# The gas inside of a container exerts 12 Pa of pressure and is at a temperature of 120 ^o C. If the temperature of the gas changes to 540 ^oK with no change in the container's volume, what is the new pressure of the gas?

Mar 7, 2016

The new pressure is $16.5 P a$

#### Explanation:

We use the ideal gas law to calculate the change in pressure. The law is written:

$P V = n R T$ where

$P$ is the pressure of the gas,
$V$ is the volume of the gas,
$n$ is the number of moles of gas particles,
$R$ is the universal gas constant and
$T$ is the temperature in degrees Kelvin of the gas.

In our problem, only the temperature and pressure change - everything else is a constant. So let's gather all of the constant terms on one side of the equation as follows:

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

We can use this to calculate the unknown pressure:

${P}_{1} / {T}_{1} = {P}_{2} / {T}_{2}$

Rearranging to find ${P}_{2}$

${P}_{2} = \frac{{P}_{1} \cdot {T}_{2}}{T} _ 1 = \frac{12 P a \cdot 540 \textcolor{red}{\cancel{\textcolor{b l a c k}{K}}}}{\left(120 + 273\right) \textcolor{red}{\cancel{\textcolor{b l a c k}{K}}}} = 16.5 P a$

Where we have added 273 to the temperature in Celsius to convert to Kelvin.