I am having such a hard time approaching this problem. It would be great if you can help me.

Question

1.0 mole of CH4 react with 1.0 mole of O2 in a sealed container. (a) When the reaction is complete, what is the container? (b) How many moles of water are produced?
CH4 + 2O2 ---> CO2 + 2H2O

a) CH4 + O2 ---> CO2 + H2O

Answer 1

Looks like the 1.0 mole of O2 is the limiting reagent. Only 0.5 moles of CH4 can react with it. So, when things are done, you are left with

0.5 mole CH4 (left over)
0.5 mole CO2
1.0 mole H2O

Answer 2

What mass of natural gas (CH4) must you burn to emit 263kJ of heat?
CH4(g)+2O2(g)→CO2(g)+2H2O(g)ΔH∘rxn=−802.3kJ