Page 44 - Theory and Problems of BEGINNING CHEMISTRY

CHAP. 2] MATHEMATICAL METHODS IN CHEMISTRY 33

DENSITY
2.61. What mass in grams is present in 45.0 mL of sulfuric acid solution, which has a density of 1.86 g/mL?
Ans. Start with the 45.0 mL, not with the ratio of grams to milliliters. Multiply that value by the ratio to get the
desired answer:
1.86 g

45.0mL = 83.7g
1.00 mL
2.62. What is the density of gold in kilograms per liter (kg/L) if it is 19.3 g/mL?
19.3g 1kg 1000 mL 19.3kg
Ans. =
mL 1000 g 1L 1L

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2.63. Calculate the density of gold (19.3 kg/L) in kilograms per cubic meter (kg/m ).

19.3kg 1000 L 19 300 kg
Ans. =
1L 1m 3 1m 3
2.64. Calculate the density of a solution of which 15.33 g occupies 8.2 mL.
m (15.33 g)
Ans. d = = = 1.9 g/mL
V (8.2mL)
2.65. The density of air is about 1.25 g/L. The density of water is about 1.00 g/mL. Which is denser?
Ans. Water is denser, 1000 g/L. Be sure that when you compare two densities, you use the same units for both.

2.66. The density of lead is 11.34 g/mL. (a) What volume is occupied by 175 g of lead? (b) What is the mass
of 175 mL of lead?
1mL 11.34 g

Ans. (a) 175 g = 15.4mL (b) 175 mL = 1980 g = 1.98 kg
11.34 g 1mL
2.67. The density of gold is 19.3 g/mL, that of lead is 11.34 g/mL, and that of liquid mercury is 13.6 g/mL.
Will a cube of solid gold float in liquid mercury? Will a cube of lead?
Ans. Lead will float in mercury, because it is less dense than mercury, but gold will not float because it is denser.

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2.68. Convert a density of 2.7 g/mL to (a) kg/L and (b) kg/m .
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3
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2.7g 1kg 10 mL 2.7kg 2.7kg 10 L 2.7 × 10 kg
Ans. (a) = (b) =
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mL 10 g 1L L L 1m 3 m 3
2.69. Calcuate the density of a board 2.00 m long, 2.5 cm thick, and 0.50 dm wide which has a mass of 2.25 kg.
Will the board float in water (density 1.00 g/mL)?
Ans. The volume of the board is length × width × thickness
100 cm 10 cm

2.00 m = 200 cm long 0.50 dm = 5.0 cm wide
1m 1dm
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V = 200 cm × 5.0cm × 2.5cm = 2.5 × 10 cm = 2.5L
The density is the mass divided by the volume:
(2.25 kg)/(2.5L) = 0.90 kg/L
The board will float in water, since it is less dense. The density of water is 1.00 kg/L.