# A 21-liter cylinder contains 1.5 moles of an ideal gas at 311 K. What is the pressure of the gas?

Jan 23, 2016

$P = \text{1.8 atm}$

#### Explanation:

This is a pretty straightforward ideal gas law equation practice problem.

As you know, the ideal gas law equation 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
$R$ - 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

So, the problem provides you with

• the volume of the gas, $V = \text{21 L}$
• the number of moles of gas, $n = 1.5$
• the absolute temperature of the gas, $T = \text{311 K}$

Since you know the value of $R$, you can use this information to find the pressure $P$. First, rearrange the ideal gas law equation to isolate $P$ on one side

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

Next, make sure that the units given to you match those used in the expression of the universal gas constant.

 {:(color(red)("Need"), color(white)(aaaaa), color(blue)("Have")), (color(white)(aaaa), color(white)(aaaa), color(white)(aaaa)), (color(white)(aa)"L", color(white)(aaaa), color(white)(aa)"L"color(white)(aaaaaa)color(green)(sqrt())), ("moles", color(white)(aaaa), "moles"color(white)(aaaaa)color(green)(sqrt())), (color(white)(aa)"K", color(white)(aaaa), color(white)(aa)"K"color(white)(aaaaaa)color(green)(sqrt())) :}

The units given to you match those used for $R$, so you're good to go. Plug in your values to get

$P = \left(1.5 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles"))) * 0.0821("atm" * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 311color(red)(cancel(color(black)("K"))))/(21color(red)(cancel(color(black)("L}}}}\right)$

$P = \text{1.824 atm}$

Rounded to two sig figs, the number of sig figs you have for the volume and number of moles of gas, the answer will be

$P = \textcolor{g r e e n}{\text{1.8 atm}}$