Question:
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First write the balanced  equation for combustion of methane and propane.
1 mole of methane needs 2 moles of O₂ gas and 1 mole of propane needs 5 moles of O₂ gas.
Total volume of O2 gas used = 16L at 1 atm pressure and 0 degree C
Use ideal gas law to know moles of O₂ needed for complete combustion of mixture.
n= PV/RT = 0.714 mol of O₂
Volume of mixture of methane and propane is 5L at 1 atm pressure and 0 degree C.
Use ideal gas law to know moles total moles in mixture.
n= PV/RT  = 0.223  moles of mixture.
If moles of methane are X then oxygen needed is 2X
If moles of propane are Y then moles of oxygen needed is 5Y .
We can say
2X + 5Y = 0.714
X + Y = 0.223
Solve for X and Y
X =0.314 and Y is 0.089
Heat released = 0.314* 890 + 0.0819 * 2220 = 317kJ