A mixture of methane and ethane is contained in a glass bulb of 500 cm3 capacity at 25°C. The pressure is 1.25 bar, and the mass of gas in the bulb is 0.530 g. What is the mole fraction of methane?

To find a solution to this problem, the student must solve a system of two equations and two unknowns. Once the number of moles of either compound is found, there is sufficient information to calculate the mole fraction of methane.

First, use the ideal gas law to find the total number of moles of gas.

so

Let nE = moles of ethane mE = mass of ethane nM = moles of methane and mM = mass of methane. Then we can write 0.0252 moles = nE + nM, and we know from the given information that 0.530 g = (30.068 g/mole)·nE + (16.042 g/mole)·nM.

This system of equations can be solved by substitution. The most direct way to determine the mole fraction of methane in the system is to solve for nM , the number of moles of methane. Proceeding along these lines one finds nM = 0.0162.

The mole fraction methane is simply the ratio of moles of methane to the total number of moles.