# Ten grams of a gas occupies 12.5 liters at a pressure of 42.0 cm Hg. What is the volume when the pressure has increased to 75.0 cm Hg?

Oct 13, 2016

At constant temperature, and constant amount of gas, ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$.

#### Explanation:

So all we have to do is convert the $c m \cdot H g$ into a pressure reading, and calculate ${V}_{2}$.

$1 \cdot a t m \equiv 760 \cdot m m \cdot H g$; of course, given the relationship the units of pressure cancel out.

${V}_{2} = \frac{{P}_{1} {V}_{1}}{P} _ 2$ $=$ $\frac{12.5 \cdot L \times 420 \cdot m m \cdot H g}{750 \cdot m m \cdot H g}$ $\cong$ $7 \cdot L$.

Note that here we use a unit of length to measure the pressure. That is $1 \cdot a t m$ will support a column of mercury that is $760 \cdot m m$ high. Ordinarily, you would be expected to calculate the pressure with authentic units of $k P a$ or $\text{atmospheres}$. Here, we can afford to be a little slack.