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# Gas mixtures

This video covers how we can adapt the ideal gas law for mixtures of gases, and introduces partial pressures.

We don’t always work with a pure gas. Gases are often mixtures. For instance, the atmosphere is a mixture of nitrogen and oxygen.

## Gas mixtures

The ideal gas law applies to both a total number of moles of gas, and also any subset of gases – i.e., different components in a mixture. The pressure of each component gas is referred to as “partial pressure”. This is the fraction of a pressure that is due to that particular gas.

Gas Equation
Gas 1 (p_1=frac{n_1RT}{V})
Gas 2 (p_2=frac{n_2RT}{V})
Both (p_{tot}=p_1+p_2=frac{left(n_1+n_2right)RT}{V})

Partial pressures are important because they are analogous to concentration. Everything involving equilibria and energy, that uses concentrations, can apply to gas phase reactions using partial pressures.

## Mole fractions

A related concept is the mole fraction. This is the fraction (in terms of moles) of a gas in the mixture. In a system with two gases, 1 and 2, the mole fraction is:

$$x_1=frac{n_1}{n_1+n_2}$$

In a mixture of 0.25 moles hydrogen and 0.5 mol of oxygen gases, the molar fraction of hydrogen is:

[frac{0.25}{0.25 + 0.5} = frac{0.25}{0.75} = 0.33]

A partial pressure is the mole fraction of the gas multiplied by the total pressure. So if the above hydrogen and oxygen mixture was at a pressure of 1.5 atm, the partial pressure of hydrogen would be:

[1.5 atm times 0.33 = 0.5 atm]

### Ideal conditions

Finally, it’s worth noting ideal conditions. Ideal conditions allow us to use pressures in thermodynamic calculations. These conditions assume:

• Zero interactions between molecules
• Molecules have zero size

And this is more valid for a real gas:

• At low pressures / concentrations
• At higher temperatures