Question

A sample of helium occupies a volume of 3.8 L at -45°C. What volume will it occupy at 45°C?

Answer 1

5.3 L.

Explanation

By Charles's Law,

• the volume of an ideal gas is proportional to its absolute temperature when its pressure is held constant.

In other words,

$\dfrac{V_2}{V_1} = \dfrac{T_2}{T_1}$,

where

• $V$ is the volume of the gas, and
• $T$ is the absolute temperature of the gas in degrees Kelvins.

As a noble gas, helium is quite "ideal" with rather weak attractions between its particles unless in direct contact.

Convert the temperatures:

• $T_1 = -45 \textdegree\text{C} = (-45 + {\bf 273.15} ) \; {\textbf{K}} = 228.15 \; \text{K}$;
• $T_2 = 45 \textdegree\text{C} = (45 + {\bf 273.15} ) \; {\textbf{K}} = 318.15 \; \text{K}$.

Apply Charles's Law,

$V_2 = V_1 \cdot \dfrac{T_2}{T_1} = 3.8 \times \dfrac{228.15}{318.15} = 5.3 \; \text{L}$.