A chemist wants to develop a fuel by converting water back to elemental hydrogen and oxygen using coupled ATP hydrolysis to drive the reaction. Given that the value of Δ f Go for water is –237 kJ•mol–1 and that one mole of ATP hydrolyzed to ADP yields –30 kJ•mol–1, how much ATP is needed to yield three moles of H2 gas?

Firstly, we need know that:

Energy of a opposite reaction will equal to = (-) energy of forward reaction.

Therefore,

H2(g) +1/2 O2(g) > H2O (g)    ΔfG = -237.13 kJ/mol (1)

ATP + H2O (l) > ADP + Pi   ΔG = -31 kJ/mol   (2)

The first equation can be written as:

H2O > H2 +1/2 O2   ΔG = 237.13 kJ/mol (3)

Equation (3) showed the formation of one mole of H2 gas required energy = 237.13 kJ/mol

Equation (2) showed that one mole of ATP on hydrolysis produces energy = 31.0 kJ/mol

Therefore, to get one mole of H2 gas means:

no of moles of ATP required = energy required for H2 production/energy produced by ATP  

= 237.13/31.00

= 7.65 moles

Therefore,  to produce one mole H2 gas = 7.65 moles of ATP is required

So in order to produce 3 moles of H2

= x ATP required for one mole

= 3 x 7.649

= 22.947 moles

Therefore, to produce three mole of H2 = 22.9 moles of ATP.

Explanation:

Considering the reaction ;

The equation changes when ATP is used for hydrolysis;

from the reaction ; 1mole of water produces 1 mole of hydrogen gas ; 1 : 1

Therefore ; ΔG(reaction) = 3 x –237 kJ•mol–1 = -711kJ

from above, it is indicative that ΔG(reaction) > ΔG(reaction) ATP