# The Volume of an enclosed gas (at a constant temperature) varies inversely as the pressure. If the pressure of a 3.46-L sample of neon gas at 302°K is 0.926 atm, what would the volume be at a pressure of 1.452 atm if the temperature does not change?

Jan 7, 2018

${V}_{2} \approx 2.21 L$

#### Explanation:

Assuming this behaves as an ideal gas, we know that:
$P \propto \frac{1}{V}$
$P = \frac{k}{V} \left(k = \text{constant}\right)$

By rearranging:
$P V = k = c o n s \tan t$

We can use this to get:
${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$

Or, $\frac{{P}_{1} {V}_{1}}{{P}_{2}} = {V}_{2}$

${V}_{2} = \frac{0.926 \cdot 3.46}{1.452} \approx 2.21 L$