Page 47 - Theory and Problems of BEGINNING CHEMISTRY

36 MATHEMATICAL METHODS IN CHEMISTRY [CHAP. 2

2.83. Express, in standard exponential notation, the number of:

(a) liters in 1.0 m 3 (d) cubic meters in 1.0 mL (g) cubic meters in 1.0 L
(b) liters in 1.0 mL (e) cubic centimeters in 1.0 L (h) cubic meters in 1.0 cm 3
(c) kiloliters in 1.0 m 3 (f) milliliters in 1.0 m 3 (i) cubic meters in 1.0 mm 3
3
Ans. (a)1.0 × 10 L (d)1.0 × 10 −6 m 3 (g)1.0 × 10 −3 m 3
3
(b)1.0 × 10 −3 L (e) 1.0 × 10 cm 3 (h)1.0 × 10 −6 m 3
6
(c) 1.0 kL (f) 1.0 × 10 mL (i) 1.0 × 10 −9 m 3

3
2.84. The density of an alloy (a mixture) containing 60.0% gold plus other metals is 14.2 g/cm . If gold costs $600.00 per
3
Troy ounce, what is the value of the gold in a 14.6-cm piece of jewelry? (1 Troy ounce = 31.103 g)

Ans. 14.6cm 3 14.2 g alloy 60.0 g gold 1 oz gold 600.00 dollars = 2400 dollars
1cm 3 100.0 g alloy 31.1 g gold 1 oz gold
2.85. A solution with a density of 1.15 g/mL contains 33.0 g of sugar per 100 mL of solution. What mass of solution will
contain 166 g of sugar? What mass of water is required to make this solution?

100 mL solution 1.15 g solution
Ans. 166 g sugar = 578 g solution
33.0 g sugar 1 mL solution
578 g solution − 166 g sugar = 412 g water
3
2
2.86. A gold alloy chain has a density of 14.6 g/cm . The cross-sectional area of the chain is 5.00 mm . What length of
chain has a mass of 9.70 g?
3
1cm 3 10 mm
Ans. V = 9.70 g = 664 mm 3
14.6g 1cm
V 664 mm 3
Length = = = 133 mm = 13.3cm
A 5.00 mm 2
2.87. How much does the chain of the prior problem cost if the gold alloy costs $500/Troy ounce? (1 Troy ounce = 31.1 g)

Ans. 9.70 g 1oz $500.00 = $156
31.1g 1oz

2.88. Calculate the density of sulfuric acid, 1.86 g/mL, in kilograms per liter.
1.86 g 1kg 1000 mL 1.86 kg
Ans. =
mL 1000 g 1L L
2.89. An ashtray is made of 55.0 g of glass and 45.0 g of iron. The density of the glass is 2.50 g/mL, and that of the iron
is 7.86 g/mL. What is the density of the ashtray?
Ans. The density of the ashtray is its mass divided by its volume. Its mass is 100.0 g. Its volume is the total of the
volumes of the glass and iron:

1mL

55.0 g glass = 22.0 mL glass
2.50 g
1mL

45.0 g iron = 5.73 mL iron
7.86 g
The total volume is 27.7 mL, and the density is
m (100.0g)
d = = = 3.61 g/mL
V (27.7mL)