He Ain't Heavy, He's My Metal

Density is defined as the amount of mass that occupies a given volume.  The most common units for density are g/ml.  See equation 1:

In equation 1,  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 (in grams)  and volume (in mL.)

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 Several Liquids:  Weigh a clean, dry 50mL plastic measuring cup. This and subsequent weighings should be to 0.01 g. (What balance should you use?)   Fill the cup as closely as you can to 30.0 ml with deionized water, and weigh the cup plus water.  Repeat the procedure. (Why should you repeat your measurements?)

Determine the density of ethanol by weighing 20mL, to determine the density of  glycerol weigh 10 mL  and weigh 25 mL of vegetable oil to determine its density.  Repeat every measurement.

Calculate the densities, the following table may be useful as a model.  

Make a density column of liquids by carefully pouring the liquids into a 100 ml graduated cylinder.  Which liquid should be put at the bottom so that the liquids do not mix?  Use your density information to determine the order of liquids in your cylinder. Add a drop of food coloring to the water, ethanol and glycerol, use different colors for a more dramatic effect.  Be sure to show your instructor your density column to verify its existence.  

Now add another 20 mL of the least dense material to the column.  What happens?  This liquid now has more mass, does it sink?  Explain your results in your conclusion.

Wash the oil out of the cylinder using lab detergent and water.

B. The densities of several metals: Obtain samples of aluminum, copper and zinc 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. (It will break and they are not cheap.)  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!

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. 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 liquids

Put your data into a neat table. 

Part B: Density of metals

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

Part C: Thickness of aluminum foil

Clearly show your calculation of the thickness of the aluminum foil.

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:

• Restate the values for the density of the liquids and the order that you placed them in your density column. Why did you repeat your measurements?
• Explain the results you observed when you added 20mL of the least dense material to the top of your density column.  You added more mass, did it sink?  Why or why not.
• Restate your values for the densities of aluminum, copper and zinc. 
• Compare all of your metal densities with the values given in The Handbook.  Report the percent error for each of your values.
• The average deviation of your three measurements of the density of aluminum
• Thickness of aluminum foil.  Is your answer reasonable? Why?
• 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.
• Are your answers precise?  Are they accurate?  What is the difference between accuracy and precision?
• 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%

Even if the lab is more than one week late and you get no points for it, you still must complete it in order to pass this class.  All labs must be completed in order to pass CHEM 2090.

Last edited by K.Stone on 02/23/2005