How many moles of ATP are required to pump one mole of Ca2+ out of a cell when the cytoplasmic concentration is 0.2 uM, the extracellular concentration is 1.8 mM, and the membrane potential is -55 mV?

 

I know I have to use deltaG= RTln([Ain]/[Aout]) + ZFdeltaPsi

 

but how do I get the number of moles of ATP from deltaG??

Perhaps you can just assume that one mole of ATP delivers that-much energy and that additional thermodynamical contributions of the ATP (say pressure or entropy of unused vs. used) can be neglected. That's just a blind guess of mine, though. I am, sadly, not familiar with the physics of transport through a membrane.

Are you told anything about the mechanisms of transporting the Ca2+? maybe the active transporter uses a certain amount of ATP when pumping across the membrane?

I solved the above equation and got deltaG= -10052.4 J

 

I know that hydrolysis of 1 mol ATP releases -30543.2 J

 

Would it make sense to just divide the energy needed (deltaG) by the amount of energy that 1 mol ATP provides?? I get a fraction of a mol of ATP though...

That sounds reasonable to me. An entire mole of ATP would be a hell of a lot of ATP so I'm not surprised it's only a fraction of a mole.