[Heater]

I have an assigenment where i need to calculate the lover heating value of  the combustion of 100 mol of a gas mixture (MJ/Nm³)

The gas mixture is made of in mol%:
91.1% CH₄
4.7% C₂H₆
1.7% C₃H₈
1.4% C₄H₁₀
0.6% N₂
0.5% CO₂

the enthalpy of the combustion reaction of methane, ethane, propane and butane, are given:
Methane combustion : -804,2 kJ/mol
Ethane combustion : -1428,9 kJ/mol
Propane combustion : -2045,5 kJ/mol
butane combustion : -2663.6 kJ/mol

we are also told the gasmixture behaves like an idealgas.

The solution in the book is given to be 38,8 MJ/m³ but i can't seem to get the right answer no matter what i do.

my main theory to calculating it was to calculate the ΔH of the combustion reaction using the enthalpy of the 4 gas combustions given by adding them together  and multiplying with their respective mol% and then dividing it with the normal volume of an idealgas 22,42 m³/kmol which gives me a solution of 38,93 MJ/M³ which is close to the solution but not quite it.

Does anyone know how what i am missing?

[Hunter2]

Calculate how many m^3 is 100 mol

Then calculate each ΔH value . Get summary and division through the volume.

[Borek]

the enthalpy of the 4 gas combustions given by adding them together  and multiplying with their respective mol% and then dividing it with the normal volume of an idealgas 22,42 m³/kmol which gives me a solution of 38,93 MJ/M³ which is close to the solution but not quite it.

I did the same and got 38.897 MJ/m³ (so more like 38.90).

Approach is correct, I would assume this is just a typo (or lousy rounding) in the answer key.