4 Mass, Volume, and Density
................................................................................................................
Background
An old riddle asks "Which is heavier, a
pound of feathers or a pound of lead?" The question is nonsensical, of
course, since a pound of feathers and a pound of lead both weigh the same, one
pound. Nevertheless, there is clearly something different about a small lead
brick and a large bag of feathers, even though they weigh the same. The key to
answering the riddle is understanding the relationship that exist between a
substance's mass and the volume it occupies. This relationship is expressed by
the physical property called density. Density is defined as the ratio of
a substance's mass to the volume it occupies.
Density = mass of substance (g) /
volume of substance (mL)
In this experiment, you will measure the mass and volume of several unknown materials. You will then use your data to explore the relationship between the mass and volume of the materials and to calculate their density.
Densities of Common Metals
|
Metal |
Densuty (g/ml) |
|
Cu |
8.96 |
|
Pb |
11.40 |
|
Fe |
7.86 |
|
Zn |
7.14 |
|
Sn |
7.30 |
|
Al |
2.70 |
Goals
- Measure the mass and volume of several samples of matter, using the centigram balance and the method of water displacement.
- Infer whether there is a constant relationship between mass and volume for each unknown substance.
- Compute the density of a solid object from its mass and volume.
Equipment
|
safety goggles |
|
1 25-mL graduated cylinder |
|
8 centigram balances / class |
|
1 ruler |
Safety
- Note the Safety Symbol used here. Review safety information on pages 7-10
- Always wear safety goggles when working in the lab.
Procedure
Copy tables 4,1, 4.2, and 4.3 into your laboratory notebook. As you perform the experiment, record your data in Tables 4.1 and 4.2.
1. Determine the mass of two different
unknown metal samples to the nearest 0.01 gram, using a centigram balance.
Record masses in Tables 4.1 and 4.2.
2. Find the volume of each metal sample by water
displacement. Fill a 25-mL graduated cylinder about half-full with water,
measure the volume, and record as "volume of water alone" in Table
4.1. Tilt the graduated cylinder and carefully slide one of the metal samples
down the side. Make sure the metal sample is completely submerged in the water.
Measure the volume and record the measurements as "volume of water +
metal" in Table 4.1.
3. Repeat step 2, using the other metal sample.
Dry both samples and return them to your teacher.
Data Record
Table 1 Group Data - Density
|
|
Metal A |
Metal B |
Additional Metal Samples (Optional) |
|
Mass (g) |
|
|
|
|
Volume of water
alone (ml) |
|
|
|
|
Volume of
water + Metal (ml) |
|
|
|
|
Volume of
metal (ml) |
|
|
|
|
Density of
metal (g/ml) |
|
|
|
|
Idnetity of
metal |
|
|
|
|
Actual density
of metal |
|
|
|
|
Percent (%)
deviation |
|
|
|
Calculations:
Table 2 Class Data: Mass and Volume of Metal Samples
|
Lab Pair |
mass A (g) |
Volume A (ml) |
Mass B (g) |
Volume B (ml) |
Mass - added metal(g) (Optional) |
Volume - added metal (ml) (Optional) |
|
1 |
|
|
|
|
|
|
|
2 |
|
|
|
|
|
|
|
3 |
|
|
|
|
|
|
|
4 |
|
|
|
|
|
|
|
5 |
|
|
|
|
|
|
|
6 |
|
|
|
|
|
|
|
7 |
|
|
|
|
|
|
|
8 |
|
|
|
|
|
|
|
9 |
|
|
|
|
|
|
|
10 |
|
|
|
|
|
|
|
11 |
|
|
|
|
|
|
Data Analysis
Note, one page of graph paper is required for your laboratory report.
1. Compute the volume of each metal sample,
using data from Table 4.1. Compute the
density of each metal sample, showing your work
(including units), in Table 4.1. Remember, density = mass (g) / volume (mL).
2. Compute Table 4.2 by recording the mass and
volume data collected by you and your classmates.
3. Using the class data, plot a graph of mass
versus volume. Represent the plotted points for each metal with a different
symbol. Draw a "best fit" straight line through each group of plotted
points.
4. Determine the slope of each of the lines on
your graph. Record the slope of each line and your method of calculation in
Table 4.3. HINT: The general equation for a line is y=mx+b where m is
the value for the slope and b is the value for the y-intercept. Pay
attention to the units of the slope.
Table 4.3 Density Calculations Class Data (slopes)
|
Metal A |
Metal B |
Additional Metal |
|
y/x = |
y/x = |
|
Conclusions
1. What does the slope of the line for each
metal represent? HINT: Look back at Table 4.1.
2. Looking at your graph, what does this
experiment demonstrate about the density of a substance? What does it demonstrate
about the densities of different substances?
3. Calculate the percent error in the density
calculations for the two samples. (See Data Analysis, step 1.) Your teacher
will provide the accepted value for the density of each metal.
percent error = |accepted value - experiment
value|/ accepted value x 100 percent
4. Calculate the percent error in the values of
density obtained from the slopes of the line in your graph.
5. Look back at the percent errors calculated in
steps 3 and 4. Generally, the slope of the line will give a more accurate value
for density than a single sample. Explain why this is usually true.
6. Can you identify a substance if you know its
density? Explain your answer. Try to identify the metals used in this
experiment by referring to tables of density.
Extensions
1. Do you think that determining the volumes
for your metal samples by measuring their dimensions and calculating would be
more or less accurate than determining these volumes by water displacement?
Explain. Would measuring the dimensions of a solid always be possible? Explain.
2. How would you modify this experiment to
determine the density of table sugar, wood chips, and milk?
