Density Measurements

Purpose:

To measure the densities of a liquid and a solid and to illustrate the concepts of precision and accuracy.

Density: Density is defined as mass per unit volume or

where d is the density of the material, m is the mass of a given amount of material, and V is its volume. Therefore, the measurement of density involves the measurement of mass and volume.

Precision and accuracy: 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 simplest measure of precision is the average deviation. Its calculation is illustrated in the following example:

Example: A student makes four measurements of the mass of an object and obtains the values 0.1010 g, 0.1020 g, 0.1012 g, 0.1015 g. Calculate the average deviation of the measurement.

These results would be reported as 0.1014 ± 0.0003 g. The smaller the average deviation, the more clearly each individual measurement agrees with the average value.

Precise measurements, however, are not necessarily accurate. The accuracy expresses the agreement of the measurement with the accepted value of the quantity. A measure of accuracy is the percent error, defined by the equation:

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

Example: A student measures the density of magnesium and finds it to be 1.50 g/ml. The accepted value from the Handbook of Chemistry and Physics is 1.74 g/ml. What is the percent error of the student's result?

          % error = (1.50 - 1.74) g/ml x 100 = - 14%
1.74 g/ml

Procedure:

A. Density of Water - The density of water will be determined graphically. Equation (1) can be rewritten as:

This can be compared to the equation of a straight line

where m is the slope and b is the y-intercept. Comparison of equations (2) and (3) 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 0.01 g. Do not handle the cylinder with your bare hands since oils and moisture from your skin will affect the mass. Handle it by means of a paper towel. Fill the cylinder as closely as you can to 10.00 ml with deionized water, and weigh the cylinder plus water. Repeat the procedure for volumes of 25, 50, 75 and 100 ml. After you have completed the mass and volume measurements, insert a thermometer in the water and determine its temperature. Record your data in a table.

Repeat the entire procedure at least once. Construct a graph of the mass of water versus the volume of water, and determine the density of water.  

B. The densities of several metals: Obtain samples of aluminum, copper and zinc from the stockroom and weigh each sample to 0.01 g.  

Determine the volume of each sample as follows: Fill a 100 mL graduated cylinder with about 50 mL of water. Note and record the water level. Immerse one of the metal samples in the water, being careful not to allow the sample to drop forcefully against the bottom of 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, and hence the volume of the sample itself. Repeat the procedure with the other samples.

Measure the mass and volume of each sample three times. Record all data in a table. For each metal, calculate the density for each trial, and then calculate the average density for each metal.

Do not discard the metal samples. Return them to the stockroom.

C. The thickness of aluminum foil: Obtain a rectangular piece of aluminum foil, measure and record its width and length in cm and its mass in grams. Using the density of aluminum which you obtained from the Handbook of Chemistry, calculate the thickness of the foil.

D. The density of a penny: Obtain ten post-1982 pennies from the Stockroom. Measure their total mass by weighing, and determine their total volume by immersing them in water and measuring the volume of the water displaced, as in Part B. Divide the total mass by the total volume to obtain the average density of a penny.

Results: 

Part A: Density of water

Put your data into a neat table.  Make a graph of the mass of water versus its volume. Draw the best straight line through the points and from the slope of this line, determine the density of water. Show a complete calculation of the slope.  Then use Excel (instructions) to make a table of your data and generate a graph.  

Part B: Density of metals

Put your data for each metal in a neat table.  Show one complete calculation of the metal density. For Aluminum, you need to calculate the average deviation (shown above) for your results.

Part C: Thickness of aluminum foil

Show your calculation of the thickness.

Part D: The density of a penny

Show your calculation of the density.  Remember, you weighed 10 pennies and found the volume of 10 pennies, therefore you do not need to divide your answer by 10.  The density of a pennies is equal to the mass of 10 pennies divided by the volume of 10 pennies.

Conclusion:  This must be written using complete sentences in well organized paragraphs!

Restate your results and discuss their significance.  Be sure to include the following:

• The values for the density of water from the graph you drew, the Excel graph and the value from the table in the Handbook of Chemistry and Physics.  
• The values did obtained  for the densities of aluminum, copper and zinc. 
• The average deviation of your three measurements of the density of aluminum
•  Compare all of your results with the values given in The Handbook.  Report the percent error for each of your values.
• Thickness of aluminum foil.  Is your answer reasonable? 
• Average value for the density of a post-1982 penny.  Compare this value to the density of copper and zinc.  Is the penny mostly copper or mostly zinc.  Justify your answer.
• For each measurement discuss all of the possible sources of error. 

Remember, late lab reports are heavily penalized. 

1 day late = -10%

More than 1 day, less than 1 week late = -50%

More than 1 week late = -100%

 

Last edited by K.Stone on 06/14/2004