# Air is approximately 79% nitrogen and 21% oxygen by volume. How many moles of oxygen are present in 22.0 L of 24 C and a pressure of 53 kPa?

May 16, 2017

According to Dalton's law of partial pressure, the total pressure of the system is

${P}_{t} = {n}_{t} \left(\frac{R T}{V}\right)$

Convert given units into appropriate units for the gas equations:

${24}^{o} C = 297 K$

and

$53 k P a = 0.52 a t m$

The total moles in the system:

${n}_{t} = \frac{\left(0.52 a t m\right) \left(22.0 L\right)}{\left(0.08206 \frac{L - a t m}{m o l - K}\right) \left(297 K\right)} = 0.47 m o l$

So, using mole fractions of each molecule,

$m o {l}_{{N}_{2}} = \left(0.79\right) \left(0.47 m o l\right) = 0.37 m o {l}_{{N}_{2}}$

and

$m o {l}_{{O}_{2}} = \left(0.21\right) \left(0.47 m o l\right) = 0.099 m o {l}_{{O}_{2}}$