I got 0.907 KJ for ΔHcomb but I don't know if its correct. I also don't know how to write the equation.

Question

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question:
A calorimeter is filled with 10.0 mole of methane gas and an excess of oxygen. When burned, the ignition wire releases 107.2 J of heat. The heat capacity of the calorimeter (including the bomb and water) is 4.319 kJ oC-1.
The initial temperature is 24.75 degrees celsius and the final temperature is 26.85 degrees celsius

Calculate ΔHcomb for methane and determine the thermochemical reaction?

Answer 1

I assume your 0.907 is from
4.319kJ/C x (2.1C) = 9.07 kJ/10 mol = 0.907 kJ/mol. But you must correct for the wire and I don't think you've done that.
The equation is
CH4 + 2O2 ==> CO2 + 2H2O + heat
When they say thermochemical reaction they may want dH = -? since it is exothermic.
I looked up the value of delta H combustion for CH4 and found about 890 kJ/mol Check those numbers.
Also I found on the web a tutorial in which all of these numbers were the same as your post EXCEPT the 10.0 mols was 10.0 millimoles. Using 10.0 mmols would make the answer come out about right.