Mole fractions and partial pressures

10 minAS Level7.1.5

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can define mole fraction and partial pressure, calculate both for a gas mixture, and move confidently between amounts in moles, mole fractions and partial pressures.

Every gas in a mixture pulls its own weight

In a mixture of gases, each gas behaves as if the others were not there. Each one collides with the walls and contributes its own share of the total pressure.

That share is called the gas's partial pressure. It is the pressure the gas would exert if it alone occupied the same volume at the same temperature.

Definition

Partial pressure

The partial pressure of a gas in a mixture, $p_{\text{A}}$ , is the pressure that gas would exert if it were the only gas present in the same volume at the same temperature.

The partial pressures add up to the total pressure:

$p_{\text{total}} = p_{\text{A}} + p_{\text{B}} + p_{\text{C}} + \dots$

This is Dalton's law of partial pressures.

Definition

Mole fraction

The mole fraction of a substance A, written $x_{\text{A}}$ , is the fraction of the total number of moles that is A:

$x_{\text{A}} = \frac{n_{\text{A}}}{n_{\text{total}}}$

It has no units and is always between 0 and 1. The mole fractions of all the substances in a mixture add up to exactly 1.

Linking the two ideas

Mole fraction measures how much of the mixture is a given gas; partial pressure measures how much of the pressure it supplies. The two are in the same proportion.

$p_{\text{A}} = x_{\text{A}} \times p_{\text{total}}$

Because $x_{\text{A}} = n_{\text{A}}/n_{\text{total}}$ , the same result comes from

$p_{\text{A}} = \frac{n_{\text{A}}}{n_{\text{total}}} \times p_{\text{total}}$

Both forms are accepted; the second is quicker when you are given moles and a total pressure.

Worked example: Worked example: an ammonia mixture

At equilibrium a mixture contains $2.0\ \text{mol}$ of $\text{N}_2$ , $3.0\ \text{mol}$ of $\text{H}_2$ and $1.0\ \text{mol}$ of $\text{NH}_3$ . The total pressure is $200\ \text{atm}$ . Calculate the mole fraction and the partial pressure of each gas.

Have a go first?

Count the molecules to get the mole fractions, then share out the total pressure in the same proportions.

Worked example: Worked example: working backwards from per cent by volume

A mixture of $\text{SO}_2$ , $\text{O}_2$ and $\text{SO}_3$ at equilibrium is $40\%$ $\text{SO}_2$ , $30\%$ $\text{O}_2$ and $30\%$ $\text{SO}_3$ by volume, at a total pressure of $300\ \text{kPa}$ . Calculate the partial pressure of each gas.

Have a go first?

Why volume percentage is mole percentage

Equal volumes of any gases at the same temperature and pressure contain equal numbers of molecules — that is Avogadro's law.

So if $40\%$ of the volume is sulfur dioxide, $40\%$ of the molecules are sulfur dioxide, and the mole fraction is $0.40$ .

Common mistakes

Mole fraction is the same as mass fraction.

Mole fraction counts moles, not grams. A mixture that is $50\%$ by mass can have a completely different mole fraction.

Partial pressures add up to the sum of the gas moles.

Partial pressures add up to the total pressure; moles add up to the total number of moles.

You can calculate a partial pressure without knowing the total pressure.

$p_{\text{A}} = x_{\text{A}} \times p_{\text{total}}$ needs the total; only a ratio of partial pressures can be found without it.

In the exam

Give the definition with the words "the pressure that the gas would exert if it alone occupied the same volume at the same temperature".
For mole fraction, state $x_{\text{A}} = n_{\text{A}}/n_{\text{total}}$ and remember it has no units.
Always show $n_{\text{total}}$ before dividing; it is worth a mark and prevents arithmetic slips.
Check that your mole fractions add to 1 and your partial pressures add to the total.
Quote partial pressures in the unit given ( $\text{atm}$ or $\text{kPa}$ ) and give the same number of significant figures as the data.

Checking the idea

Multiple choiceQuestion 1 · Recall

Fill in the blanksQuestion 2 · Apply

CalculateQuestion 3 · Apply

Answer the 3 questions above to continue.