# When a supply of hydrogen gas is held in a 4 liter container at 320 K it exerts a pressure of 800 torr. The supply is moved to a 2 liter container, and cooled to 160 K. What is the new pressure of the confined gas?

Dec 19, 2014

The answer is ${P}_{2} = 800$ $t o r r$.

The best way to approach this problem is by using the ideal gas law, $P V = n R T$. Since the hydrogen is moved from a container to another, we presume that the number of moles remains constant. This will give us 2 equations

${P}_{1} {V}_{1} = n R {T}_{1}$ and ${P}_{2} {V}_{2} = n R {T}_{2}$. Since $R$ is a constant as well, we can write

$n R = \frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2 \to$ the combined gas law.

Therefore, we have

${P}_{2} = {V}_{1} / {V}_{2} \cdot {T}_{2} / {T}_{1} \cdot {P}_{1} = \frac{4 L}{2 L} \cdot \frac{160 K}{320 K} \cdot 800 t o r r = 800 t o r r$.