Answer sheet
Mass, Volume, and Density
1. Study the matter shown in Figure 1. Each dot
represents a particle of matter. [Assume the
particles are uniformly distributed throughout
each object, and particles of the same size have the
same mass.]
FIGURE
Figure
1 1
A
B
B
A
a) In the table below, show how the masses,
volumes, and densities of A and B compare by
adding the symbol <, >, or = to the statement
in the second column.
b) Explain your reasoning for each answer in
the last column.
Property
Relationship
Mass
A < B
Reasoning
Since particles with same size have same mass, B has
more so should have greater mass than A.
A < B
Width and depth of A is same as B but the height of B
is much greater so volume of B is greater than A
Volume
Density
A = B
Density is how much stuff in how much space. A and
B have the same number of particles in the same
space so they have the same density.
2. Study the matter in Figure 2. In the
table below show how the masses,
volumes, and densities compare by
adding the symbol <, >, or = to the
statement in the second column.
Explain your reasoning for each
answer in the last column. Assume the
particles are uniformly distributed
throughout each object, and particles of
the same size have the same mass.
Property
Mass
Relationship
A < B
A < C
Volume
A < B
A = C?
Density
A = B
A < C
FIGURE 2
A
B
C
Reasoning
A has the least number of particle (same
mass for each particle), so should have
less mass than B or C
C and A look like they have the same
volume. B volume is clearly larger
Looks like A and B have the same number of
particles in the same space so they have
same density. C clearly has more in
same space.
3. Is object E or object F more dense? [Assume the
particles are uniformly distributed throughout
each object, and particles with a larger size have
a larger mass.] Explain your reasoning.
FIGURE 3
E
F
Both E and F have the same number of
particles. Since particles with larger size
have greater mass, then E must have greater
mass. Volumes appear equal so E has
greater density.
Substance
4. Refer to the table of densities at the right to
answer the following questions.
Aluminum
Titanium
Zinc
Tin
Iron
Nickel
Copper
Silver
Lead
Mercury
Gold
HHg
HCu
HTi
Density
(g/mL)
2.70
4.54
7.13
7.31
7.87
8.90
8.96
10.50
11.35
13.55
19.30
a) Sketch a graph of mass vs volume for
titanium, copper and mercury.
Ti 45.5 g/10 cm3, Cu 89.6 g/10 cm3, Hg
135.5 g/ 10 cm3 = 67.8 g/ 5 cm3
b) You made some cubes out of each metal in the table that each measures 2.00 cm on every
side. (all except mercury – why can’t you make a cube of mercury?) What is the volume of
each cube in cm3? in mL?
(Show your thinking)
V = (2.00 cm)(2.00 cm)(2.00 cm) = 8.00 cm3
V = 8.00 mL since 1 cm3 = 1 mL
Note : because 1 cm3 = 1 mL is a definition, it has infinite sig figs.
c) Find the mass of these metal cubes:
(Show your work below)
lead cube
8.00 cm3 • 11.35 g/cm3 = 90.8 g
nickel cube
8.00 cm3 • 8.90 g/cm3 = 71.2 g
zinc cube
8.00 cm3 • 7.13 g/cm3 = 57.0 g
5. In Figure 4 below, a graph shows the relationship between mass and volume for two
substances, A and B. Use the graph to answer questions about these two substances.
Two Pan Balance
A
B
a) You have built a simple two-pan balance
shown above to compare the masses of
substances A and B. a) What would happen to
the balance if you put equal masses of A and B
in the two pans? b) Equal volumes of A and B
in the two pans? Explain your reasoning.
a) Equal masses - Pans would be balanced
since have same mass on both sides.
b) Equal volumes - A pan would be tilted
down because it has greater mass in same
volume. For example at 10 mL, B would have
mass of 5 g, while A would be 17 g.
c) Find the slope of the line for both A and B using correct units. State the physical meaning of the slope for
each substance.
Using 50 mL, B slope would be 20. g/ 55 mL = 0.36 g/mL; A slope would be 57 g/ 50. mL = 1.14
g/mL. The slope of a line with volume as x variable and mass as y is the density.
d) If you put 10.0 mL of A in one balance pan, what volume of B would you need in the other
pan to make it balance? Explain your reasoning.
Ratio method) From a) the ratio of densities of A to B is 1.14/0.36 = 3.2, so A is about 3.2
times as dense as B. If 10 mL of A = 10 g then 32 mL of B has same mass (10 g)
Graphing method) I used the graph to find mass of 10 mL of A and then move horizontally
to find volume of B which has same mass. That is roughly 32 mL.
e) If you put 35.0 mL of B in one balance pan, what volume of A would you need in the other
pan to make it balance? Explain your reasoning.
Graphing method) 35 mL of B has a mass of about 12 g. This would be about 13 mL of A.
Ratio method) A is 3.2 more dense than B so volume of A would be 35.0/3.2 = 11 mL of A
f) Water has a density of 1.00 g/mL. Sketch the line representing water on the graph in Figure
4.
g) Determine whether substance A and B will sink
or float when placed in a bucket of water.
A: sink
WWater
float B: sink
float
h) Defend your answer using the m-V graph, and
your current understanding of density.
Density is the slope of a plot of mass (y-axis) vs.
volume. The steeper the slope the higher the
density. Anything less dense than water floats on
water (actually water pushes it up). So B would
float and A would sink.
7. Alicia’s cheapskate boyfriend gave her a ring he claims is 24 carat (pure) gold. Alicia is
skeptical. After chem class the next day she measures the mass of the ring, finds the
volume of the ring by water displacement, and then calculates the density of the ring.
Should she treasure the ring as his first truly generous gift to her, or throw it at him the
next time he walks by? Defend your answer.
DATA:
Mass:
15.28 g
Final volume:
43.7 mL
Initial volume:
42.2 mL
Volume of ring:
43.7 – 42.2 = 1.5 mL Density = 15.28/1.5 mL = 10. g/mL
Clearly Alicia should find a new boyfriend. This ring can’t be gold as the calculated density
(10. g/mL) is way too low for gold (19.30 g/mL).
8. A student filled a graduated cylinder with water and read the meniscus at 25.8 mL. The student
then dropped a solid material into the graduated cylinder and the water level rose to 35.9 mL. If
the solid material had a density of 2.99 g/mL, determine the mass of the solid object.
35.9 mL – 25.8 mL = 10.1 mL (volume of solid object).
If D = m/V, then D•V = mass = 10.1 mL • 2.99 g/mL = 30.2 g
9. As you saw in the Ring of Truth video, gold has the unique property that it can be pounded VERY
thin. In fact, gold leaf is so thin that 1000 page book made from gold leaf would be as thick as
one page in a normal book. You can buy different kinds of gold leaf at The Gold Leaf Company
(http://www.goldleafcompany.com ). According to the info at their website, the mass of 1000
sheets of 7.94 cm x 7.94 cm of Deep Double gold leaf is 18 g while the mass of 1000 sheets of
Deep gold leaf is 16 g. Using this information and the same calculations as you did with the
aluminum foil, calculate the maximum size of a gold atom.