# What is the initial pressure of a gas having an initial temperature of 90.5K, an initial volume of 40.3 L, final pressure of .83 atm, a final temperature of .54 K and a final volume of 2.7L?

Dec 5, 2015

The initial volume is $\text{9.3 atm}$.

#### Explanation:

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

Given
${V}_{1} = \text{40.3 L}$
${T}_{1} = \text{90.5 K}$
${P}_{2} = \text{0.83 atm}$
${V}_{2} = \text{2.7 L}$
${T}_{2} = \text{0.54 K}$

Unknown
${P}_{1}$

Equation
$\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$

Solution
Rearrange the equation to isolate ${P}_{1}$ and solve.

${P}_{1} = \frac{{P}_{2} {V}_{2} {T}_{1}}{{T}_{2} {V}_{1}}$

P_1=((0.83"atm" xx2.7cancel"L"xx90.5cancel"K"))/((0.54cancel"K"xx40.3cancel"L"))="9.3 atm"