[joyb]

The question asks:
"The redox couple NAD⁺/NADH has E°' = -0.45 V, while the couple O₂/H₂O has E°' = 0.8 V at 298K.
a) Calculate the free energy change when 1 mol of NADH is oxidised by O2 at 298 K under standard conditions (biochemical). [I have calculated this to be -241kJ/mol]
b) If this reaction is used to build up an electrochemical gradient of protons, with 9 protons pumped per NADH oxidised, calculated the maximal pH gradient which can be achieved."

I am stuck on b. I have the sneaking suspicion I'll have to use the calculated change in free energy and maybe an equation along the lines of  Δμ_H+= FΔΦ-2.303RTΔpH (am I on the right track?), but I'm not really sure how to begin...

[Babcock_Hall]

I would write an equation that is the sum of the two processes that you describe.  You appear to be on the right track, as far as I can tell.

[joyb]

I'm still unsure what to do...

[Babcock_Hall]

Start by writing a full cell reaction between NADH and O₂.  Then I would add 9H⁺_inside to the reactant side and 9H⁺_outside to the product side of this equation.

[Babcock_Hall]

The maximum pH gradient will occur at equilibrium, where the favorable free energy of electrons flowing downhill just matches the unfavorable free energy of protons being transported uphill.