# Why is enthalpy change of combustion reactants minus products when the enthalpy of formation is products minus reactants? Isn't one just a generalization of the other one? I'm confused.

mvcdc | Student, Graduate | (Level 2) Associate Educator

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Actually, you're right. The difference arises depending on what's given in the problem.

It is true that Enthalpy of reaction (general) is calculated as enthalpy of products minus enthalpy of reactants:

`Delta H_(rxn) = sum_(prdcts) Delta H_(formation) - sum_(rctnts) Delta H_(formation)` .

It's true that this is the general formula for all kinds of enthalpies - that is, if you are given the heat of formation.

In the case that you are GIVEN the heat of combustion of each species in your reaction, you do the reverse:

`Delta H_(rxn) = sum_(rctnts) Delta H_(combustion) - sum_(prdcts) Delta H_(combutstion).`

This can be explained simply by Hess' Law.

Let's take a very ugly example:

Say `Delta H_(combustion 1)`  is  associated with the combustion of A, while `Delta H_(combustion2)` is associated with the combustion of B, and we want to calculate the enthalpy change associated with the reaction `A rArr B` , then, we simply have to subtract the heat of combustion of B, the product from A, the reactant.

Combustion is reaction with oxygen:

A + O2 = Water + Carbon dioxide

B + O2 = Water + Carbon dioxide

Now, we only want A -> B. Hence, we simply flip the second reaction (the enthalpy change then is multiplied by negative 1), and then add the two equations. By adding the two equations, we get the desired reaction (A -> B), and to get the heat of reaction, we simply add the enthalpy changes associated with the individual reactions (which is simply adding the enthalpy of combustion of A to the negative of the enthalpy of combustion of B, which is another way of saying enthalpy of combustion of the reactant MINUS enthalpy of combustion of the product). [ ## Note that this is really an ugly example, but I hope it gets the idea across ].

In summary, you are right on the general formula. Enthalpies of reactions are calculated by getting the sum of enthalpies of FORMATION of the products LESS enthalpies of FORMATION of the reactants. However, if you are given enthalpies of COMBUSTION, you use the other formula: enthalpies of COMBUSTION of reactants minus enthalpies of COMBUSTION of products - in order to get the enthalpy of REACTION.

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