Question

A gas mixture containing only helium and neon is 27.1 %% neon (by volume) and has a total pressure of 759 mmHgmmHg. What is the partial pressure of neon?

Answer 1

Step 1 - Understanding the relation between volume percent and parcial pressure

The parcial pressure of a gas in a mixture can be obtained by the following expression:

`p_p=x* p_t`

In the equation above, pp represents the parcial pressure and pt the total pressure. x is the molar fraction, which can be defined as:

`x=\frac{n_(gas)}{n_{\text{total}}}`

I.e., is the quociente between the number of moles of the gas you want to calculate the parcial pressure of and the total number of moles.

Since, for a gas, the number of mols is proportional to the volume, the molar fraction is equal the volume percent:

`n\propto V\rightarrow x=\frac{kV_(gas)}{kV_{\text{total}}}`

K is a constant of proportionallity. It doens't matter its value, since it will be cancelled. We obtain thus:

`x=\frac{V_(gas)}{V_{\text{total}}}`

I.e., the molar fraction is exactly equal the volume percentage.

Step 2 - Using the relation between parcial pressure and volume percentage to solve the exercise

Since, as we saw, the molar fraction x is exactly equal to the volume percentage, we can substitute it by the volume percentage in the formula for the parcial pressure:

`p_p=V_{\text{percentage}}* p_t`

From the exercise, we know that:

Substituting these values on the equation we obtain the parcial pressure of Neon:

`p_p=0.271*759=205.6\text{ mmHg}`

The parcial pressure of Neon is thus 205.6 mmHg.