Experiment+1 +Grav Vol Stat Methods Fall+2013 1

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EXPERIMEN T1: Methods

Experiment 1, Page 1

EXPERIMENT1

INTRODUCTION TO GRAVIMETRIC,VOLUMETRIC,AND

STATISTICAL METHODS

PRELAB ASSIGNMENT

READING: "Essential Guide to Chem 15" (on bspace under "Resources")

Appendices A and B (on bspace under "Resources")

Harris (8th Edition): Chapters 2, 3, and 4

1. Prepare a flow chart of Experiment 1 from the laboratory procedure given here to follow

during the laboratory period.

2. You will be using the following chemicals during the semester. Describe why they are

hazardous (see the Merck Index).

a. HCl (hydrochloric acid)

b. HNO3 (nitric acid)

c. NaOH (sodium hydroxide)

d. CH3OH (methanol)

3. Make a sketch of the layout of the Chem 15 lab and indicate the location of the safety

equipment (This section may be completed in the laboratory).


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PURPOSE AND OVERVIEW

In this experiment you will learn how to use an analytical balance, how to measure liquid

volumes, and how to interpret experimental data. First, you will weigh accurately both a penny

and a nickel. Each of you will be loaned a penny (youre welcome!), but unfortunately each

section will have only one nickel and everyone will weigh it. In order to determine the weight of

an average penny and the average weight of the nickel, the results of the entire section will be

compiled. In addition, a comparison of the weights of pennies dated 1981 and before versus 1982

and after will be done. You will also learn and practice how to measure and transfer a volume of

liquid and will determine the precision and accuracy of different techniques. The uncertainty in

the data acquired in the experiments will be determined using statistical methods.

INTRODUCTION TO GRAVIMETRIC AND VOLUMETRIC TECHNIQUES

The ability to measure liquid volumes precisely and accurately is of great importance in the

chemistry laboratory. Volumetric measurements can be done with great precision and accuracy:

0.1% and better is achievable (seeHarris (8th Edition), Chapter 2). Note also that the ability to

discern whether a less precise or less accurate but faster method of measurement will suffice is

often just as important!

Gravimetric measurements using an analytical balance are capable of an even higher degree of

precision and accuracy than volumetric measurements. For example, one can measure the mass

of a 10 gram object to 0.1 mg (0.001 %) with a good analytical balance. For this reason, the

calibration of volumetric apparatus usually involves measurement of the mass of the volume of

liquid it contains, as you will do in the latter part of this experiment in determining the volume of

liquid delivered by your pipet.

INTRODUCTION TO THE STATISTICAL ANALYSIS OF DATA

Every measurement has some uncertainty associated with it. This experimental error can be

broken down into two different categories:

Systematic Error: has a definite value, an identifiable cause, and is of the same sign and

magnitude for replicate measurements made in the same way. Systematic error

leads to a bias and results in inaccurate data.


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Random Error: is always present, has an equal chance of being positive and negative,

and cannot be corrected. This indeterminate error results from noise or fluctuations

and is reflected in the range of the data.

In the absence of systematic error, the results are clustered symmetrically about the

mean, and replicate measurements improve the precision of the data.

In the Chemistry 15 laboratory, you will learn how to analyze quantitatively a variety of different

chemical systems. It is important that you learn to recognize the significance of the results you

obtain. Since all real measurements contain experimental error, it is never possible to be

completely certain of a result. In order to determine the uncertainty of an experimental result,

statistical techniques must be applied to the data. The penny experiment and the nickel

experiment represent two different situations. In the former case you will determine the weight

of an average penny by sampling a limited subset of pennies which is assumed to be

representative of the entire collection ofallpennies. In the nickel experiment the entire class

will be trying to determine the best value for the weight ofjust one nickel. Both of these

problems will be analyzed using statistical methods to determine the expected spread in

measurements of a sample of randomly distributed variables (as in the nickel experiment) and

also the error introduced by using only a finite set of data to represent a theoretically infinite set

(as in the penny experiment).

We begin by describing what is called the parent distribution of the quantity in which we are

interested. This tells us how a theoretically infinite collection of such quantities would be

distributed, i.e., the distribution ofmasses of an infinite number of pennies or the distribution of

random errors in an infinite number ofmeasurements of the mass of one nickel. If the errors

in measurements are strictly random, the data approximate the bell-shaped curve. For a large

number of data points, a Gaussian ornormal error curve fits the data best. (See Harris (8th

Edition), Figure 4-1.)


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The parent distribution is characterized by thepopulationmean () which is the average value of

the quantity measured (x) in the limit of an infinite number of measurements and a variance (2)

which is a measure of the dispersion, or width, of the distribution.

= limN

1

Nx i

i

(1)

2 = lim

N

1

Nx i ( )

2

i

(2)

Thepopulation standard deviation () is the square-root of the variance. The absolute deviation

(d) is the difference (with a + or sign) between the mean and a measured quantity (xi)

di = xi (3)

The mean () is the true value of the measured quantity,x, in the absence ofsystematic errors;

the standard deviation (), or the precision of the method, characterizes the uncertainties

associated with our experimental attempts to measure . Precision signifies the bestconsistency

we can obtain for any set of measurements ofx by that method. Different methods will in general

give different values of but the same value of .

In practice, we must deal with a finite number of measurements. From this finite set we extract

an experimental mean (x ) and an experimental standard deviation (s):

=

i

ix

N

x1

(4)

( )

1

2

=

N

xx

s ii

(5)

The quantity x is ourapproximation to the true mean () and s is ourapproximation to the true

standard deviation (). Clearly, these approximations will resemble more closely the parent


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parameters and as we make more and more measurements (with no systematic errors). We

note that the denominator ofs contains the term N 1 rather than N. This is because when we

use Equation 4 to extract the estimate of the mean we no longer have N independent pieces of

data. Our degrees of freedom, or independent pieces of data, are thusN 1 rather thanN.

One further important quantity is the standard deviation of the mean (m) and our experimental

approximation to it (sm). By using some simple calculus we can show that

m =

N (6)

and therefore

N

ss =m . (7)

We must emphasize the distinction between the standard deviation () and the standard

deviation of the mean (m). characterizes the uncertainty associated with each experimental

measurement; it is the half-width of the Gaussian distribution between the points where thecurve drops to e1 of its maximum value (e is the irrational number 2.71828). m

characterizes the uncertainty in the mean which tends to zero asNtends to infinity. Clearly, the

more times we measure a quantity the better we know its mean. However, the uncertainty

decreases only as the square rootof the number of measurements.

The area bounded by the Gaussian curve and thex axis between two values ofx, sayx1 andx2, is

the probability that a measurement lies between x1 and x2. The probability for a measurement

lying between + and is normalized to unity; i.e., we think there is a 100 % chance of finding

this measurement atsome value ofx. In terms of calculus, the area under a curve is equal to the

integral of the function (the Gaussian in this case) that defines the curve.

The Gaussian function is


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P =1

2e

1

2

x

2

(8)

where P describes the probability for finding a given value ofx. Note that this function is

symmetric about the mean (because of the square). The actual probability for finding x in an

interval x much smaller than is given by the product Px.

The integral of (8), which represents the area under the Gaussian curve, has no analytical form.

The value of the integral can be calculated, however, and tables of it are readily available in

many texts (see Harris (8th Edition), Table 4-1). From such tables of values we find that the

probability that asingle measurement is within of the mean is 68 %, within 2 is 96 %, and

within 3 is 99.7 %. These intervals about the mean () are called the confidence intervals.

So far, the discussion of probability applies to a true Gaussian distribution, when and are

known. This is the case only when a large number ( N ) of measurements have been made.

Usually we have only enough time to make a few measurements, and therefore only x and s, the

approximations to and , are known. To treat the probability problem and obtain the

confidence intervals in this more practical case is more complex. If youre interested, see E.B.

Wilson, Introduction to Scientific Research, pp. 239242. The problem was solved by W.S.

Gosset (who called himself Student) around 1930. The result is called Students t-

distribution. A table of values of t is given in Harris (8th Edition), Table 4-2. To use the

table, look in the proper row for our degrees of freedom (N1) and in the proper column for the

desired confidence level (80 %, 90 %, etc.) and find the value of t. The confidence interval for

the mean is then given by Nts . This means that in the absence of systematic errors, there is a

probability given by the confidence level (80 %, 90 %, etc.) that the true mean (or our true

value) lies within Nts of our experimental mean (x ).

The most useful way to report a result is in terms of Ntsx . In this course you will report

all laboratory results with a confidence interval corresponding to 95 %.


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EXPERIMENTAL PROCEDURES

WEIGHTS OFPENNIES AND THENICKEL:

1. Your Graduate Student Instructor (GSI) will give a demonstration on the use of the

analytical balance and you should review Appendix A (on bspace) before lab. Pay

attention to the GSI and read the instructions on the balance as well before you start.

Make sure to use the same balance for all of the measurements you make.

2. You will be given a penny to weigh. Wipe off the penny with a Kimwipe. Record its

weight to the nearest 0.1 mg. Be careful not to touch the penny with your fingers. Use

clean tongs or forceps. Note any strange features (holes, gouges, etc.) in your notebook.

Also, make sure you note which balance you use and the date of the penny.

3. Now exchange pennies with one of the other students who are using the balances and

weigh it. Repeat this until you have weighed six different pennies, three dating before

1982, and three dating after1982. Record all observations and results.

4. When everyone has weighed their six pennies, hold one of the pennies which you have

weighed in your hand. Reweigh it and notice if there is a difference in weight.In general,

you should never touch the object you are trying to weigh because you may

contaminate it with moisture and oil and change its weight.

5. Weigh the class nickel to 0.1 mg.

6. Write the weight of youroriginal penny and the nickel weight, along with your locker

number on the board.

7. Record the penny and nickel data for the entire lab section in your notebook.

TRANSFER OF10mL OFWATER WITH A VOLUMETRICPIPET:

1. Your GSI will give a demonstration on the use of a volumetric pipet. In addition, be sureto have already reviewedHarris (8th Edition), Section 2-6, and Appendix B (on bspace).

2. Fill your 250-mL beaker with room temperature distilled water and measure the initialtemperature to the nearest 0.1 C. (Note there is usually a mark at the bottom of the

thermometer somewhere below the last gradation. This is the immersion depth. You must

immerse the thermometer to this point to get a correct reading, no more, no less!)


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3. Practice filling your 10-mL volumetric pipet with water from the beaker and transferringit to another container several times before proceeding with Step 3. Take care not to not

to lift the pipet tip out of the liquid you are pipetting while you are applying suction to the

pipet.

4. Wipe dry the outside of your 50-mL volumetric flask (it should be clean, but the insidedoes not have to be dry), stopper it, and weigh it on the analytical balance. PLEASE

KEEP THE ANALYTICAL BALANCE DRY; LIQUIDS MAY CAUSE DAMAGE!

Wipe up any spills.

5. Record the temperature of the water in the beaker again, and then use your 10-mL pipetto transfer 10 mL of water from the beaker to the volumetric flask.

6. Stopper the flask, wipe the outside of it to remove any dust or water droplets, and weighit again.

7. Repeat steps 4 and 5, adding more water to the flask each time and then weighing it, atleast 3 times. If time permits, repeat until you have obtained at least three values for the

weight of water transferred that are in reasonable agreement ( 0.1 to 0.5 % is achievable

with practice).

TRANSFER OF10mL OFWATER WITH A GRADUATED CYLINDER:

1.

Using the procedure above of weighing your 50-mL volumetric flask before and afteradding water, now use your50-mL graduated cylinder to measure 10 mL of water at a

known temperature from your 250-mL beaker and transfer it to your flask.

2. Repeat until you have 3 measurements of the weight of water transferred using your 50-mL graduated cylinder.

TRANSFER OF10mL OFWATER WITH ABURET:

1. Your GSI will give you a demonstration on proper buret technique. Also be sure youhave reviewedHarris (8th edition), Chapter 2 and Appendix B (on bspace).

2. Clean your buret and dry the outside. Make sure that the stopcock assembly is complete.If you have a glass stopcock, you should have a green clip holding the stopcock in. If you

have a Teflon stopcock, you should have a Teflon washer, rubber washer, and a nut on


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your buret in that order. If you are missing pieces, or want to double check your buret,

see the Stockroom.

3. Using the procedure above of weighing your 50-mL volumetric flask before and afteradding water, now use your 50-mL buret to measure 10 mL of water at a known

temperature from your 250-mL beaker and transfer it to your flask. Read the volume

dispensed by the buret compare that to the volume calculated from the mass of water

dispensed.

4. Repeat 3 times or until you can comfortably and correctly read the buret.

TRANSFER OFSMALL VOLUMES OFWATER WITH ABURET:

If time permits, practice dispensing small volumes from your buret. Your GSI can show you

a couple of techniques to dispense small volumes. With practice, you can dispense volumes

as small as 0.01 mL.

INFORMALLABREPORT:

See the Lab Reports subsection in the "introduction to the laboratory" section of this manual for

general guidelines on how to prepare an informal report of the experiment and your results.

In addition, be sure to include the following in your report:

Calculations:

Report the mean value with the 95% confidence interval in the format + ts/N where is

the mean value, s is the standard deviation, t is the value from the Student's t table for the

appropriate degrees of freedom and the desired confidence level (Harris [8th edition], Table 42),

and N is the number of measurements, for the following data sets:

1. Pre 1980 Pennies Individual Data Set

2. Post 1982 Pennies Individual Data Set

3. Pre 1980 Penny Class Data Set

4. Post 1982 Penny Class Data Set

5. Nickel Class Data Set

6. Water Data Volumetric pipette method

7. Water Data Graduated cylinder method

8. Water Data Buret method


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Organize these data in tables and/or figures and always explicitly indicate the appropriate units

of any numerical values.

Discussion/Results:

Comment on the accuracy/precision of each set of measurements

Did you find a significant difference between the pre and post1980 Pennies? Comment.

Comment on whether you detected any effect due to handling a penny and then not wiping it

clean.

Comment on the relative precision of the various methods by which you

measured a given volume of water.

Finally, don't forget to attach the duplicate pages from your lab notebook for this experiment at

the end of your informal report.

v. 27 August 2013

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Experiment+1 +Grav Vol Stat Methods Fall+2013 1