South Pasadena • Honors Chemistry Name
1 • Chemistry Foundations Period Date
1.3 PROBLEMS – DENSITY
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 = 1420 g
V = 0.315 L = 315 cm3
D = = = 4.51 g/cm3 Titanium
2. Acetone (active chemical in nail polish remover) has a density of 0.7857 g/cm3.
(a) What is the mass, in g, of 28.56 mL of acetone?
m = V × D
= 28.56 mL = 22.44 g
(b) What is the volume, in mL, of 6.54 g of acetone?
V = = 6.54 g = 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.
4. A thin sheet of gold is called “gold leaf.” If a 200-mg 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)
m = 200 mg = 0.200 g
V = (2.4 ft)(1.0 ft)(x cm)
= 2230x cm3
D = à (19.32 g/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?
V = (105.50 g − 43.50 g) = 62.00 mL
m = (96.75 g – 43.50 g) = 53.25 g
D = = = 0.8589 g/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 nucleus? (Volume of a sphere = r3)
m = 2.0 ×10−23 g
V = π
= 1.4 × 10−44 cm3
D = = = 1.4 × 1021 g/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) + (9.85 g – mgold)
= 0.675 cm3
10.5x + 190.105 – 19.3x = 136.78875
8.8x = 53.31625
x = 6.1 g
% gold = × 100% = 62% gold
(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 12-carat. State the purity of this jewelry in carats.
Purity = (% gold)
= (62% gold) = 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
= 0.0427 cm3