Density is defined as the mass per unit volume of a substance or, mathematically,

r = m/v

In this lab, we are going to find density by two different techniques: direct computation and graphing.  In addition, we'll look up the correct density values for our substances and calculate the relative error on our results.

Part A: Finding Density by Direct Computation

The easiest approach to finding density is to directly measure both mass and volume and solve by computation.  Masses can be found with a balance, but volume can be a bit tricky.  If the substance is a liquid, volume can be measured directly with a graduated cylinder.  A common approach to finding volume of solids is water displacement, where the solid is dropped into a known quantity of water.  The rise in water level is then equal to the volume of the solid.

Since this is our first lab involving real computation, we need to be aware of the way we handle the precision of our measurements.  All measurements must be recorded to the precision available to the measuring device.  A balance will display mass values explicitly.  All digits read by the balance are significant, so don’t drop trailing zeroes!  A graduated cylinder can be difficult to read, so be careful to record your measurements to a proper degree of precision.  You should be able to read one significant digit beyond the scale’s markings by estimating the distance between the lines.  Remember that there is an assumed ±1 on the final recorded digit.

Once you calculate your density values, you will need to be concerned with your accuracy.  Relative error is a measure of how far your answer is from the accepted theoretical value.  For each substance measured, you can look up the accepted value for its density.  Then, using

	| theoretical – experimental |
RE = ---------------------------------------
		theoretical

you can determine the relative error on your measurement.

Methodology

1.	Measure the mass of a clean, empty 10 mL graduated cylinder.  Then add 10 cm3 of distilled water and mass again.  Record the exact mass and volume of the water.

2.	Repeat step 1 with methanol, ethanol, acetone, and isopropanol.

3.	Obtain a sample of aluminum and record its mass.  The sample should be at least 1 g.

4.	Half-fill a 50 mL or 100 mL graduated cylinder with water.  Then, carefully drop the metal sample into the water and record the change in volume.

5.	Repeat steps 3-4 with zinc, lead and copper samples.

6.	Place wet metal samples on a paper towel to dry.  Flush all liquid samples down the drain with plenty of running water.

Analysis

For each sample, find the density by dividing mass by volume.  Make sure that you keep the correct number of significant digits on your answers.  Remember that, if the values differ in the number of significant digits, the one with the least number of digits is the limiting factor.

Once you have found the densities, you will need to look up the theoretical values.  The CRC Handbook is a good resource and is available in my classroom and most libraries.  You should also be able to find density data on the internet, but be careful to choose trustworthy sources!  Once you have your experimental value and the theoretical value, calculate your relative error.  You should then convert the relative error to a percentage by multiplying by 100.  Be sure to state each result with its percent error in your discussion section.

Part B: Finding Density by Graphing

While direct computation of density is quick and easy, it is prone to error, especially when the masses and volumes are rather small.  A better approach is to make mass and volume measurements for several groups of small objects and then graph the results to get the average density.

If we rearrange the density equation, we see that

m = rV

which is the equation of a straight line with slope equal to r and an intercept of zero.  Thus, we can graph mass and volume data and find the density by measuring the slope of the line.  The graph tends to average out laboratory errors and give a better result than direct computation.

Methodology

1.	Obtain a sample of a metal.  Be sure to record which metal you selected.

2.	Find the mass and volume of a small sample of your metal.  Then measure the mass and volume of a sample roughly twice the size of your original sample.  Continue measuring samples of increasing size until you have at least five data points.

3.	Repeat step 2 with two other metals.

4.	Graph the results for each of your metals with mass on the y-axis and volume on the x-axis.  Find the slope of each graph.

5.	Place the wet metals on a paper towel to dry.

Analysis

Construct a graph with mass on the y-axis and volume on the x-axis.  The graphs should be straight lines, so draw regression lines and find the slopes and intercepts.  The slopes should be equal to the densities of your metals.  Look up the true density values and find your relative error.  Also, the intercepts should be zero (why?) so you can use that as a way of determining how good your results are.

Questions

1.	In part A, did you have more error on the liquids or the solids?  Propose an explanation for this.

2.	Does the size of the sample affect your results?  Explain.

3.	Which gave you more accurate results for the metals, direct computation or graphing?  Why?

4.	In part B, two students perform the experiment.  Student 1 adds a 1 g sample of zinc to the graduated cylinder, then empties the cylinder and refills it, adding a 2 g sample, then empties again and adds a 3 g sample, and so on.  Student 2 adds a 1 g sample of zinc to her cylinder, then adds another 1 g sample to the original, making a total of 2 g, then adds a third gram, and so on.  Will the students get different results?  Why or why not?

5.	Sodium metal reacts violently with water.  Propose a method by which you could find its density.