Page 190 - Theory and Problems of BEGINNING CHEMISTRY

CHAP. 12] GASES 179

The fact that the volume of a gas varies linearly with temperature is combined with the concept of absolute
temperature to give a statement of Charles’ law:
At constant pressure, the volume of a given sample of gas is directly proportional to its absolute
temperature.

Expressed mathematically,
V = kT (at constant pressure)

This equation can be rearranged to give
V
= k
T
Since V/T is a constant, this ratio for a given sample of gas at one volume and temperature is equal to the
same ratio at any other volumes and temperatures. See Table 12-3. That is, for a given sample at constant
pressure,
V 1 V 2
= (at constant pressure)
T 1 T 2
One can see from the data of Table 12-3 that absolute temperatures must be used.

Table 12-3 Volumes and Temperatures of a Given Sample of Gas

Volume V Temperature T Temperature t V/T V/t
(L) (K) ( C) (L/K) (L/ C)
◦
◦
1.0 125 −148 8.0 × 10 −3 −6.8 × 10 −3
2.0 250 −23 8.0 × 10 −3 −8.7 × 10 −2
3.0 375 102 8.0 × 10 −3 +2.9 × 10 −2
4.0 500 227 8.0 × 10 −3 +1.8 × 10 −2

EXAMPLE 12.7. A 22.5-mL sample of gas is warmed at constant pressure from 291 K to 309 K. What is its final volume?
Ans.
1 2

V 22.5mL V 2
T 291 K 309 K
22.5mL
V 1 V 2 V 2
= = =
T 1 T 2 291 K 309 K
V 2 = 23.9mL

EXAMPLE 12.8. A 22.5-mL sample of gas is warmed at constant pressure from 18 Cto36 C. What is its final volume?
◦
◦
Ans. This example is a restatement of Example 12.7. The conditions are precisely the same; the only difference is that the
temperatures are expressed in degrees Celsius and first must be converted to kelvins.
◦
◦
18 C = 18 C + 273 = 291 K
◦
◦
36 C = 36 C + 273 = 309 K
◦
◦
The example is solved as shown above. Note again that V is directly proportional to T , but not to t. In this example,
t doubles but T does not double, and so V does not double.