# 500.0 liters of a gas are prepared at 700.0 mmHg and 200.0 C. The gas is placed into a tank under high pressure. When the tank cools to 20.0 C, the pressure of the gas is 30.0 atm. What is the volume of the gas?

Jul 29, 2017

The key to answering this question is to know that $1 \cdot a t m$ pressure will support a column of mercury that is $760 \cdot m m$ high...I gets a final volume of approx. $10 \cdot L$.

#### Explanation:

And thus $760 \cdot m m \cdot H g \equiv 1 \cdot a t m$

The combined gas equation tells us that $\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$ given a constant molar quantity of gas.

So we solve for ${V}_{2}$, where ${V}_{2}$ is conceived to be the volume of the tank.....

${V}_{2} = \frac{{P}_{1} {V}_{1}}{T} _ 1 \times {T}_{2} / {P}_{2}$, and we immediately see (do we?) that we gots units of volume.........

${V}_{2} = \frac{\frac{700 \cdot m m \cdot H g}{760 \cdot m m \cdot H g \cdot a t m} \times 500 \cdot L}{473.15 \cdot K} \times \frac{293.15 \cdot K}{30 \cdot a t m} \cong 10 \cdot L$