If hydrogen were used as a fuel, it could be burned according to the following reaction: h2(g)+1/2o2(g)→h2o(g). use average bond energies to calculate δhrxn for this reaction use average bond energies to calculate δhrxn for the combustion of methane (ch4). which fuel yields more energy per mole and per gram?

The deltaHrxn = -243 kJ/mol the deltaHrxn of CH4(methane) = -802 kJ/mol 

The fuel that yields more energy per mole is METHANE. The negative sign merely signifies the release of energy. Thus, 802 kJ/mol is greater than 243 kJ/mol.

The fuel that yields more energy per gram is HYDROGEN. Here is the computation:
deltaHrxn = (-243 kJ/mol)(1 mol/2.016 g H2)  = -120.535714286 kJ/g or -121 kJ/g

deltaHrxn of CH4(methane) = (-802 kJ/mol)(1 mol/16.04 g) 
= -50 kJ/g 

As discussed the negative sign serves as the symbol of released energy. Thus, 121 is greater than 50.