Page 197 - Theory and Problems of BEGINNING CHEMISTRY

186 GASES [CHAP. 12

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12.10. A 1.00-L sample of gas at 25 C and 1.00-atm pressure is changed to 3.00-atm pressure at 25 C. What
law may be used to determine its final volume?
Ans. Boyle’s law may be used because the temperature is unchanged. Alternately, the combined gas law may be
used, with 298 K, the Kelvin equivalent of 25 C, used for both T 1 and T 2 .
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12.11. A sample of gas occupies 2.48 L. What will be its new volume if its pressure is doubled at constant
temperature?
Ans. According to Boyle’s law, doubling the pressure will cut the volume in half; the new volume will be 1.24 L.
A second method allows us to use unknown variables for the pressure:
1 2

P P 1 P 2 = 2P 1
V 2.48 L V 2
2.48 L
P 1 V 1 P 1 V 1 V 1
V 2 = = = = = 1.24 L
P 2 2P 1 2 2
GRAPHICAL REPRESENTATION OF DATA
12.12. On a graph, what criteria represent direct proportionality?
Ans. The plot is a straight line and it passes through the origin.

12.13. What is the pressure of the gas described in Table 12-1 at 10.0 L? Answer first by calculating with
Boyle’s law, second by reading from Fig. 12-2, and third by reading from Fig. 12-3. Which determination
is easiest (assuming that the graphs have already been drawn)?
Ans. The pressure of the gas is 0.80 atm. The second method involves merely reading a point from a graph. To
use Fig. 12-3, you have to calculate the reciprocal of the pressure. None of the methods is difficult, however.

12.14. Plot the following data:
V (L) P (atm)

1.50 4.00
3.00 2.00
6.00 1.00
12.00 0.500
Replot the data, using the volume and the reciprocal of the pressure. Do these values fall on a straight
line? Are volume and the reciprocal of pressure directly proportional? Are volume and pressure directly
proportional?
Ans. The points of the second plot fall on a straight line through the origin, and so the volume and reciprocal of
pressure are directly proportional to each other, making the volume inversely proportional to the pressure.

CHARLES’ LAW
12.15. Plot the following data:
V (L) t ( C)
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4.92 100
4.26 50
3.60 0
2.94 −50
Dothevaluesfallonastraightline?ArevolumeandCelsiustemperaturedirectlyproportional?Replot
the volume versus the Kelvin temperature. Are volume and Kelvin temperature directly proportional?
Ans. The points of the first plot fall on a straight line, but that line does not go through the origin (the point at
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0 L and 0 C), and so these quantities are not directly proportional. When volume is replotted versus Kelvin