In terms of bond energies of the chemicals involved, why can hydrogen can be used as a fuel?

see below

Explanation:

Hydrogen reacting with oxygen to generate water produces a relatively large amount of thermal energy. As requested and in terms of bonding energies, a Hydrogen - Oxygen fuel cell reaction could be illustrated as follows...

                     H - H              +           1/2(O = O)              =>           H - O - H

ΔHb:     1mol(-436Kj/mol)          1/2mol(498 Kj/mol)               1mol(-463 Kj/mol)

              = -436Kj                             = -249Kj                               = -926Kj

ΔH(Rxn) =  ∑ΔH(Products) - ∑ΔH(reactants)

=  [(-926kj)] - [(-436Kj) + (-249Kj)]

= (-926 + 436 + 249)Kj = -241Kj (=> which is the Standard Heat of Formation of Water => See Thermo Tables in text appendix).

This means, on reaction of Hydrogen and Oxygen, 241Kj energy is released by exothermic process. The challenge now, is to direct this 241Kj of energy into a material substance so as to generate useful outcomes (work).      

Now one should understand that the source of the energy in this problem is from the hydrogen - oxygen reaction, however, there are other mechanisms and reactions that generate thermal energy. Hydrogen fuel cell is but one.

So, now what does one do with the thermal energy generated in the fuel cell reaction. That is, what application would be needing 241Kj of energy per mole water formed? Consider two needed (hypothetical) applications    => 1. to boil water and the other 2. to warm a tub of bathwater.          

Our physics friends tell us that the amount of thermal heat used is related to the mass of substance receiving the heat and the resulting temperature change accompanying the transfer of thermal energy by the following equation ...

q = mcΔT where q = thermal energy. m = mass, c = specific heat & ΔT = Temperature change.

Given that both applications will receive the same amount of thermal energy ( => 241Kj) the question is reduced to how much mass would be needed to heat the water to boiling for application 1 vs amount of water to moderately heat water for a bath.          

Application 1 (Boiling water)  => 241Kj energy would only need a small quantity of water to achieve a high enough temperature to reach boiling point where as, Application 2 (Warming bath water) => 241Kj energy would be applied to a much larger quantity of water to limit the heating effect to a  moderate temperature level.

In summary, the hydrogen-oxygen fuel cell reaction produces thermal energy => the thermal energy is directed into a mass of substance that is then heated to a needed temperature level to perform a functional service.  The services derived from the H/Oxy rxn are, in essence, the utility of the process as a fuel. :-)        

Addendum => The Hydrogen Electrochemical fuel cell process is the same except the process is galvanic in nature but still generates the same amount of thermal energy which is translated directly into electrical energy for needed applications.

the ideal gas law equation is as follows

pv = nrt

where p - pressure

v - volume

n - number of moles

r - universal gas constant

t - temperature

so if the pressure, volume and temperature are already known

we are left with n and r

since r is the universal gas constant that has a known fixed value then r too is known

so we are left with 'n'

once we know temperature volume and pressure

we can find the number of moles of gas present using the ideal gas law equation

this is not my own answer, this is an answer for the same question by the user blahblahmali. i do not claim ownership of this account.