South Pasadena • Honors Chemistry
Name
1 • Chemistry Foundations
Period
1.3
1. A bicycle frame made of a single metal displaces
0.315 L of water and has a mass of 1.42 kg. What
is the density of the metal in g/cm3? Of which
metal is the frame made?
Chromoly (chrome molybdenum) steel
density = 7.85 g/cm3
Aluminum
density = 2.70 g/cm3
Titanium
density = 4.51 g/cm3
Carbon fiber
density = 1.75 g/cm3
m = 1.42 kg 
1000 g
 1 kg  = 1420 g
1000 mL1 cm3
3
V = 0.315 L 
 1 L  1 mL  = 315 cm
m
1420 g
D=
=
= 4.51 g/cm3
Titanium
V 315 cm3
2. Acetone (active chemical in nail polish remover)
has a density of 0.7857 g/cm3.
PROBLEMS
Date
–
DENSITY
4. A thin sheet of gold is called “gold leaf.” If a 200mg piece of gold is hammered into a rectangular
sheet with dimension 2.4 ft × 1.0 ft, what is the
average thickness of the sheet in meters? The
density of gold is 19.32 g/cm3. (1 inch = 2.54 cm)
1g 
m = 200 mg 
1000 mg = 0.200 g
12 in2 2.54 cm2
V = (2.4 ft)(1.0 ft)(x cm)
 1 ft   1 in 
3
= 2230x cm
m
0.200 g
D=

(19.32 g/cm3) =
V
2230x cm3
x = 4.6 × 10−6 cm
5. A flask weighs 43.50 g when it is empty and 105.50
g when filled with water. When the same flask is
filled to the same volume with another liquid, the
mass is 96.75 g. What is the density of the second
liquid?
(a) What is the mass, in g, of 28.56 mL of acetone?
V = (105.50 g − 43.50 g)
m=V×D
= 28.56 mL 
1 cm3 0.7857 g
 1 mL  1 cm3  = 22.44 g
(b) What is the volume, in mL, of 6.54 g of
acetone?
V=
m
1 cm3   1 mL
= 6.54 g 
D
0.7857 g 1 cm3 = 8.32 mL
3. Small spheres of equal mass are made of lead
(density = 11.3 g/cm3), silver (10.5 g/cm3), and
aluminum (2.70 g/cm3). Which sphere has the
greatest diameter? Smallest diameter?
Aluminum has the lowest density and lead has
the highest density. Density is a measure of the
compactness of a substance, so at a given mass,
an object that is more dense would occupy a
smaller volume (density and volume are
inversely related). Therefore, the largest sphere
(has the greatest diameter) is aluminum, while
the smallest sphere (has the smallest diameter) is
lead.
1 mL
 1 g  = 62.00 mL
m = (96.75 g – 43.50 g) = 53.25 g
m
53.25 g
D=
=
= 0.8589 g/mL
V 62.00 mL
6. Assume that the entire mass of an atom is
concentrated in its nucleus, a sphere of radius
1.5 ×10−5 pm. If the mass of a carbon atom is
2.0 × 10−23 g, what is the density of a carbon
4 3
nucleus? (Volume of a sphere =
r)
3
m = 2.0 ×10−23 g
4
10−10 cm3
V = π 1.5 × 10−5 pm 
3 
 1 pm 
−44
3
= 1.4 × 10 cm
m
2.0 × 10−23 g
D=
=
= 1.4 × 1021 g/cm3
V 1.4 × 10−44 cm3
7. *Gold is alloyed (mixed) with other metals to
increase its hardness in making jewelry. A piece of
jewelry containing only gold (density 19.3 g/cm3)
and silver (10.5 g/cm3) has a mass of 9.85 g and a
volume of 0.675 cm3. (Assume the volumes of the
metals are additive.)
(a) Calculate the percentage of gold (by mass) in
the jewelry.
Vgold + Vsilver = Vtotal
(mgold)
1 cm3 
1 cm3 
+ (9.85 g – mgold)
19.3 g
10.5 g
= 0.675 cm3
10.5x + 190.105 – 19.3x = 136.78875
8.8x = 53.31625
x = 6.1 g
6.1 g
% gold =
× 100% = 62% gold
9.85 g
(b) The purity of gold is expressed in carats: pure
gold is 24-carat, and the percentage of gold in
an alloy is given as a percentage of this value.
For example, an alloy that is 50% gold is 12carat. State the purity of this jewelry in carats.
Purity = (% gold) 
24 carat
 100% 
24 carat
= (62% gold) 
 100%  = 15 carat
8. Carat is also a unit of mass for gemstones and
pearls: 1 carat = 200 mg. What is the volume of a
0.750-carat diamond (density = 3.51 g/cm3)?
0.750 carat 
200 mg  1 g   1 cm3 
 1 carat  1000 mg 3.51 g
= 0.0427 cm3