Page 186 - Theory and Problems of BEGINNING CHEMISTRY

CHAP. 12] GASES 175

The term inversely proportional in the statement of Boyle’s law means that as the pressure increases, the
volume becomes smaller by the same factor. That is, if the pressure is doubled, the volume is halved; if the
pressure goes up to 5 times its previous value, the volume goes down to 1 of its previous value. This relationship
5
can be represented mathematically by any of the following:
1 k
P α P = PV = k (at constant temperature)
V V
where P represents the pressure, V represents the volume, and k is a constant.

EXAMPLE 12.2. What is the value of constant k for the sample of gas for which data are given in Table 12-1?
Ans. For each case, multiplying the observed pressure by the volume gives the value 8.0 L·atm. Therefore, the constant k
is 8.0 L·atm.

If for a given sample of a gas at a given temperature, the product PV is a constant, then changing the pressure
from some initial value P 1 to a new value P 2 will cause a corresponding change in the volume from the original
volume V 1 to a new volume V 2 such that

P 1 V 1 = k = P 2 V 2
or P 1 V 1 = P 2 V 2

Using the last equation makes it unnecessary to solve numerically for k.

EXAMPLE 12.3. A 2.00-L sample of gas at 675 torr pressure is changed at constant temperature until its pressure is
925 torr. What is its new volume?
Ans. A useful first step in doing this type of problem is to tabulate clearly all the information given in terms of initial and
final conditions:
P 1 = 675 torr P 2 = 925 torr
V 1 = 2.00 L V 2 = ?
Let the new, unknown volume be represented by V 2 . Since the temperature is constant, Boyle’s law is used:
P 1 V 1 = P 2 V 2 = (675 torr)(2.00 L) = (925 torr)V 2
Solving for V 2 by dividing each side by 925 torr yields
(675 torr)(2.00 L)
V 2 = = 1.46 L
925 torr
The final volume is 1.46 L. The answer is seen to be reasonable by noting that since the pressure increases, the
volume must decrease.

Note that the units of pressure must be the same on both sides of the equation, as must be the units of volume.

EXAMPLE 12.4. To what pressure must a sample of gas be subjected at constant temperature in order to compress it from
122 mL to 105 mL if its original pressure is 1.71 atm?
Ans. V 1 = 122 mL V 2 = 105 mL
P 1 = 1.71 atm P 2 = ?
P 1 V 1 = P 2 V 2 = (1.71 atm)(122 mL) = P 2 (105 mL)
P 2 = 1.99 atm
The pressure necessarily is increased to make the volume smaller.

12.4. GRAPHICAL REPRESENTATION OF DATA
Often in scientific work it is useful to report data in the form of a graph to enable immediate visualization
of general trends and relationships. Another advantage of plotting data in the form of a graph is to be able to
estimate values for points between and beyond the experimental points. For example, in Fig. 12-2 the data of