Density Measurements

        References:

Chemistry, 4th ed, by J. McMurry and R. Fay. Prentice Hall, 2004, Sections 1.10-12

        Purpose:

There are four parts to this experiment.  

            1,2  - To measure the density of water by 2 methods.

    3 -     To measure the density of an unknown solid.

    4 -     To measure the density of pennies and estimate their elemental composition. 

You should work with a partner to do Parts 1, 2 and 4.  Each person must do their own unknown sample for Part 3.

Background:

A very important aspect of this experiment is to learn to apply the measures of accuracy and precision to all quantitative laboratory measurements.

Accuracy is a measure of the agreement of a measurement with its accepted value.  Usually, it is expressed as a percent error, which is defined by the equation:

%-error = measured value - accepted value x 100
         accepted value

Accepted, measured values for many properties are found in the Handbook of Chemistry and Physics or published in some other reputable format.  Other excellent sources are textbooks or online (try Google).  Any value which used in your report must be accompanied by a proper citation.

Precision : The precision of a measurement is a measure of the mutual agreement of repeated determinations; it is a measure of the reproducibility of an experiment. The most useful measure of precision is the standard deviation (std).  This is the range of values within which 68% of all measured values are likely to fall.  The smaller this range, the more precise are the results.  Std is given by:

where N is the number of measurements and xbar is their average. 

An example is shown below:

A student makes four measurements of the density of an object and obtains the values 10.10 g/cm3, 10.20 g/cm3, 10.12 g/cm3 and 10.15 g/cm3

i

xi (g/cm3)

xi - xbar (g/cm3)

(xi - xbar)2 (g/cm3)2

1 10.10 0.04 16 x 10-4
2 10.20 0.06 36 x 10-4
3 10.12 0.02 4 x 10-4
4 10.15 0.01 1 x 10-4

xbar = 10.14

sum = 57 x 10-4

   

std = 0.04 g/cm3

These results would be reported as 10.14 0.04 g/cm3. The smaller the standard deviation, the more closely each individual measurement agrees with the average value and the better the precision.

Remember, all entries in your lab book must be made, in ink, directly in your tables, in your book, before you leave the lab.  All  measurements made in the laboratory must be reported with an appropriate number of significant figures and with the correct units.  In the column heading for each column in all tables, enter the uncertainty of the measurement as, for example, 0.001, along with its units.  The results of all calculations made with these measured values must also be reported with an appropriate number of significant figures.  In the column heading for each column of calculated values, enter the uncertainty of the calculated result as, for example, 0.001, along with its units. This is a very important part of this experiment and all of the experiments which follow.  It will always be a factor in the grade you receive for your lab report!  It is not unusual to make measurements that give very suspicious results.  A suspicious measurement can be ignored, if there are other good measurements and if there is reason to believe it is bogus.  However, you must not remove or delete it from your report, simply draw a line through it and indicate why you are not using it for your average value.  Just because it is not the result you think you should get is not a sufficient reason. You might consider putting a copy of this box at the top or each experiment in your notebook.  It is that important.

Procedure:

1. Density of Water Choose a 30 or 50 mL beaker from your drawer.  Determine the mass of the empty, dry beaker and record the value in your notebook, in a clearly labeled Table, with the correct number of significant figures.  Add water to the beaker, filling it to a calibration line.  The bottom of the meniscus, the curved water surface, should be at the line.  Record the volume of the water.  Determine the mass of the filled beaker and record the value.  As always, use the number of significant figures appropriate to the measuring device.  Repeat these measurements at least two more times.

2. A Better Value for the Density of Water The density of water can be determined graphically. The equation for density can be written as:

m = dV (1)

This can be compared to the equation of a straight line

y = mx + b (2)

where m is the slope and b is the y-intercept. Comparison of equations (1) and (2) shows that if we plot the mass of a liquid vs. its volume, we should obtain a straight line which passes through the origin, and which has a slope equal to the liquid density. In this experiment you will determine the mass of several different volumes of water, and then graph the mass versus the volume. The slope of the best line through the points will be equal to the density.

Weigh a clean, dry 100 ml graduated cylinder. This and subsequent weighings should be to  0.001 g. Do not handle the cylinder with your bare hands since oils and moisture from your skin will affect the mass. Handle it with a paper towel. Fill the cylinder as closely as you can to 10 ml with deionized water, read and record, in your Table, the volume of the water, estimating the last significant figure, measured to the bottom of the meniscus, as appropriate.  Weigh the cylinder with the water and record your result.  Repeat the procedure for volumes of about 25, 75 and 95 ml, always reading the exact volume and entering it with all significant figures into your Table. After you have completed these mass and volume measurements, insert a thermometer in the water and determine the water temperature. 

Repeat the entire procedure twice more. 

3. The Density of an Unknown Metal: Obtain an unknown metal sample.  Depending on its size, you may want to use more than one piece to improve your precision.  Wipe it with a paper towel to be sure it is clean and dry.  Record the sample ID in your Notebook.  Determine the mass of the sample to 0.001 g and record the value. 

Determine the volume of the sample as follows: Fill a 100 mL graduated cylinder with about 50 mL of water. Note and record the exact water level, as above.  Immerse a clean, dry metal sample in the water, being careful not to allow it to drop forcefully against the bottom of the cylinder. You don't want to pay to replace it.  Dislodge any water droplets from the metal by gently tapping the cylinder.  Note and record the final water level. The difference in the water levels before and after the immersion of the sample is the volume of the water displaced by the sample, i.e., the sample volume. 

Measure the mass and volume of your sample three times, recording all data in your Table. 

Do not discard the metal sample. Dry it and return it to the Stockroom!

4. The Density of Pennies: Obtain ten post-1982 pennies from the Stockroom. Determine their density.  You may design your own specific method, but however you do it, you must describe your method in the Procedure section of your notebook.  Please return the pennies when you are finished.

Results: 

In every part of this section, you must provide sample calculations, written in your notebook, using the correct number of significant figures and including all units.

Part 1: Density of Water  Use Excel to calculate the value of the density for each trial.  Calculate the average value and the standard deviation.  Pay attention to significant figures and units  in your calculations and record the results in your Table.

Part 2A Better Value for the Density of Water  

Use Excel (instructions) to make tables of your data, generate graphs for each trial and calculate the slopes.  Calculate the average density from the slopes and the standard deviation of your measured densities.

Part 3: Density of Unknown Metal Sample

Use Excel to calculate the density of the unknown metal sample from the data for each trial. Calculate the average density and the standard deviation.

Part 4: The Density of Pennies

Use Excel to calculate the density of the pennies from the data for each trial, the average density and the standard deviation of the measured densities.

Conclusions:  

Summarize your key results in a well-organized format.  Be sure to include the following:

bulletThe values for the density of water from each method.  Compare the two values and their standard deviations.  Are the results reasonable?  Why?  Refer to the reported values in the Handbook of Chemistry and Physics and report the percent error for each of the methods.  
bulletThe value obtained  for the average density of your unknown metal, expressed with the appropriate number of significant figures, the standard deviation and the sample ID. 
bulletThe average value for the density of post-1982 pennies, expressed with the appropriate number of significant figures and the standard deviation.  
bullet Compare your value of the penny density to the densities of copper and zinc.  What can you conclude about the composition of a post-1982 penny from your results?  Explain briefly.   Determine a quantitative estimate of the percent of copper in a penny from your data using the equation  given below. Pay careful attention the significant figures in your calculation. How does your result compare to the reported value for the percent of copper in a post-1982 penny?   Be sure you clearly cite your reference to the reported (accepted) value.  

where dCu and dZn are the accepted values for the densities of copper and zinc and dmeas is your measured penny density.

Your grade on this experiment will be based on the following:

bulletThe accuracy and precision of your results.
bulletYour correct use of significant figures and units.
bulletThe clarity of your report, including sample calculations, tables and graphs.
bulletThe correctness of your discussion.
bulletDid you follow the instructions?
bulletDid you turn it in on time? 

Last edited by J. Byrd on 09/14/2005.