Problem
A hydrogen gas thermometer is found to have a volume of 100.0 cm3 when placed in an ice-water bath at 0°C. When the same thermometer is immersed in boiling liquid chlorine, the volume of hydrogen at the same pressure is found to be 87.2 cm3. What is the temperature of the boiling point of chlorine?
Solution
For hydrogen, PV = nRT, where P is pressure, V is volume, n is number of moles, R is the gas constant, and T is temperature.
Initially:
P1 = P, V1 = 100 cm3, n1 = n, T1 = 0 + 273 = 273 K
PV1 = nRT1
Finally:
P2 = P, V2 = 87.2 cm3, n2 = n, T2 = ?
PV2 = nRT2
Note that P, n, and R are the same. Therefore, the equations may be rewritten:
P/nR = T1/V1 = T2/V2
and T2 = V2T1/V1
Plugging in the values we know:
T2 = 87.2 cm3 x 273 K / 100.0 cm3
T2 = 238 K
Answer
238 K (which could also be written as -35°C)
