Ideal Gas Law Multiple Gases Partial Pressures using Mole Fractions (Ex4)

You may have a mixture of gases together. It will have a total pressure, but that total pressure will be the sum of all the partial pressures (this is called Dalton's Law). You can find the partial pressures by finding the mole fraction of the species and multiplying by the total pressure. Here's a practice example:

A gas mixture contains 20g of \({O_2}\) and 30 g of \(C{O_2}\). What is the partial pressure of \(C{O_2}\)?

Convert the masses into moles by dividing by each species's molar mass:

\[\frac{{30g}}{{44g/mol}} = 0.682mol\]

\[\frac{{20g}}{{32g/mol}} = 0.625mol\]

Find the total amount of moles:

\[0.682mol + 0.625mol = 1.307mol\]

Then find the mole fraction of \(C{O_2}\) by dividing the moles of \(C{O_2}\) by the total moles in the mixture:

\[{x_{C{O_2}}} = \frac{{0.628mol}}{{1.307mol}} = 0.522\]

And the partial pressure is the mole fraction of \(C{O_2}\) multiplied by the total pressure. Remember, the mole fraction is unitless. Don't use the mass fraction by mistake!

\[{P_{C{O_2}}} = (0.522)(3450kPa)\]

\[{P_{C{O_2}}} = 1800kPa\]

Done!

Please see our other worked-out examples of the ideal gas law below:

Ideal Gas Law with Molecules (Ex1)

Ideal Gas Law Mole Fractions (Ex2)

Ideal Gas Law Two Gases Combined (Ex3)

Ideal Gas Law Mixing Two Gas Vessels Together (Ex5)

Alternatively, return to the Ideal Gas Law hubpage below:

Ideal Gas Law Examples (Mixing Gases, Molecules, Partial Pressure)

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