Question

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?

Answer 1

Answer:

Explanation:

Considering the reaction ;

• 2H2 + O2 .............> 2H20

The equation changes when ATP is used for hydrolysis;

• 2H20 + yATP...........> 2H2 + O2 + ADP + Phosphate

• where y = number of ATP Molecules

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

• As such, 3moles of H20 will be required to produce 3moles of H2

• but ΔG(H20) = –237 kJ•mol–1

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

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

• = -711kJ > –30 kJ moles of ATP

• As such, -711kJ/ –30 kJ < moles of ATP

• = At least 23.7moles of ATP is needed to yield three moles of H2 gas

Answer 2

Answer:

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.