THe amount o energy released in kJ per mole during cobustion of octance is 5460. How would you find the amount of energy release in kJ/mol of Carbon Dioxide.
The way I do it is to write Octane's combustion reaction and balance it.
C8H18 + O2 --> CO2 +H2O
When you balance it, the ratio of octane to carbon dioxide is 1:8. Wouldn't that mean that the amount of energy carbon dioxide releases is 5460 x 8 = 43680. But in the answers, they do 5460/8 = 682.5.
Why do they divide instead of multiply
Very interesting question! Never seen anything like it before. So, looking at the reaction, we have
} +25O_{2(g)} \rightarrow 18H_2O_{(l)}+16CO_{2(g)})
As you've stated, the relationship between Octane and Carbon dioxide is clearly

. We know that 5460kJ of energy is released in the combustion of one mole of Octane. How can we think about this question?
Well, if the forward reaction RELEASES 5460 kJ of energy, the backwards reaction (ie. Carbon dioxide and Water turning into Octane and Oxygen) must ABSORB 5460 kJ of energy (switch the arrow the other way around, and switch the sign of the heat of reaction). Therefore, we can say that the '8' moles of Carbon dioxide is ALSO associated with 5460 kJ of energy. Thus, to get ONE mole of Carbon dioxide, we divide the total energy (5460 kJ) by the number of moles (

to get our answer (682.5 kJ). I have the say, this is a really strange question, and I've never seen anything like it in the HSC. I also don't think I've explained in brilliantly, but that's my answer to the best of my knowledge. Does it sort of make sense? Don't worry too much if it doesn't; it's not very important in the HSC.
Great question though! Very hard, but you were on the right track!
(Mod edit: Fixing the LaTex)