Ideal Gas Law - Worked Chemistry Problems

By Anne Marie Helmenstine, Ph.D., About.com

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)

From: about.com