# What is the temperature of 2.0 moles of a gas occupying a volume of 5.0 L at 2.46 atm?

Dec 16, 2015

$T = \text{75 K}$

#### Explanation:

This is a fairly straightforward application of the ideal gas law equation, which looks like this

$\textcolor{b l u e}{P V = n R T} \text{ }$, where

$P$ - the pressure of the gas
$V$ - the volume it occupies
$n$ - the number of moles of gas present in the sample
$R$ - the universal gas constant, usually given as $0.0821 \left(\text{atm" * "L")/("mol" * "K}\right)$
$T$ - the temperature of the gas, always expressed in Kelvin

Rearrange this equation to solve for $T$, the temperature of the gas

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

Before plugging in your values, check to make sure that the units given to you match the units used in the expression of the universal gas constant.

As it stands, moles, atm, and liters are all units used for $R$, so you're good to go.

Plug in your values to get

T = (2.46 color(red)(cancel(color(black)("atm"))) * 5.0 color(red)(cancel(color(black)("L"))))/(2.0 color(red)(cancel(color(black)("moles"))) * 0.0821 (color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * "K")) = "74.91 K"

Rounded to two sig figs, the answer will be

$T = \textcolor{g r e e n}{\text{75 K}}$