# A 5.00 L flask contains 0.02 moles oxygen at 22°C, what is its pressure, in kilopascals? What is the pressure in atm?

Aug 6, 2016

The pressure of the gas is 10 kPa or 0.1 atm.

This looks like the time to apply the Ideal Gas Law:

color(blue)(|bar(ul(PV = nRT)|),

where

• $P$ is the pressure
• $V$ is the volume
• $n$ is the number of moles
• $R$ is the gas constant
• $T$ is the temperature

We can rearrange the Ideal Gas Law to get

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

$n = \text{0.02 mol}$
$R = \text{8.314 kPa·L·K"^"-1""mol"^"-1}$
$T = \text{(22 + 273.15) K" = "295.15 K}$
$V = \text{5.00 L}$

P = (nRT)/V = (0.02 color(red)(cancel(color(black)("mol"))) × "8.314 kPa·" color(red)(cancel(color(black)("L·K"^"-1""mol"^"-1"))) × 295.15 color(red)(cancel(color(black)("K"))))/(5.00 color(red)(cancel(color(black)("L")))) = "10 kPa"

To calculate the pressure in atmospheres, repeat the calculation using the value

$R = \text{0.082 06 L"·"atm"·"K"^"-1""mol"^"-1}$

P = (nRT)/V = (0.02 color(red)(cancel(color(black)("mol"))) × "0.082 06 L·" color(red)(cancel(color(black)("atm"·"K"^"-1""mol"^"-1"))) × 295.15 color(red)(cancel(color(black)("K"))))/(5.00 color(red)(cancel(color(black)("L")))) = "0.1 atm"