Final answer:
The heat of combustion per mole of methane in a mixture cannot be precisely calculated without knowing the proportion of methane to propane in the mixture. If only methane was present, we would use the ideal gas law to find the moles and then divide the total heat produced to get the heat per mole.
Step-by-step explanation:
The question pertains to the calculation of the heat of combustion per mole of methane when burned in a mixture with propane. We know that when methane (CH₄) is combusted, it releases 890.4 kilojoules of heat per mole, as shown in the thermochemical equation:
CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l) + 890.4 kJ
However, the question specifies a mixture of methane and propane, and we have a total heat release of 777 kJ for burning 12.2 liters of the mixture at given pressure and temperature. To find the molar heat of combustion for methane, we would need to know the proportion of methane to propane in this mixture which unfortunately is not provided in the student’s question. Without this proportion, it is impossible to give an exact value for the molar heat of combustion of methane in the mixture.
If only methane were combusted in the 12.2 liters, we could use the ideal gas law to calculate the moles of methane and then find the heat per mole by dividing the total heat released (777 kJ) by the number of moles of methane. But since we also have propane in the mixture, this calculation cannot be accurately performed.
Assuming we had the proportion of methane in the mixture, we would use that proportion to calculate the moles of methane and divide the total heat released by this number to find the heat of combustion per mole of methane.