Question

When a 6.79-g mixture of methane, CH4, and ethane, C2H6, is burned in oxygen at constant pressure, 369 kJ of heat is liberated. What is the percentage by mass of CH4 in the mixture? The standard enthalpies of combustion for CH4 and C2H6 are -890.3 kJ mol-1 and -1569.7 kJ mol-1, respectively.
Two equations and two unknowns.
Let X = g CH4
and Y = g C2H6
------------------
eqn 1 is X + Y = 6.79g

eqn 2 is heat generated by CH4 + heat generated by C2H6 = 369 kJ.
heat from CH4 is 890.3 kJ/mol x (X/16)
heat from C2H6 is 1569.7 kJ/mol x (Y/2*30) so all of that together is
X+Y = 6.79
(890.3)(X/16) + (1569.7)(Y/2*30) = 369

Solve for X and Y, then
%CH4 = (mass CH4/6.79)*100 = ?
%C2H6 = (mass C2H6/6.79)*100 = ?

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