# What is the initial pressure of a gas having an initial temperature of 90.5 K, an initial volume of 40.3 L, a final pressure of 0.83 atm, a final temperature of 0.54 K and a final volume of 2.7 L?

## EDIT: This pressure is moderate, but the temperature is quite low. So the gas is probably not very ideal. Nevertheless, the idea is probably to assume ideality anyway. - Truong-Son

Jul 24, 2017

${P}_{1} \approx 9.3 a t m$

#### Explanation:

$P V = n R T$

$\frac{P V}{T} = n R$

$\therefore \frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$, the combined gas law.

$\left({P}_{1} \cdot \text{40.3 L")/("90.5 K")=("0.83 atm"*"2.7 L")/("0.54 K}\right)$

${P}_{1} \approx 9.3 a t m$