[pagoda]

Here’s the problem:
Some bacteria live at low pH and can couple ATP synthesis to the flow of sodium ions instead of protons.  These cells live in an environment that has 150mM of sodium chloride while inside the cell the concentration of sodium chloride is 15mM.  There is a difference in electrical potential of around 110mV due to this concentration gradient.  We know deltaG for ATP hydrolysis is about -31jk/mol, calculate the number of ATP that can be made by letting this cell go to equilibrium at 25 degC.

I can’t seem to wrap my head around the second part of this problem.  I know I need to use the Nernst Eq to get the amount of free energy for each mol of Na+ pumped down the gradient.  This is the energy being harvested to make ATP (I got -17kj/mol of Na+). What I don’t understand is how to apply this to get the amount of ATP being synthesized.  If the cell goes to electrochemical equilibrium, very little Na actually needs to move, the concentrations inside and outside of the cell stay relatively the same, right?
 
Any help to point me in the right direction would be very appreciated!!

[Babcock_Hall]

Do I understand correctly that the membrane potential, sometimes given the symbol ψ or V_m[/sub] is 0.110 volts?  If so, you will need an equation of transport that takes both the concentration gradient and the membrane potential into account.

[Babcock_Hall]

One other thing that might be helpful in this problem is to draw a distinction between ΔG and ΔG°', the latter being the biochemical standard state.  The value of -31 kJ/mol is close to the value I have heard for ΔG°' for the hydrolysis of ATP.