If the H of a reaction is known, then heat can be treated as though it were a reactant or a product; that is, the amount of heat absorbed or released can be related to the amount of material produced or consumed during a reaction by using the stoichiometry of the reaction.

Someone determined that burning a mole of CH3OH releases 676.5 kJ of heat; this is usually written Hcombustion = -676.5 kJ/mol for CH3OH.

How much heat energy is released when 5.8 g methanol are burned?

The balanced reaction is:

Well actually, the question is, if 2 mol CH3OH of produces 1353 kJ of heat then how many kJ are produced when 5.8 g of CH3OH are burned.

H = -123 kJ

It is important to note that H = -123 kJ, when asked how much heat is released by the reaction the the response is

123 kJ of heat are released,

not -123 kJ of heat are released.

The statement "-123 kJ of heat are released" would actually mean heat was being absorbed.

This is the energy released as heat. Remember the reaction creates gases, and the gases expand into the room/container, so there is work being done by the reaction. That is, some of the energy of the reaction goes into expanding the gases which are produced and when we measure or discuss H we are ignoring the energy which is used to expand the gas.