# Ideal gas law problem check?

## If I have 4.1 moles of a gas at a pressure of 5.6 atm and a volume of 12 liters, what is the temperature? I want to check that I completed this problem right before continuing with the rest of my problems to ensure I'm doing them correctly. Thanks!

Apr 25, 2018

The temperature is $2.0 \times {10}^{2}$ $\text{K}$.

#### Explanation:

Equation for the ideal gas law:

$P V = n R T$,

where:

$P$ is pressure, $V$ is volume, $n$ is moles, $R$ is the gas constant (varies with units for pressure), and $T$ is temperature in Kelvins.

Known

$P = \text{5.6 atm}$

$V = \text{12 L}$

$n = \text{4.1 moles}$

$R = \text{0.082056 L atm K"^(-1) "mol"^(-1)}$

Unknown

$T$

Solution

Rearrange the equation to isolate $T$. Plug in the known values and solve.

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

$T = \left(5.6 {\textcolor{red}{\cancel{\textcolor{b l a c k}{\text{atm"))xx12color(red)cancel(color(black)("L")))/(4.1color(red)cancel(color(black)("mol"))xx0.082056 color(red)cancel(color(black)("L")) color(red)cancel(color(black)("atm")) "K"^(-1) color(red)cancel(color(black)("mol}}}}}^{- 1}\right) = 2.0 \times {10}^{2}$ $\text{K}$ (rounded to two significant figures)

Apr 25, 2018

$T = 199.73 K$

#### Explanation:

Use the formula

$P V = n R T$

re-arranging for temperature:

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

Plug-in values:

Remember R is a constant = 0.08206 (L*atm)/(mol *K)

T = ((5.6 atm)(12 L)) / ((4.1 mol) (0.08206 (L*atm)/(mol *K))

cancel units and solve:

$T = 199.73 K$