Question

A mixture of methane (CH4) and ethane (C2H6) is stored in a container at 294 mm Hg. The gases are burned in air to form CO2 and H2O. If the pressure of CO2 is 346 mm Hg measured at the same temperature and volume as the original mixture, calculate the mole fraction of the gases.

Mole fraction of methane: _____________

Mole fraction of ethane: _________________

Answer 1

The balanced chemical equations are:
CH4 + 2O2 ==> CO2 + 2 H2O
C2H6 + 7/2O2 ==> 2CO2 + 3 H2O

If we let x = pressure CH4 and y = pressure C2H6, then
x + y = 294 mm is the first math equation.

Looking at the chemical equations, if x is pressure CH4, then x = pressure of CO2 produced from the CH4 and 2y is the pressure produced by the C2H6; therefore,
x + 2y = 346 mm is th second math equation. Writing them together and solving, we have
x + y = 294
x + 2y = 346

By solving: x= 242 mm of Hg

                 y = 52 mm of Hg

Then since P_CH4 = X_CH4 * P_total

Rearrange to obtain X_CH4 = (P_CH4/Ptotal)

and X_C2H6 = P_C2H6/P_total.

X_CH4 = 242 mm of Hg / 294 mm Hg

       = 0.824

X_C2H6 = P_C2H6/P_total. = 52 mm of Hg / 294 mm Hg

                               = 0.176