A mixture of CH_{4} (g) and C_{2} H_{6} (g) has a total pressure of 0.54 atm . Just enough O_{2} (g) is added to the mixture to bring about its complete combustion to CO_{2} (g) and H_{2} O(g). The total pressure of the two product gases is 2.3 atm .

Assuming constant volume and temperature, find the mole fraction of CH_{4} in the mixture.

We’re being asked to **calculate the mole fraction of CH _{4}** in a

Recall that the ** partial pressure of a gas (P_{Gas})** in a mixture is given by:

$\overline{){{\mathbf{P}}}_{{\mathbf{gas}}}{\mathbf{}}{\mathbf{=}}{{\mathbf{\chi}}}_{{\mathbf{gas}}}{{\mathbf{P}}}_{{\mathbf{total}}}}$

where **χ**** _{Gas}** = mole fraction of the gas and

The ** mole fraction of the gas** is then given by:

$\overline{){{\mathbf{\chi}}}_{{\mathbf{gas}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{moles}\mathbf{}\mathbf{gas}}{\mathbf{total}\mathbf{}\mathbf{moles}}}$