# a mixture of methane and ethane is stored in a container at 294 mmHg. The gases are burned in air to form co2 and h2o. if the pressure of co2 is 357 mmhg measured at the same temperature and volume as the original mixture, calculate the mole fraction of the gases.

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1. Two equations and two unknowns; solve simultaneously.
Write and balance the chemical equations.
CH4 + 2O2 ==> CO2 + H2O
C2H6 + 7O2 ==> 2CO2 + 6H2O
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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 = 357 mm is th second math equation. Writing them together and solving, we have
x + y = 294
x + 2y = 357
Solve simultaneously, and I obtained
x = 231 and y = 63. You should confirm all of that.
Then since PCH4 = XCH4Ptotal
Rearrange to obtain XCH4 = (PCH4/Ptotal)
and XC2H6 = PC2H6/Ptotal.
I've estimated
XCH4 = 0.786
XC2H6 = 0.214

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