Scientific Measurements

Scientific MeasurementsUnits of MeasurementsConversion ProblemsDensityMeasurements and their Uncertainty

Do any of these signs list a measurement?- Measurements contain BOTH a number and a unit.In the signs shown here, the distances are listed as numbers with no units attached. Without the units, it is impossible to communicate the measurement to others. When you make a measurement, you must assign the correct units to the numerical value.

2All measurements depend on units that serve as reference standards. The standards of measurement used in science are those of the metric system. Based on multiples of 10

The International System of Units (abbreviated SI, after the French name, Le Systme International dUnits) is a revised version of the metric system.

1. Measuring with SI UnitsMetric system was originally established in 1795. The SI was adopted by international agreement in 1960.3What do the SI prefixes deci, centi, and milli mean? Think about the word decimal, century, and millennium.

Factor is also called scientific notation. Have students acknowledge the cut off for the prefix of smaller units and larger units.5The five SI base units commonly used by chemists are the meter, the kilogram, the kelvin, the second, and the mole.

What metric units are commonly used to measure length, volume, mass, temperature and energy?

Units & Quantities Think and answer for yourself7In SI, the basic unit of length, or linear measure, is the meter (m). For very large or and very small lengths, it may be more convenient to use a unit of length that has a prefix.

Units of Length

Ask students what the common metric units of length are? (gold stars identify)8Volume - space occupied by any sample of matterUnits of VolumeHow do you calculate the volume of a cube?

The SI unit of volume is the amount of space occupied by a cube that is 1 m along each edge. This volume is the cubic meter (m)3Volume = length x width x height. The unit of volume is derived from units of length which is measured in meter. 9Units of VolumeThe liter is a NON SI unit of measurement!A liter (L) is the volume of a cube that is 10 centimeters (10 cm) along each edge (10 cm 10 cm 10 cm = 1000 cm3 = 1 L).What unit of volume are you most familiar with? Ill have a liter of cola

10Common quantitiesUnits of Volume

The volume of 20 drops of liquid from a medicine dropper is approximately 1 mL.

A sugar cube has a volume of 1 cm3. 1 mL is the same as 1 cm3.The mass of an object is measured in comparison to a standard mass of 1 kilogram (kg), which is the basic SI unit of mass.

Common metric units of mass include kilogram, gram, milligram, and microgram.

Unit of Mass

How does weight differ from mass?Unit of MassWeight is a force that measures the pull on a given mass by gravity.

Mass is a measure of the quantity of matter. (the space it occupies)

The astronaut shown on the surface of the moon weighs one sixth of what he weighs on Earth. An astronauts weight on the moon is one sixth as much as it is on Earth. Earth exerts six times the force of gravity as the moon. Inferring How does the astronauts mass on the moon compare to his mass on Earth?

13Units of Temperature

Temperature - is a measure of how hot or cold an object is. Thermometers are used to measure temperature. Substances expand with an increase in temperature. Thermometers are used to measure temperature. a) A liquid-in-glass thermometer contains alcohol or mineral spirits. b) A dial thermometer contains a coiled bimetallic strip. c) A Galileo thermometer contains several glass bulbs that are calibrated to sink or float depending on the temperature. The Galileo thermometer shown uses the Fahrenheit scale, which sets the freezing point of water at 32F and the boiling point of water at 212F.

14When 2 objects at different temperatures are in contact, heat travels from: Heat of Transfer

Lower temperatureHighertemperature

Scientists commonly use two equivalent units of temperature, the degree Celsius and the Kelvin.Units of Temperature

Celsius Kelvin

Reference points

Fahrenheit 16The zero point on the Kelvin scale, 0 K, or absolute zero, is equal to 273.15 C.

Units of Temperature

Because one degree on the Celsius scale is equivalent to one Kelvin on the Kelvin scale, converting from one temperature to another is easy. You simply add or subtract 273, as shown in the following equations.

Units of Temperature

18Converting Between Temperature ScalesNormal human body temperature is 37C. What is that temperatures in kelvins?

Analyze: List the known and the unknown.KnownTemperature in C = 37CUnknownTemperature in K = ?KEquation: K= C + 273

Calculate: Solve for the unknown. K= C + 273 37 + 273 = 310K

Practice Converting Between Temperature ScalesLiquid nitrogen boils at 77.2 K. What is this temperature in degrees Celsius?

Analyze: List the known and the unknown.

Calculate: Solve for the unknown.

Practice Converting Between Temperature Scales-196CEnergy - the capacity to do work or to produce heat. The joule and the calorie are common units of energy.

Joule (J) is the SI unit of energy.1 calorie (cal) is the quantity of heat that raises the temperature of 1g of pure H2O by 1C.Units of Energy

1 J = 0.2390 cal 1 cal= 4.184 J1.) Ask students before clicking to view picture of house with solar panels: What is the major external source of energy? The Sun. What forms does the sun provide energy? Light and Heat. 2.) This house is equipped with solar panels. The solar panels convert the radiant energy from the sun into electrical energy that can be used to heat water and power appliances.

211. Which of the following is not a base SI unit?metergramsecondmoleWere you paying attention?222. If you measured both the mass and weight of an object on Earth and on the moon, you would find thatboth the mass and the weight do not change.both the mass and the weight change.the mass remains the same, but the weight changes.the mass changes, but the weight remains the same.

Were you paying attention?233. A temperature of 30 degrees Celsius is equivalent to303 K.300 K.243 K.247 K.Were you paying attention?K = C + 27324

Ask students: What are we looking at? Current Currency Exchange Rates. How would you decide which amount of money would be worth more 75 euros or 75 British pounds? Convert these values to a familiar currency US dollars25Can you think of any other examples in which quantities can be expressed in several different ways?

Consider the conversion units of distance:

1 meter = 10 decimeters = 100 centimeters = 1000 millimeters When 2 measurements are equivalent, a ratio of the 2 measurements equals 1

Conversion factor orRemember: even though the numbers in the measurements 1 m and 100 cm differ, both measurements represent the same lengthThese are all different ways to express the same length.In addition, conversion factors within a system of measurement are defined quantities or exact quantities. 27What happens when a measurement is multiplied by a conversion factor?

When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same.2. Conversion Problems

3.3Conversion FactorsA conversion factor is a ratio of equivalent measurements.The ratios 100 cm/1 m and 1 m/100 cm are examples of conversion factors.

Fig. 3.1129The two parts of a conversion factor, the numerator and the denominator, are equal.

3.3Conversion FactorsThe scale of the micrograph is in nanometers. Using the relationship 109 nm = 1 m, you can write the following conversion factors.

30In this computer image of atoms, distance is marked off in nanometers (nm). Inferring What conversion factor would you use to convert nanometers to meters?Dimensional analysis is a way to analyze and solve problems using the units, or dimensions, of the measurements.

Why is dimensional analysis useful?

An alterative way to problem solvingDimensional Analysis

Ask students first: What does the word dimension mean? a measure of spatial extent, especially width, height, and length. Dimensional there for means of or referring to dimensions; measurements. Analysis is defined as the identification or separation of ingredients of a substance into its constituent parts; its components. The best way to explain this problem solving technique is to use it to solve an everyday situation. Its more easily stated as: (CLICK to appear bullet) An alternative way to problem solving.31How many seconds are in a workday that lasts exactly eight hours?

Analyze: List the knowns and the unknown.KnownTime worked = 8 h1 hour = 60 min1 minute = 60 sUnknownSeconds worked = ? s

Calculate: Solve for the unknown.Example of Using Dimensional Analysis

Sample Problem 3.51.) How many minutes are there in exactly one week?Analyze: List the knowns and the unknown.Known

Unknown

Calculate: Solve for the unknown.

2.) How many seconds are in exactly a 40-hour work week?Analyze: List the knowns and the unknown.Known

Unknown

Calculate: Solve for the unknown.1.0080x104min1.44000x105s1.) The directions for an experiment ask each student to measure 1.84g of copper (Cu) wire. The only copper wire available is a spool with a mass of 50.0g. How many students can do the experiment before the copper runs out?

2.) A 1.00-degree increase on the Celsius scale is equivalent to a 1.80-degree increase on the Fahrenheit scale. If a temperature increase by 48.0C, what is the corresponding temperature increase on the Fahrenheit scale?

27 students86.4 F34What types of problems are easily solved by using dimensional analysis?

Problems in which a measurement with one unit is converted to an equivalent measurement with another unit are easily solved using dimensional analysis.

Converting Between units

Converting Between Metric Units

Express 750 dg in grams.Analyze: List the knowns and the unknown.KnownMass = 750 dg1 g = 10 dg

UnknownMass = ? g

Calculate: Solve for the unknown.

Conversion unitInform students that they will need to refer to their notes of the commonly used metric prefixes. Deci (d) = 10 times smaller than the unit it precedes. Factor is 10-1Evaluate; does the result make sense? Because the unit gram represents a larger mass than the unit decigram, it makes sense that the number of grams is less than the given number of decigrams.36Practice ProblemsConvert the following.15 cm3 to liters7.38 g to kilograms6.7 s to milliseconds94.5 g to micrograms1.5 x 10-2L7.38 x 10-3kg6.7 x 103ms9.45 x 107g

Sports Stats Entertainment & Chemistry Learning NetworkPurpose: to use dimensional analysis to convert between English and metric units.

Procedure: Using the player stats for the New England Patriots, convert heights and weights into heights and masses expressed in meters and kilograms, respectively. You must document your approach: Identify the known, unknown, and conversion factor. Must show all calculations.

2.54 cm = 1 inch454g = 1 lbECLNMultistep Problems What is 0.073 cm in micrometers?Analyze: List the knowns and the unknown.KnownLength = 0.073 cm = 7.3x10-2 cm102 cm = 1m1m = 106 m

UnknownLength = ? m

Calculate: Solve for the unknown.

When converting between units, it is often necessary to use more than one conversion factor.

39

The radius of a potassium atom is 0.227nm. Express the radius to the unit centimeters.

The diameter of Earth is 1.3 x 104km. What is the diameter expressed in decimeters?Practice Problems

1.3 x 108 dm2.27 x 10-8 cmThe mass per unit volume of a substance is a property called density. The density of manganese, a metallic element, is 7.21 g/cm3. What is the density of manganese expressed in units kg/m3?Converting Complex UnitsAnalyze: List the knowns and the unknown.KnownDensity of manganese = 7.21 g/cm3103 g = 1kg106cm3 = 1m3

UnknownDensity manganese = ? kg/m3

Many common measurements are expressed as a ratio of two units. If you use dimensional analysis, converting these complex units is just as easy as converting single units. It will just take multiple steps to arrive at an answer.

41Calculate: Solve for the unknown.

Density of manganese = 7.21 g/cm3103 g = 1kg106cm3 = 1m3g/cm3kg/m37.21 x 103 kg/m342Gold has a density of 19.3 g/cm3. What is the density in kilograms per cubic meter?

There are 7.0 x 106 red blood cells (RBC) in 1.0 mm3 of blood. How many red blood cells are in 1.0 L of blood?Practice Problemsg/cm3103 g = 1 kg106 cm3 = 1 m3

1.93 x 104 kg/m37.0 x 1012 RBC/L mm3 = 1 m3106 cm3 = 1 m31cm3 = 1 mL103mL = 1 L

Volume is of any cube is found by multiplying length by width, by height. The volume of a cubic meter is 1 m3. If you are converting to centimeters, the factor for centi is 10-2 but because this is volume, it needs to be cubed so that 10-2 (length) x 10-2 (width) x 10-2 (height) = 106 cm3 = 1 m3

431 Mg = 1000 kg. Which of the following would be a correct conversion factor for this relationship? 1000. 1/1000. 1000.1000 kg/1Mg.Were you paying attention?44The conversion factor used to convert joules to calories changesthe quantity of energy measured but not the numerical value of the measurement.neither the numerical value of the measurement nor the quantity of energy measured.the numerical value of the measurement but not the quantity of energy measured.both the numerical value of the measurement and the quantity of energy measured.

Were you paying attention?45How many g are in 0.0134 g?

1.34 1041.34 1061.34 1061.34 104

Were you paying attention?46Express the density 5.6 g/cm3 in kg/m3.

5.6 106kg/m35.6 103kg/m30.56 kg/m30.0056 kg/m3Were you paying attention?47Which is heavier, a pound of lead or a pound of feathers?

Most people are incorrectly applying a perfectly correct idea: namely, that if a piece of lead and a feather of the same volume are weighed, the lead would have a greater mass than the feather. If would take a much larger volume of feathers to equal the mass of a given volume of lead.48Why can boats made of steel float on water when a bar of steel sinks?

Prompt students to think about what measurements they would need to make to determine whether an object would float in water. (Measure the objects volume and mass; then compute its density and compare the result to the density of water.)49What determines the density of a substance?

Density is the ratio of the mass of an object to its volume.

3. Determining Density

The important relationship between how a steel ship can float is between its mass and its volume.

50Each of these 10-g samples has a different volume because the densities vary.

Density

Which substance has the highest ratio of mass to volume?- A 10-g sample of pure water has less volume than 10 g of lithium, but more volume than 10 g of lead. The faces of the cubes are shown actual size. Inferring Which substance has the highest ratio of mass to volume? LeadAsk students: What would be the volume of a 10-g sphere of each of the substances shown? The volumes would all remain the same because each sample is still Lithium, water, and lead, and the masses of each have not changed. Just because you change the shape does not mean that the mass or volume has changed and thus the density hasnt either. This is your seg-way into the next slide: The volumes of each of these substances vary because they have different densities. 51Define what an intensive property is.Provide 3 examples of an intensive property.Provide 2 examples of an extensive property.

Bell Ringer

Date: 10/11/2012Density is an intensive property that depends only on the composition of a substance, not on the size of the sample.

Density

Ask students: What is the meaning of the term intensive property? (a property that does not depend on the size of the sample its in the definition of density above) Ask students to conclude what other properties may be intensive? (acceptable answers include temperature and color) Point out to students that mass, unlike density, is not an intensive property. On the contrary, it is an extensive property. Have students infer the meaning of the term extensive property. (a property that depends on size)53For example, a 10.0-cm3 piece of lead has a mass of 114 g. What is the density of lead?

Unit of density: g/cm3What would happen if corn oil is poured into a glass containing corn syrup?

OILSYRUPDetermining DensitySimulation 1

Rank materials according to their densities.

ChemASAP/dswmedia/rsc/asap1_chem05_cmsm0301.html56Volume as temperature

The mass remains the same despite the temperature and volume changes.

Recall:

Density and Temperature

If volume changes with temperature and mass stays the same, then density must change.

The density of a substance generally decreases as its temperature increases.

DENSITYTEMPERATURE

50 F100 F0 F

A copper penny has a mass of 3.1 g and a volume of 0.35 cm3. What is the density of copper?Sample Problem Analyze: List the knowns and the unknown.KnownMass = 3.1 gVolume = 0.35 cm3

UnknownDensity = ? g/cm3

8.8571 g/cm3

A student finds a shiny piece of metal that she thinks is aluminum. In the lab, she determines that the metal has a volume of 245 cm3 and a mass of 612g. Calculate the density. Is the metal aluminum?

A bar of silver has a mass of 68.0g and a volume 6.48 cm3. What is the density of silver?Practice Problems2.50 g/cm3 - NO 10.5 g/cm3 What is the volume of a pure silver coin that has a mass of 14 g? The density of silver (Ag) is 10.5 g/cm3.

Practice Problem Using Density to Calculate VolumeAnalyze: List the knowns and the unknown.KnownMass of coin = 14 gDensity of silver = 10.5 g/cm3

Unknownvolume of coin= ? cm3

1.3 cm3 of Ag Use dimensional analysis and the given densities to make the following conversions. 14.8 g of boron to cm3 of boron. The density of boron is 2.34 g/cm3.

4.62 g of mercury to cm3 of mercury. The density of mercury is 13.5 g/cm3.

Rework the preceding problems by applying the following equation. Practice Problems

Volume of B = 6.32 cm3Volume of Hg = 0.342 cm362Make the following conversions:

2.53 cm3 of gold to grams (density of gold = 19.3 g/cm3)

1.6 g of oxygen to liters (density of oxygen = 1.33 g/L)

25.0 g of ice to cubic centimeters (density of ice = 0.917 g/cm3)48.8 g 1.2 L27.3 cm3If 50.0 mL of corn syrup have a mass of 68.7 g, the density of the corn syrup is

0.737 g/mL.

0.727 g/mL.

1.36 g/mL.

1.37 g/mL.

Were You Paying Attention?64What is the volume of a pure gold coin that has a mass of 38.6 g? The density of gold is 19.3 g/cm3.

0.500 cm3

2.00 cm3

38.6 cm3

745 cm3

Were You Paying Attention?65As the temperature increases, the density of most substances

increases.decreases.remains the same.increases at first and then decreases.Were You Paying Attention?66Todays current weather in Eastville is

The Weather Channel projected forcast:

Eastern Shore News What everyday activities involve measuring?

Recall which units of measure are related to each of the examples you provide. Estimate how tall you are in inches.Have your lab partner estimate how tall you are with a yard stick.Compare the estimates with the yard stick value.Examples include buying consumer products, doing sports activities and cooking68A measurement is a quantity that has both a number and a unit. Ex.Height Weight

4. Measurements and Their Uncertainty Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is correct.

Cooking Speed In scientific notation, a given number is written as the product of two numbers: a coefficient and 10 raised to a power.

Using and Expressing Measurements

Example: 602,000,000,000,000,000,000,000Scientific notation = 6.02x1023

- In chemistry, you will often encounter very large or very small numbers. You can work with very small and very small numbers when they are in scientific or exponential notation.- The number of stars in a galaxy is an example of an estimate that should be expressed in scientific notation.

703.1What is the difference between accuracy & precision?

71The distribution of darts illustrates the difference between accuracy and precision. a) Good accuracy and good precision: The darts are close to the bulls-eye and to one another. b) Poor accuracy and good precision: The darts are far from the bulls-eye but close to one another. c) Poor accuracy and poor precision: The darts are far from the bulls-eye and from one another.Accuracy - a measure of how close a measurement comes to the actual or true value of whatever is measured.

Precision - a measure of how close a series of measurements are to one another.

To evaluate the accuracy of a measurement, the measured value must be compared to the correct value.

To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

3.1Accuracy, Precision, and ErrorDetermining Error

Suppose you are using a thermometer to measure the boiling point of pure H2O at STP. The thermometer reads 99.1C. The true, or accepted value of the boiling point of pure H2O under these conditions (STP) is actually 100 C.

Which is the accepted value?

Which is the experimental value?

What is the error?74The accepted value is the correct value based on reliable references.

The experimental value is the value measured in the lab.

The difference between the experimental value and the accepted value is called the error.

Error can be positive or negative depending on whether the experimental value is greater than or less than the accepted value.The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%.

Suppose you are using a thermometer to measure the boiling point of pure H2O at STP. The thermometer reads 99.1C. The true, or accepted value of the boiling point of pure H2O under these conditions (STP) is actually 100 C.

Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the persons weight is inaccurate.

The scale below has not been properly zeroed, so the reading obtained for the persons weight is inaccurate. There is a difference between the persons correct weight and the measured value. Calculating What is the percent error of a measured value of 114 lb if the persons actual weight is 107 lb?

78Suppose you estimate a weight that is between 2.4 lb and 2.5 lb to be 2.46 lb. The first two digits (2 and 4) are known. The last digit (6) is an estimate and involves some uncertainty. All three digits convey useful information, however, and are called significant figures.

The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.

Significant Figures in MeasurementsMeasurements MUST ALWAYS be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation.

Animation See how the precision of a calculated result depends on the sensitivity of the measuring instruments.Significant Figures in Measurements3.1

81Three differently calibrated meter sticks are used to measure the length of a board. a) A meter stick calibrated in a 1-m interval. b) A meter stick calibrated in 0.1-m intervals. c) A meter stick calibrated in 0.01-m intervals. Measuring How many significant figures are reported in each measurement?

How many significant figures are in each measurement?123 m40.506 mm9.8000 x 104 m22 meter sticks0.07080 m 98,000 m Counting Significant Figures in Measurements3 sig figs (rule 1)5 sig figs (rule 2)5 sig figs (rule 4)Unlimited (rule 6)4 sig figs (rule 2, 3,4 )2 sig figs (rule 5)Have students refer to their significant figure rule sheet.82How many significant figures are in each length?0.05730 meters8765 meters0.00073 meters40.007 metersHow many significant figures are in each measurement?143 grams0.074 meter8.750 x 10-2 gram1.072 meter4 sig figs4 sig figs2 sig figs5 sig figs3 sig figs2 sig figs4 sig figs4 sig figsHow does the precision of a calculated answer compare to the precision of the measurements used to obtain it?

Significant Figures in Calculations

Significant Figures in CalculationsIn general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated.

The calculated value must be rounded to make it consistent with the measurements from which it was calculated.

3.185To round a number, you must first decide how many significant figures your answer should have. The answer depends on the given measurements and on the mathematical process used to arrive at the answer.

Rounding If the digit immediately to the right of the last significant digit is less than 5, it is simply dropped and the value of the last significant digit stays the same.

If the digit in question is 5 or greater, the value of the digit in the last significant place is increased by 1 2.691 m 2.69 m294.8 mL 295 mLRound off each measurement to the number of significant figures shown in parentheses. Write the answer in scientific notation. 314.721 meters (4)

0.001775 meter (2)

8792 meters (2)Sig. Fig.s - Rounding Measurements

Round each measurement to three significant figures. Write your answers in scientific notation.87.073 meters4.3621 x 108 meters0.01552 meter9009 meters1.7777 x 10-3 meter629.55 metersPractice Problems8.71 x 101 m4.36 x 108 m1.55 x 10-2 m9.01 x 103 m1.78 x 10-3 m6.30 x 102 mThe answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.Example:12.52 meters + 349.0 meters + 8.24 metersStep 1 align the decimal points and identify least # of decimal places. 12.52 meters 349.0 meters + 8.24 meters 369.76 meters Sig. Fig.s - Addition and Subtraction - 2 decimal places- 1 decimal places- 2 decimal places369.8 metersor 3.698 x 102 metersPerform each operation. Express your answers to the correct number of significant figures.61.2 meters + 9.35 meters + 8.6 meters

9.44 meters 2.11 meters

1.36 meters + 10.17 meters

34.61 meters 17.3 meters

Practice79.2 m7.33 m11.53 m17.3 mIn calculations involving multiplication and division, you need to round the answer to the same number of significant figures as the measurement with the least number of significant figures.

The position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements.

Sig. Fig.s - Multiplication and Division Perform the following operations. Give the answers to the correct number of significant figures.

7.55 meters x 0.34 meter

2.10 meters x 0.70 meter

2.4526 meters 8.4Practice= 2.576 (meter)2 (3)2.6 m2(2)= 1.47 (meter)2 (3)Step 1 determine # of sig figsStep 2 calculate answerStep 3 determine answer w/ correct # of sig figs.(2)1.5 m2(5)(2)= 0.291976 meter 0.29 mWere You Paying Attention?In which of the following expressions is the number on the left NOT equal to the number on the right?

0.00456 108 = 4.56 1011454 108 = 4.54 106842.6 104 = 8.426 1060.00452 106 = 4.52 10993Were You Paying Attention?Which set of measurements of a 2.00-g standard is the most precise?

2.00 g, 2.01 g, 1.98 g2.10 g, 2.00 g, 2.20 g2.02 g, 2.03 g, 2.04 g1.50 g, 2.00 g, 2.50 g

94A student reports the volume of a liquid as 0.0130 L. How many significant figures are in this measurement?2345Were You Paying Attention?95