# 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?

##### 1 Answer
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.........

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