[treadlightly]

One of the problems on my assignment asks to calculate  ⌂G°' for the pyruvate dehydrogenase reaction using the sum of a redox reaction and acetyl-CoA formation.
This is my attempt at the problem:


As you can see, my answer is REALLY off from the actual answer. I am not sure what I did wrong. Please help me understand.

[Borek]

1. Neither of the three reactions listed is balanced - I understand there is some flexibility built into the use of moieties like Pyruvate, still, at least charge should be clearly conserved. It is not.

2. E°_total is not 0.16 V. It is E°_higher-E°_lower, not E°_higher+E°_lower.

3. You have lost the minus sign somehow.

To be honest, I didn't get -41 kJ/mol neither.

[Babcock_Hall]

I obtained -31 kJ/mol.  If this is a homework problem, is it possible that the key is incorrect.

[Babcock_Hall]

Geoffrey Zubay (Biochemistry, 4th edition) discusses a related reaction, the oxidation decarboxylation of alpha-ketoglutarate and coenzyme A to succinyl CoA and carbon dioxide, with the conversion of NAD to NADH.  He gives ΔG°' = -33 kJ per mole.  Therefore, I think that values of ΔG°' in the range of -30 to -40 kJ per mole for the oxidative decarboxylation of pyruvate are plausible numbers.

[mjc123]

2. E°total is not 0.16 V. It is E°higher-E°lower, not E°higher+E°lower.

0.16V is correct because the OP is adding a reduction half-reaction to an oxidation half-reaction, therefore adding the E°s is correct, assuming that the E° values are those for the half-reactions as written (i.e. not using a reduction potential for the oxidation reaction etc.) You subtract when you are comparing two electrode (reduction) potentials.

[Borek]

2. E°total is not 0.16 V. It is E°higher-E°lower, not E°higher+E°lower.

0.16V is correct because the OP is adding a reduction half-reaction to an oxidation half-reaction

To be honest I was never able to understand where does the idea that oxidation potential is different from the reduction potential comes from. Assuming standard states of all reagents, both reactions occur at exactly the same potential.

[Babcock_Hall]

I attempted this problem using a reduction potential for acetate and carbon dioxide to pyruvate from a Table I found.  I needed to use a value for the free energy of hydrolysis of acetyl CoA in part I.  In part II, I used the well-known value for the reduction potential of NAD and my answer from part I.


Part I, calculate the half-cell for the reduction of acetyl CoA to pyruvate:
                                                                                   E°’      ΔG°’ (kJ/mol)   
Acetate + CO₂ +2e^- + 2H⁺                ⇒ Pyr + H₂O       -0.70     135.1

Acetyl CoA + H₂O                       ⇒ acetate + CoASH + H⁺           -31.4

Acetyl CoA + CO₂ + 2e^- + H⁺   ⇒ Pyr + CoASH                   -0.538   103.7


Part II, Calculate the full cell for the pyruvate dehydrogenase reaction:

NAD + 2e^- + H⁺                          ⇒ NADH                  -0.32 v   61.75

Acetyl CoA + CO₂ + 2e^- + H⁺   ⇒ Pyr + CoASH                           103.7

Pyr + CoASH         ⇒ Acetyl CoA + CO₂ + 2e^- + H⁺                -103.7

NAD + Pyr + CoASH      ⇒ NADH + Acetyl CoA + CO₂                -41.95

References
For the value of E°’ for reduction of acetate:
http://employees.csbsju.edu/hjakubowski/classes/ch331/oxphos/standredpotentialtab.htm

For the value of ΔG°’ for the hydrolysis of acetyl CoA to acetate and CoA:
Nelson and Cox, Biochemistry, 6th ed., p. 521.

Comment: My answer (-42 kJ/mol) does not agree quantitatively with the value I previously calculated (approximately -31 kJ/mol) using the numbers provided by the OP.  However, this may be because of possible differences in the assumed values of E° or ΔG°, apopposed to a calculational error.