Page 34 - Theory and Problems of BEGINNING CHEMISTRY

CHAP. 2] MATHEMATICAL METHODS IN CHEMISTRY 23

Use of the equation requires manipulation of the basic equation followed by substitution. Dividing by a ratio of units
also may cause confusion. The factor-label method gives the same result by merely relying on the units. It also allows
combination of the solution with other conversions.

EXAMPLE 2.34. What mass of sulfuric acid is there in 44.4 mL of solution of density 1.85 g/mL which contains 96.0%
sulfuric acid by mass?
Ans. Note that the solution has the density 1.85 g/mL and that every 100.0 g of it contains 96.0 g of sulfuric acid.

1.85 g solution 96.0 g acid
44.4 mL solution = 78.9 g acid
1 mL solution 100.0 g solution

2.7. TEMPERATURE SCALES
Scientists worldwide (and everyone else outside the United States) use the Celsius temperature scale, in
which the freezing point of pure water is defined as 0 C and the normal boiling point of pure water is defined as
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100 C. The normal boiling point is the boiling point at 1.00-atm pressure (Chap. 12). The Fahrenheit temperature
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scale is used principally in the United States. It has the freezing point defined as 32.0 F and the normal boiling
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point defined as 212 F. A comparison of the Celsius and Fahrenheit temperature scales is presented in Fig. 2-2.
The temperature differences between the freezing point and normal boiling point on the two scales are 180 F
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and 100 C, respectively. To convert Fahrenheit temperatures to Celsius temperatures, subtract 32.0 F and then
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multiply the result by 100 or .
180 9
212°— –—Normal boiling point of water–— 100° ————— 373 K
180°F 100°C 100 K
32°— ———Freezing point of water——— 0° ————— 273 K

°F °C K
Fig. 2-2. Comparison of Celsius, Fahrenheit, and Kelvin temperature scales

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EXAMPLE 2.35. Change 98.6 F to degrees Celsius.
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Ans. ◦ C = (98.6 F − 32.0 F) = 37.0 C
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To convert from Celsius to Fahrenheit, multiply by , then add 32.0 F.
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EXAMPLE 2.36. Convert 20.0 C to degrees Fahrenheit.
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Ans. (20.0 C) + 32.0 F = 68.0 F
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Kelvin Temperature Scale
The Kelvin temperature scale is defined to have the freezing point of pure water as 273.15 K and the normal
boiling point of pure water as 373.15 K. The unit of the Kelvin temperature scale is the kelvin. (We do not
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use “degrees” with kelvins.) Thus, its temperatures are essentially 273 higher than the same temperatures on
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the Celsius scale. To convert from degrees Celsius to kelvins, merely add 273 to the Celsius temperature.
To convert in the opposite direction, subtract 273 from the Kelvin temperature to get the Celsius equivalent.
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(See Fig. 2-2.)
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EXAMPLE 2.37. Convert 100 C and −27 C to kelvins.
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Ans. 100 C + 273 = 373 K
−27 C + 273 = 246 K
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