assumption is confirmed F ~ l 2

In the experiment on page 25, a permanentmagnet in an external magnetic field experi-ences a force proportional to the current inten-sity. Here, however, the piece of iron is firstmagnetized by the coil field. It then experi-ences the corresponding force F, which on theone hand depends on the magnetic fieldstrength H of the coil field and on the otherhand on the magnetization J of the piece ofiron.The proportionalities F~H ⋅J, H ~ l and F ~ l 2

allow the conclusion J ~ l, i.e. in the observedfield strength range, magnetization of the ironpiece is proportional to the electric fieldstrength.

27

Chem

istry

28

How much sodium bicarbonatedoes an effervescent tablet contain?

Effervescent tablets (vitamin tablets, lemonade, etc.) contain sugar, flavoring and foodcolorings as well as tartaric acid and sodium bicarbonate in addition to the actual activesubstance. When such a tablet is added to water, the sodium bicarbonate reacts with thetartaric acid to form the very soluble sodium tartrate together with carbon dioxide and water.Carbon dioxide is evolved as a gas and the tablet dissolves.

The sodium bicarbonate content can be derived from the amount of carbon dioxide evolved.

METTLER TOLEDO precision balance (readability 0.01g), wide-necked conical flask 300 ml,glass rod, effervescent tablets, pocket calculator, disposable drinking cups, dish towels,bucket for waste.

1. Add approx. 2 dl tap water to the conical flask, dry the outside well, place on the balanceand tare.

2. Put an effervescent tablet next to the conical flask on the weighing pan, determine itsweight and note the result.

3. Tare again with the tablet.4. Add the tablet carefully (without splashing) to the water, wait for the completion of reaction,

stir well with the glass rod and determine the mass of the evolved carbon dioxide. Note theresult.

5. If desired, you can pour the drink into a cup and drink it. Otherwise, pour the solution away.6. Rinse the conical flask thoroughly and dry the outside carefully. It is now ready for the next

experiment.

Theory

Material

Experimental procedure

Results and evaluation

Numerical example

27

The following was found in an experiment:Mass of tablet: a = 4.38 g; mass of CO2:b = 0.23 g

The percentage of NaHCO3 in the tablet is: 1.91 · 0.23 · 1004.38

% = 10.03% ~ 10%

Mass of tablet: a = …g; mass of CO2:b = …g

1 g of evolved carbon dioxide corresponds to an NaHCO3 content of 1.91 gb g of evolved carbon dioxide corresponds to an NaHCO3 content of 1.91· b g

The percentage of NaHCO3 in the tablet is: 1.19 · b · 100a %

H H H H

2 NaHCO3 + HOOC C C COOH → NaOOC C C COO Na + 2 CO2 + 2 H2O

CH CH O HO Hsodium tartaric acid sodium tartrate carbon dioxidebicarbonate

2928

Determination of fat in soja and nuts

Many vegetable foodstuffs such as soja beans, peanuts, hazelnuts, sunflower seeds, etc.contain vegetable fats, which can be recovered relatively easily by extraction with a lipophilicsolvent. These foodstuffs are also important on a large scale for the production of edible oilsand fats.To determine the fat content, the finely milled nuts, seeds or beans are extracted with petroleumether, hexane or the like. Anhydrous magnesium sulfate is added to bind any water present.Filtration of the solution and evaporation of the solvent gives the pure fat, which is thenweighed.

METTLER TOLEDO precision balance (readability 0.01 g), conical flask 100 ml with taperstopper or a suitable measuring cylinder, petroleum ether or hexane, anhydrous magnesiumsulfate, funnel, filter paper or cotton wool, beaker 100 ml, pipette 10 ml. Soja, hazelnut orpeanut flour.

1. Approximately 3 g soja, hazelnut or peanut flour are weighed.2. The flour is added to the conical flask or the measuring cylinder, 40 ml petroleum ether or

hexane poured in, 5 g anhydrous magnesium sulfate added and the vessel shakenthoroughly from time to time over a 5 minute period. To equalize the pressure, the taperstopper is opened briefly before and after shaking.

3. Part of the suspension obtained is filtered through filter paper or cotton wool into a dryvessel which can be closed off (e.g. conical flask with stopper or beaker with a watchglass cover). Closing off the vessel prevents evaporation of the solvent.

4. Exactly 10 ml of the filtered solution are now pipetted into a small, weighed beaker and thesample evaporated in the fume cupboard on a water bath until the odor of solvent hasdisappeared completely.

5. The sample is allowed to cool and then reweighed.

The fat content can be determined from the weight of the foodstuff (a = … g) and the mass ofthe residue (b = … g), which comprises pure fat:

From a 3.00 g weighing (= a) of hazelnut flour, a residue of 0.52 g (= b) wasfound after evaporation of 10.0 ml filtered extract. This corresponds to a fat contentof approx. 70%.

Theory

Material

Experimental procedure

Results and evaluation

Numerical example

Fat content = %100 · 4 · ba

Chem

istry

30

Determination of chalk in rockand soil samples

Chalk can be determined in rock and soil samples by reaction of the calcium carbonate withhydrochloric acid. The calcium carbonate reacts to form calcium chloride, water and carbondioxide, and the carbon dioxide evolved by the reaction solution is weighed:

CaCO3 + 2 HCI Õ CaCI2 + H2O + CO2

This is a simple and really accurate method of determination.

METTLER TOLEDO precision balance (readability 0.01g), conical flask 100 ml, conc. HCI,dist. water, rubber puffer, limestone (approx. 1 g).

1. Approximately 8 ml conc. HCI and approximately 10 ml dist. water are added to theconical flask.

2. The flask containing the hydrochloric acid is placed on the balance and tared.3. The limestone is placed next to the flask on the weighing pan, its mass is determined and

the whole retared.4. The limestone is then added to the solution. A violent reaction ensues immediately and

carbon dioxide is evolved.5. After completion of the reaction, a little air is blown into the gas space of the flask with the

aid of the rubber puffer and a pipette to expel any CO2 present.6. The flask is reweighed and the CO2 loss determined.

Conical flask withhydrochloric acidand limestone

1.58 g limestone evolve 0.386 g CO2. From the reaction equation and the correspondingstoichiometric composition

are expected. Since, however, only 0.386 g CO2, namely 55.54%, were evolved from0.695 g, the calcium carbonate content of the limestone sample investigated is 55.54%.

The method’s accuracy can be checked with pure CaCO3.

Theory

Material

Experimental procedure

Results and Evaluation

Please note

29

CaCO3 + 2 HCI Ý CaCl2 + H2O + CO2

100 g/mol 44 g/mol1.58 g x g

from 1.58 g pure CaCO3, = = x = 0.695 g CO21.58 g · 44 g /mol

100 g /mol

3130

Determination of the water of crystallization in salts

The crystalline forms of many salts contain bound water, which can be expelled by heating.The water molecules are cleaved from the hydrated salt and evaporate leaving the anhydroussalt:

hydrated salt heat anhydrous salt + water

If the exact water loss is determined by weighing, the number of bound water molecules of theso-called “water of crystallization” can be calculated.Note: A side reaction can set in on too powerful or prolonged heating. If, for example, thewater of crystallization content of copper(ll) sulfate is determined, copper(ll) oxide can beformed from the anhydrous salt with cleavage of sulfur trioxide; this can be seen from adarkening of the white product:

CuSO4 (anhydrous) heat CuO + SO3

This side reaction leads to a smaller mass for the reaction product, that is to an apparentlylarger weight loss which, in turn, leads to a greater than actual value for the water of crystal-lization in the calculation.

METTLER TOLEDO precision balance (readability 0.01g), porcelain crucible with lid, tripod,burner, clay triangle (appropriate to the crucible), crucible tongs, glass rod, crystalline saltsuch as copper sulfate, alum, gypsum, etc.

1. The empty crucible and lid are weighed.2. The crystalline salt (approx.1 g) is added to the crucible and weighed exactly.3. The crucible is now heated with a small, non-luminous flame. The open crucible is held

with the tongs and the contents stirred with the glass rod.4. When the salt is dehydrated, which can be seen either by the color change, e.g. with

copper sulfate or by completion of the reaction (no water vapor development, no “crater”formation), the crucible is covered and allowed to cool to room temperature.

5. It is reweighed when cool.6. The experiment is repeated with weighings of 2, 3 and 4 g.

Experimental arrangement

1. The water loss is calculated in g for each experiment from the exact weighing and the massof the residue.

2. The water losses are plotted graphically against the respective weighing. Within a certainscatter, the experimental points should lie on a straight line passing through the origin ofthe coordinates. This serves as an additional check on the measurement accuracy.

Theory

Material

Experimental procedure

Results and evaluation

Chem

istry

32

3. From the reaction equation and the corresponding stoichiometric composition

hydrated salt Õ anhydrous salt + watera = ...g b = ...g c = ...g(weighing) (residue) (water loss)

the number of molecules of bound water of crystallization x is given by:

where MMsalt represents the molar mass of the anhydrous salt.

4. The value of x is calculated for each individual experiment and compared with theliterature values.

The following values found in an experiment with crystalline copper(II) sulfate:Weight of salt: a = 2.48g; residue: b = 1.57gWater loss: c = (a–b)g = 0.91 g

The copper sulfate thus crystallizes with 5 molecules of water of crystallization.Formula: CuSO4 · 5 H2O.

Numerical example

31

x = =c · MMsalt

(a–c) · 18

(a–b) · MMsalt

b · 18

x = = 5.140.91 · 159.5

1.57 · 18

3332

Thermolysis of salts

Thermolysis is understood to mean the degradation of a substance with the aid of heat(“thermal decomposition”). Thermolyses can occasionally proceed violently and uncontrol-lably, or side or parallel reactions set in at the relatively high temperatures needed for thermol-ysis; this complicates or even precludes a stoichiometric evaluation of the weighing results.Substances which decompose quantitatively on moderate heating are particularly suitable forstoichiometric investigations. The following experimental directions were tested with the twomodel substances sodium bicarbonate and magnesium carbonate. The “historical” experimentinvolving the thermolysis of mercury(ll) oxide was not carried out for reasons of technicalsafety and on ecological grounds.

In the thermolysis of sodium bicarbonate, sodium carbonate (“soda”) is formed with splittingoff of water vapor and carbon dioxide.

This process plays an important role in technical soda manufacture (productionof “calcined soda”).In the thermolysis of magnesium carbonate, carbon dioxide is split off:

This reaction proceeds analogously to the manufacture of quicklime from calciumcarbonate:

The thermolysis of magnesium carbonate is thus a model reaction for the technically impor-tant calcination of limestone in cement manufacture. The decomposition of MgCO3 into theoxide proceeds at lower temperature however, so this reaction is better suited for investigationin the laboratory or for demonstration purposes.

METTLER TOLEDO precision balance (readability 0.01g), tripod, burner, clay triangle, porce-lain crucible (several if possible), crucible tongs, magnesium carbonate, sodium bicarbonate(anhydrous).

1. The empty crucible is weighed, approx. 0.5 g magnesium carbonate or sodium bicarbonateadded and the crucible reweighed.

2. The crucible is now carefully heated with a non-luminous flame. Water vapor and carbondioxide are split off and escape from the reaction mixture; this can be observed by “craterformation”. The sample must be heated carefully at the beginning to ensure that gas forma-tion leads to no loss of material from the crucible by spattering.

3. When diminished gas evolution shows that the reaction is nearing completion, powerfulheating to red heat is applied. The heating is discontinued when gas evolution is no longervisible.

4. The crucible is allowed to cool to room temperature and weighed with the reaction productformed.

5. The experiment is repeated with 1 g,1.5 g, 2 g and 2.5 g.

Theory

Material

Experimental procedure

2 NaHCO3 Na2CO3 + H2O + CO2∆T

MgCO3 MgO + CO2∆T

CaCO3 CaO + CO2∆T

Chem

istry

34

Experimental arrangement

1. The dependence of the residue masses on the weighings is plotted graphically.The experimental points lie on a straight line passing through the origin of the coordinates.

2. On the basis of the reaction equation and the corresponding stoichiometry, the theoreticalvalue for a particular weighing, e.g. 1.000 g sodium bicarbonate, is calculated:

From 1.00 g sodium bicarbonate, theoretically

are formed.

For magnesium carbonate, the following holds:

from which it follows that for 1.000 g magnesium carbonate

3. The values found in the experiment are compared with those calculated theoretically.

Results and evaluation

33

2 NaHCO3 Na2CO3 + CO2 + H2O2 · 84 g/mol 106 g /mol

∆T

g = 0.631 g sodium carbonate106168

MgCO3 MgO +CO2

84.31 g/mol 40.31 g /mol

∆T

g = 0.478 g magnesium oxide are formed.40.3184.31

3534

Synthesis of copper sulfide

When a metal, e.g. copper, combines with a non-metal, e.g. sulfur, a salt-like product isformed. The ratio of the quantity of metal used to the chemically-bound non-metal remainsconstant, independent of the amount of copper used (law of constant proportions). The pur-pose of the present experiment, which is best carried out several times and as a pupil exer-cise, is to confirm this law. Further, the empirical formula of the compound formed should bedetermined. The law of constant proportions is only applicable when the product formed ishomogeneous, namely when it has, for example, the same crystalline form. This is not quitethe case here (copper sulfide is a non-daltonide compound), but the experiment is valuablefor didactic reasons.For the synthesis, copper is used as the metal and sulfur as the non-metal to form coppersulfide:

copper + sulfur Õ copper sulfideThe synthesis is performed with an exactly-known amount of copper and with an excess ofsulfur to ensure that all the copper reacts with the sulfur. After the sulfur has melted, it reactsimmediately with the copper present.The excess sulfur sublimes or combusts to SO2, which is evolved as a gas.

sulfur+ oxygenÕ sulfur dioxideSince sulfur dioxide is poisonous, work must be carried out in a fume cupboard.The reaction is performed in a porcelain crucible. After the residue has been weighed, the ratioof the amount copper used to the amount of bound sulfur, the percentage of the elements inthe compound and the empirical formula are determined. Minimum three and if possiblemany more independent experiments are performed. A graphical plot increases the accuracyof the evaluation.

METTLER TOLEDO precision balance (readability 0.01 g), tripod, Bunsen burner, porcelaincrucible with lid, crucible tongs, clay triangle, copper sheet, powdered sulfur.

1. Pieces of approx. 0.5 g, 1 g, 1.5 g and 2 g are cut from a sheet of copper and weighed tothe nearest mg.

2. A particular copper piece is cut into smaller pieces of approx.1.5 cm x 1.5 cm; these areadded to the empty crucible (previously weighed with lid), covered with a small excess ofpowdered sulfur and heated with a small, non-luminous flame on the tripod in a fumecupboard.

3. When the excess sulfur has been completely volatilized, which can be recognized by theabsence of any flame or brownish-yellow sulfur vapor, the crucible is closed with the lidand heated strongly for 2 minutes.

4. The burner is now shut off, the crucible cooled to room temperature (air cooling) and thenweighed.

Theory

Material

Experimental procedure

Chem

istry

36

Experimental arrangement

The following values were found in a school experiment:

From these results, it can clearly be seen that the ratio of the mass of copper to that of sulfuris constant and independent of the initial amount used. In addition, the series of experimentsshows that, despite a certain scatter in the individual measurements, when the series isconsidered as a whole, there is no ambiguity. The experimental points lie on a straight linepassing through the origin.

To calculate the empirical formula, the following composition is used:

Results and evaluation

35

Measurement a g Copper b g Sulfur % Copper % Sulfur a : b(bound)

1 1.162 0.282 80.47 19.53 4.122 1.450 0.370 79.67 20.33 3.923 0.745 0.203 78.58 21.45 3.674 1.715 0.436 79.73 20.27 3.935 1.631 0.441 78.72 21.28 3.706 0.585 0.166 77.90 22.10 3.527 1.408 0.343 80.41 19.59 4.10

1.242 0.320 79.51 20.49 3.88

Cu: 79.51% : 63.54g/mol Õ 1.251 Õ 2S: 20.49% : 32.06g/mol Õ 0.629 Õ 1 empirical formula: Cu2S

Crucible withoutlid at the startand during the reaction

Crucible with lidafter reaction completion;for heating, cooling andweighing

3736

Molar mass determination ofliquified gas

The determination of the molar mass of a gas is carried out by evacuating a known volume ofa vessel, e.g. a 1-liter round-bottomed flask fitted with a stopcock at the side, filling this withthe gas concerned and then determining the mass of this volume of gas. Conversion of thevolume obtained to standard conditions (STP: temperature T= 273 K; pressure p = 1013 mbar)gives the volume of the measured amount of gas at STP. From the general gas law, it followsthat 1 mole of any gas occupies a volume of 22.4 dm3 at STP. This allows simple derivationof the molar mass. The present experiments are not concerned with the determination of themolar mass of gases in general, but rather with that of a particular type of gas, namely aliquified gas. Butane, which is obtainable in cylinders from any department store, is used.This liquified gas is supplied for refilling gas lighters. On the one hand, the experiment showsthe method of molar mass determination and, on the other hand, it is suitable for use as anintroduction to stoichiometry and the gas laws.

METTLER TOLEDO precision balance (readability 0.01g), pneumatic trough with 1-litermeasuring cylinder as collection vessel, short length of thin inlet tubing, inlet tube, syringe100 or 200 ml, stand, clamp, barometer, thermometer, cylinder of liquified gas.

Measurements with the pneumatic trough1. The collection vessel is a 1-liter measuring cylinder which is filled with water, stoppered

with a rubber bung and then immersed upside down in the water of the pneumatic trough.2. The measuring cylinder is now opened under water. No air must enter the cylinder.3. The measuring cylinder is then fixed with a clamp on the stand such that the edge of the

measuring cylinder and the bottom of the trough are separated by approx.1 cm.4. The liquified gas cylinder is weighed.5. Gas (approx. 800–900 ml) is passed into the measuring cylinder through the inlet tube,

which is connected by means of a short length of thin tubing to the gas cylinder.6. Since the gas expands when leaving the cylinder, it is cooled, but then warms up to room

temperature. Five minutes should be allowed to elapse before the gas volume is read.7. In the meantime, the liquid gas cylinder is reweighed.8. The amount of gas which has entered the measuring cylinder is then calculated.

Theory

Material

Experimental procedure

Chem

istry

38

In an experiment with the pneumatic trough method,1.908 g gas were introduced. The measured volume was 830 ml at 20.5 °C and the air pressure 988 mbar.

The calculated volume at STP is

In 753 ml = 0.753 dm3, 1.908 g of the gas in question are present.

A volume 22.4 dm3 therefore contains g = 56.8 g

The experimental value of the molar mass of the gas is thus 56.8 g/mol. The calculated valuefor butane (C4H10) is 58 g/mol. When it is considered that the volume of the piece of tubingand the inlet tube could also be taken into consideration, the measurement provides astonish-ingly good results. The fact that the gas volume has been measured “wet”, namely over awater vapor atmosphere, has been neglected in the evaluation, however.It must also be considered that the scale division on the standard cylinders and syringe is notaccurate. A more accurate determination of the molar mass is possible only by performing theexperiment with a glass weighing sphere (compare experiment «Density of air». The volumeof the glass sphere can be determined by weighing the amount of water it can hold.Evaluation of the experimental results obtained using the syringe is performed in an analo-gous manner. This measurement is also quite accurate; values of 60.5 and 60.9 g/mol werefound. The pressure of the glass plunger on the gas is not taken into consideration.

Results and evaluation

37

Vo =Vexp. · pexp. · To

po · Texp.

830 ml · 988 mbar · 273 K1013 mbar · 293.5 K

= 753 ml=

1.908 · 22.40.753

Measurements with the syringe1. A 100 ml or 200 ml syringe is secured to the

stand in a manner which ensures convenientintroduction of the gas from the cylinder into thesyringe opening.

2. The cylinder is weighed,100 or 200 ml gasintroduced and the volume read immediately(leaks in the syringe have a greater adverseeffect on the experimental results than the smallerror arising from cooling of the gas when itflows out of the cylinder).

3. The cylinder is weighed again and the amount ofgas introduced is calculated.

3938

Rate of evaporation

The evaporation of liquids or volatile solids is a phenomenon associated with particle motion,namely with the kinetic energy of the molecules. The rate of evaporation depends on severalfactors but primarily on the instantaneous temperature, the pressure and the intermolecularforces between the individual molecules. The molar mass and the molecular shape, which inturn influence the intermolecular forces, also play a part. Evaporation and its rate can beconveniently followed and measured on a balance.

METTLER TOLEDO precision balance (readability 0.01 g), 1 large Petri dish (diameter 8–12 cm), various liquids such as acetone, ethanol, hexane, etc.

The Petri dish is placed on the balance, the appropriate liquid added to a height of approx. 5 mm, the whole tared and the mass of the evaporated quantity read every 15 seconds. The measurements are discontinued after 3 minutes.Important: The same Petri dish must be used for all measurements to ensure a constantevaporation area.It must also be ensured that no drafts due to open windows or doors appear during themeasurement. Direct sunlight should also be avoided.

1. The measured values are plotted on graph paper. The quantity of evaporated liquid isplotted against time.The following values were found for acetone in an esperiment with a Petri dish of 9 cmdiameter at 21°C:

Theory

Material

Experimental procedure

Results and evaluation

Time: 0 15 30 45 60 75 90 105 120 135 150 s

Amount: 0 4 8 12 15 19 22 26 30 33 37 mg

Petri dishwith liquid

METTLER TOLEDOprecision balance

Chem

istry

40

The evaporation rates of ethanol, ethyl acetate and butyl acetate were determined in the samemanner.The following values were found:

Acetone: 15.0 mg per minute b.p. 56°CEthanol: 3.7 mg per minute b.p. 78°CEthyl acetate: 6.5 mg per minute b.p. 77°CButyl acetate: 1.7 mg per minute b.p. 126°C

The interpretation of these values is difficult since the extent to which the different factorsmentioned in the theoretical section contribute to the whole differs widely.An attempt will be made at an interpretation, however.

1. Acetone has the greatest rate of evaporation. Obviously, the intermolecular forces arerelatively weak and this is reflected in the low boiling point of acetone. These forces are inany case smaller with acetone than with ethanol since ethanol is capable of forming inter-molecular hydrogen bonds, which retard evaporation.

2. Evaporation of ethanol is slower than that of ethyl acetate even though the molar mass ofethanol is smaller and the boiling points are about the same. Again, the hydrogen bonds atthe ethanol surface are probably responsible as they “hold back” the evaporating mole-cules. This is not the case with ethyl acetate; here, only the much weaker Van de Waal’sforces are operative.

3. The rate of evaporation of ethyl acetate is greater than that of butyl acetate.This correlates with the boiling points and the molar masses as well as with the molecularsize. Probably, the stronger Van de Waal’s forces in the case of butyl acetate are responsi-ble for its lower rate of evaporation.

Interpretation

39

41

Theory

40

Homogeneous catalysis:The decomposition of H202

A catalyst is a substance that initiates or accelerates a reaction without itself undergoingchange. The reaction accelerating effect of the catalyst is due to a lowering of the activationenergy of the respective reaction.If the catalyst is present in a phase different from that of the substances participating in the re-action, this is known as heterogeneous catalysis. If, on the other hand, the catalyst is in thesame phase as the reactants, homogeneous catalysis occurs.The decomposition of H2O2 is represented by the equation:

and can be catalyzed both homogeneously and heterogeneously. Substances such as silver,manganese(l\/) oxide (MnO2, “pyrolusite”) are used as heterogeneous catalysts; potassiumiodide solution or a solution of the enzyme catalase are examples of homogeneous catalysts.In the following experiments, the homogeneous catalysis of the reaction with potassium iodidesolution is investigated and the dependence of the evolved oxygen on time measured. By variation of the amount of catalyst, its influence on the reaction can be established.Further, the manner in which the reaction itself proceeds can also be deduced. Thus, if theprocess occurs in a single step according to the general scheme:

R (reactants) Õ P (products)

oxygen formation sets in immediately after addition of the catalyst. However, if the processproceeds in two steps via an intermediate according to the scheme:

R (reactants) Õ I (Intermediate) Õ P (products)

oxygen is formed only after a certain time, the so-called “induction period” has elapsed.This difference between the two reaction models can also be recognized from the slope of theexperimental curve obtained by plotting the mass of evolved oxygen against time.

In these experiments, the balance is not simply a weighing instrument; it assumes thefunction of a measuring instrument for observation of the process which occurs during thereaction. Naturally, the experimental values found can also be evaluated with a computer. If a Mettler overhead projection display is available, the series of experiments can also becarried out in a demonstration and can be evaluated conveniently and interpreted togetherwith a class.

2 H2O2 2H2O + O2catalyst

Chem

istry

42

METTLER TOLEDO precision balance (readability 0.01g, with overhead projection display forthe demonstration), 1 beaker 250 ml, syringe or graduated pipette 0–10 ml, glass rod, 500 ml freshly-prepared H2O2 solution 1%, sat. Kl solution, clock with second hand, graphpaper for the evaluation.

1. The beaker is tared on the balance.2. 100 g 1% H2O2 solution are now added.3. Sat. Kl solution (2.0 ml) are added with a pipette or syringe, the solution stirred briefly with

the glass rod and the whole retared.4. The mass loss of the evolved oxygen is read every 15 seconds and the experimental

values noted down. The measurements can be discontinued after 5–6 minutes.5. Further series of measurements with 4.0 ml and 8.0 ml sat. Kl solution are performed.

If need be, additional measurements with 3.0 ml, 6.0 ml and 9.0 ml Kl solution can alsobe carried out. Larger quantities of catalyst should not be employed as a dilution effectoccurs due to the increase in the total volume of the reaction solution; this effect must becompensated in the calculation. For the given catalyst concentrations, reconciliation of thisdilution effect is not necessary.

6. The mass values found are plotted graphically against time.

Note: If lack of time (e.g. when the measurements are carried out as a demonstration experi-ment) demands a faster reaction, the entire series of experiments can also be performed with50 ml 3% H2O2 using 0.75 ml, 1.5 ml and 3.0 ml Kl solution as catalyst. The experimentalvalues are then subject to a certain error, however, since the solutions are warmed slightly bythe exothermic process. They are nonetheless accurate enough for an evaluation.

In a series of experiments employing 100 ml freshly-prepared H2O2 1% with either 2.0 ml,4.0 ml or 8.0 ml sat. Kl solution as catalyst, the following values were found at a temperatureT = 21°C:

Material

Experimental procedure

Results and evaluation

41

4342

The following facts can be derived from the present experimental results and from the graph:1. The reaction under investigation occurs not in one but rather in two steps

according to the scheme:R (reactants) Õ l (intermediate) Õ P (products)

2. The reaction rates obtained when the slopes of the lines L1, L2 and L3 aredetermined at the inflection points of the respective curves are proportional to the amount ofcatalyst.

Slope L1: reaction rate v1 ≈ 40 mg O2 per minuteSlope L2: reaction rate v2 ≈ 80 mg O2 per minuteSlope L3: reaction rate v3 ≈ 120 mg O2 per minute

Similar behavior is also frequently observed in enzyme reactions. The present reaction canserve as a model for such reactions.

3. With decreasing catalyst concentration, not only is the reaction rate lowered, but onset ofoxygen evolution is retarded. The induction period of the reaction is clearly longer.

Interpretation

Chem

istry

44

An explanation of these facts is provided by the reaction profile:In the first reaction step, iodide ions and H2O2 react to form hypoiodite ions:

which then react further with a second molecule of H2O2 to water, oxygen and iodide ions:

The iodide ions formed in the second reaction step are available for the first step. Since bothindividual reaction steps proceed much more rapidly than the overall reaction without iodideaddition, the iodide ions have a catalytic effect on the formation of the intermediate IO-

(hypoiodite). They lower the activation energy of H2O2 decomposition to water and oxygen.

A further reaction occurs, at least immediately after the addition of iodine, parallel to the reac-tion mentioned so far, but soon reaches equilibrium and hence stops. Here, iodide is oxidizedto elemental iodine by the oxygen formed:

The formation of elemental iodine can be recognized by formation of a yellow color in thereaction mixture. The H30+ ions arise from water:

Since the H30+ ions are “consumed” in the formation of iodide, their concentration is loweredrapidly so that iodine formation ceases after the equilibrium concentration is reached. This parallel reaction has no influence on the evaluation of the present experimental results.

43

I– + H2O2 Õ IO– + H2O,

IO–+ H2O2 Õ I– + H2O + O2.

2 H3O+ + 2 I– + [O] 3 H2O + I2ÕÕ

2 H2O H3O+ + OH–ÕÕ

Note

45

Biol

ogy Transpiration in plants

– Detection of water loss through the plant leaf– Dependence of transpiration on plant ecotype and environmental conditions– Dependence of transpiration on the width and expanse of the stomata

METTLER TOLEDO precision balance (minimum readability 0.01 g)Conical flasks with narrow neck, 100 or 200 mlStoppers with boreCotton woolParaffin oil (possibly colored with a lipophilic dyestuff)Table lampHair dryerWith sensitive balances and if short measuring intervals are desired, it is advisable to constructa windbreak tunnel from plexiglass (can be purchased cut to the desired dimensions andeasily glued with a suitable adhesive)Plant material: There are many possibilities during the summer term. A branch from a plant ina warm, dry location and one from a plant in a moist location is a minimum requirement,however. Readily available throughout the whole year from gardens or parks:Yew (other conifers are also suitable)Evergreen snowball species (Viburnum rhytidophyllum, V. fragrans)Evergreen cotoneaster species (e.g. Cotoneaster salicifolius)Laurel (Prunus laurocerasus, which is extremely suitable for the preparation of thin sectionsfor microscope)HollyOleander

Fill the conical flask with water. Insert freshly cut branch. Carefully add a little paraffin oil witha pipette on the water surface (to prevent direct evaporation). A stopper with a bore or cottonwool or a combination of both should be used to hold the branch loosely in an uprightposition.

The conditioned branch is weighed at suitable time intervals (depending on the sensitivity ofthe balance and the size and type of the branch) and a table of values constructed.

The loss in weight is primarily dependent on the leaf area used, the time and the relativeatmospheric humidity. It is thus practical to calculate the amount of water transpired per cm2

leaf area per minute. It thus remains to determine the leaf area in the following manner:The leaves are laid on a fixed sheet of paper and traced out with a pencil. The leaf outline isthen cut out and its weight determined.The weight of a sample area of, for instance, 100 cm2 is also determined.

Objectives

Material

Experimental arrangements

Procedure

Evaluation

Biol

ogy

4646

Example:Pelargonium branch Time Weight of vessel Weight

with branch and water difference

0 min 108.187 g –5 min 108.135 g 52 mg

65 min 107.585 g 550 mg

Weight of paper leaf area: 2.927 gWeight of paper sample area: 1.172 g (100 cm2)

Specific transpiration = weight loss per cm2 per min

= 0.0370 mg/cm–2/min–1

The procedure can be simplified by referring the water loss to the plant mass (transpiredamount per g fresh weight per minute). This allows different plants to be compared with oneanother more rapidly.

Branches kept in the dark are weighed rapidly on the balance; an increase in transpirationoccurs when the stomata open.The specific transpiration for different plants is determined. Microscopic leaf sections can becombined with this. The environmental conditions can be changed using the same plants:moist air (glass bell lined with blotting paper or by covering the windbreak tunnel mentionedabove)dry air (room)warm air (with heating lamp)moving air (with hair dryer)

The branches should be placed in water immediately after cutting and possibly nicked againunder water. The branches should be collected when the plant is well supplied with waterotherwise they will take up water, but will not transpire at the outset when the stomata areclosed. The weight loss is then very small. This difficulty can be circumvented by conditioningthe plants for a few hours before the start of the experiment.

Extension of the experiment

Concluding remarks

Leaf area in cm2: · 100 = 250 cm2weight of paper leaf areaweight of sample area

weight losstime in min · leaf area

60265 · 250

= =

47

Intake of water vaporby lichens

This experiment can be used to show how plants can absorb water from moist air. Further, it will become apparent why trees in locations where the (unpolluted!) air is moist and subjectto heavy fog have a heavy growth of lichens.

METTLER TOLEDO precision balance (minimum readability 0.01 g)Petri dish (high wall) with 12 cm ΒPetri dish or plastic cover with approx. 6 cm ΒFilter paperAir-dried frondous or fructicose lichens (e.g. Pseudoevernia furfuracea, cetraria and stereo-caulon species)

The moist chamber is prepared according to the sketch.

An air-dried lichen thallus of suitable size must now beweighed accurately and then placed in the moistchamber, which is well sealed. After 1/2h, the thallusis reweighed (work quickly!) and then returned to themoist chamber. The weighings should be initiallyrepeated every 1/2h then later at longer intervals untilno change in weight occurs.

The dependence of the water intake on time is plotted graphically along the following lines:

A condensate is formed on the lichen thallus in the moist chamber. This condensed water isinitially absorbed rapidly in the air-filled voids present in the dry lichen thallus (steep increasein curve). The walls of the fungal hyhae subsequently swell up until complete water saturationis attained (shallow increase in curve). Water intake causes the initially brittle and friablelichen thallus to become soft and elastic.

Objectives

Material

Procedure

Evaluation

47

Biol

ogy

4848

Water intake and loss in mosses

Water intake from the soil by mosses is insignificant. The water is predominantly absorbedfrom rain, dew, fog and water vapor. The experiments show what significant water quantitiesare retained by mosses and why these plants are thus of such considerable importance invarious ecosystems. The experiments also provide a good introduction to anatomical andphysiological problems with mosses.The comparison of the water budget of mosses and vasculiferous plants is illuminating.

METTLER TOLEDO precision balance (minimum readability 0.01 g)Glass dishesAbsorbent paperDifferent mosses (e.g. polytrichum, leucobryum, sphagnum)

An air-dried mossy cushion is weighed and then completely immersed in a glass dish filledwith water. First at short, then at longer time intervals the cushion is taken out of the water,freed from any adhering water by a brief shaking, dried by pressing gently on absorbent paperand weighed. When no further change in weight occurs, the maximum water intake has beenreached.

This can be carried out along the following lines:

Extreme values are found under laboratory conditions. In the natural habitat, the maximumwater storage is reached only momentarily during heavy precipitation. At this point, the oppor-tunity to demonstrate the water cells of sphagnum and leucobryum under the microscopeshould on no account be missed. Compare here STEINECKE and AUGE (1963).

The water-saturated mosses can also be used to measure the water loss. The moss cushionis laid on a dry support and examined at intervals lasting several hours (several days). The above-mentioned authors also describe experiments for the water conduction of mosses.For comparison purposes, fungi and lichens can be investigated for water intake and loss inthe same manner.

Objectives

Material

Procedure

Evaluation

Extension of the experiment

49

Water and ash contentof different plant organs

The experiments are suitable for group instruction and the attainment of the following teachingobjectives:– Insights into the material composition of the plant body– Familiarization with analytical methods– Illustration of the concepts of fresh weight, dry weight, water content, organic and inorganic

substances, and ash content.The pupils should be familiar with the following topics: water and mineral salt intake, photo-synthesis; and have a basic knowledge of chemistry.

METTLER TOLEDO precision balance (minimum readability 0.01 g)Petri dishes or beakersPorcelain dishesDrying cabinetBunsen burner with tripod, porcelain triangle, magnesia or glass rod, possibly a muffle furnacePlant material such as leaves, bulbs or tubers, roots, fruit

The technical procedure is discussed on the basis of the following scheme:

The plant material, which must be as fresh as possible, is weighed and then quickly placed inthe drying cabinet. It is dried for 10 min at 105 °C (rapid destruction of the tissue to avoid res-piration losses) and then dried at 80°C to constant weight (1–2 days). Use of a constant dry-ing temperature of 105 °C has been abandoned primarily because different plant substances(e.g. ethereal oils) volatilize or undergo thermal decomposition at this temperature. The dry-weight determination is now performed.If a muffle furnace is available, the dried plant material is ashed at approx. 500 °C; otherwise,this is carried out in a porcelain dish over a Bunsen burner beginning with a small flame andthen later switching to a more powerful flame. The carbonizing material should be stirred oc-casionally. To remove clumps of carbon particles, the material is allowed to cool, moistenedwith a few drops of alcohol, the particle clumps powdered and the whole reheated. The ashremaining is weighed.

Objectives, preconditions

Material

Procedure

49

Biol

ogy

5050

The water content is determined from the formula water content = fresh weight – dry weight.The ash content is expressed in % of the fresh weight and the dry weight.The following table may serve as a basis:

If the experiment is carried out in a practical class, it is essential to include a discussion ofpossible error sources in the evaluation.

– Qualitative ash analysis– Investigation of different leaf types (summergreen, evergreen, succulent)– Sun and shade leaves or leaves at different heights or wind-protected and wind-

exposed leaves of one species of plant.

Evaluation

Additional possibilities

51

Concerning alcoholic fermentation

Carbon dioxide is evolved during alcoholic fermentation. The fermentation substrate becomeslighter and this can be detected easily with a balance. When the external conditions are heldconstant, the evolution of carbon dioxide per unit time is thus a measure of the metabolicactivity of the yeast fungus. By modification of a basic experiment, the effects of different exter-nal factors on the fermentation activity can be investigated. The basic problem always remainsthe same: The determination by weighing of the dependence of the weight on time.Level of knowledge required from the pupils: respiration and fermentation: course, significance,and chemical events in the sphere of empirical formulae.If the experiments are performed during a practical class, the pupils themselves can plan thedifferent series and carry them out. In class instruction with a lesson of 45 minutes duration,demonstration of the temperature dependence is certainly possible: One flask in the room, one in the drying oven and a third in the refrigerator. A complete fermentation curve cannot,however, be constructed

METTLER TOLEDO precision balance (readability 0.01 g)Pressed yeastGlucoseConical flask of 100 ml capacity with a stopper bored through once and with loose cottonwool fillingDrying oven and refrigerator; if necessary, water bath or thermo-lamps.

Tap water (90 ml) and 10 g pressed yeast are added to a conical flask. The yeast is sus-pended by stirring and shaking. Immediately before the start of the experiment and after thesuspension has assumed the desired reaction temperature, 5 g glucose are added. The firstweighing is then carried out (with stopper); the second weighing is performed after 10 min-utes, the third after 20 minutes, etc. The suspension must be shaken thoroughly after everyweighing.If typical fermentation curves are requiredduring a double lesson, it is essential towork at the optimum temperature of 3 °C.Uniform, well-controlled shaking is impor-tant and must be carried out at least afterevery weighing. If the experiment is con-ducted at room temperature, the use of amagnetic stirrer is advised.

This is carried out using the method shownin the example below. The values weredetermined at a room temperature of 19 °C.It thus shows what can be achieved withvery simple apparatus in the field offermentation activity.

Objectives and formulationof the problem

Material

Procedure

Evaluation

51

Biol

ogy

5252

After a slow start (induction phase), the reaction accelerates and then proceeds at a constantrate; this rate decreases with decreasing sugar content. Complete reaction requires severalhours.At 35 °C, the slightly S-shaped curve can be obtained within 90 minutes.The yield of CO2 from a specific weight of sugar can be calculated stoichiometrically (48.8%).In our experiment, therefore, 2.44 g carbon dioxide should be evolved (it must be borne inmind, however, that part of the pressed yeast material consists of fermentable substances).

The dependence of the fermentation activity on the following factors can be determined:– on the temperature

e.g. in the range 0 to 60 °C, with determination of the optimum. At this point, the rulegoverning the dependence of the reaction rate on temperature can also be demonstrated.

– on the amount of yeast cells or the quantity of enzymeExperiments with different quantities of yeast from 2 to 20 g, for example.

– on the amount of sugarExperiments with 2.5, 5,10 and 20 g sugar, for example.

– on the type of sugar– on the pH value

Different buffer solutions are prepared from sodium phosphate and sodium dihydrogenphosphate and their pH value determined. The optimum value lies in the weakly acidicregion.

– on shakingTo what extent does thorough shaking or stirring promote the fermentation activity?

– on nutrientsEffect of meat extract, ammonium sulfate and potassium dihydrogen phosphatein the substrate.

– of preservatives and disinfectantsFor example, the preservative sorbic acid, added in the form of potassium sorbate invarious amounts (100, 250, 500, 1000 and 2000 mg), can be tested.

To obtain comparable results, the following must be observed:– the same type of yeast must be used in all experiments and it must be fresh.– picking up, carrying and setting down the conical flasks must always be carried out care-

fully to avoid shocks if possible; these may adversely affect the experimental results.– when experiments are conducted at different temperatures, weighings should be carried out

as quickly as possible to keep cooling or warming within acceptable limits.

Additional possibilities

Concluding remarks

For more informationwww.mt.com/education-line

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