I will be happy to critique your thinking on this. First, calculate the moles of H2 used.

Question

2.0e8 L H2/22.4 L H2 = 8.9e6 mol H2

For every 2 mol H2 used -572 kJ of energy is produced

-572 kJ/2 mol H2 = -2.86e2 kJ/mol

I have a balanced equation with this problem. It is: 
2 H2 + O2 --> 2 H2O 
(where the change in heat is -572 kJ)

I have to discover the heat that is evolved from this equation. Would you have to convert the moles of H2 to kJ of energy using stoichiometry?

I would convert the moles of H2 to kJ by mulitiplying the number of moles of H2 times the heat per mole of H2, which was given in the problem, as I recall.