## The free energy change question

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### The free energy change question

All right, I'm honest...It's my homework, but I don't ask anyone to do it for me. I did it myself, the only thing is, I'm not sure if it's correct. I would appreciate any suggestions. Here it goes:

The Na+/K+ pump illustrates "active transport" since it moves Na+ and K+ against their concentration gradients. In order to transport the ions against their gradients, energy (ATP) is required. Hydrolysis of 1 ATP under cellular conditions yields -ΔG = 7.3 kcal/mol. ATP hydrolysis is coupled to the pumping of protons across the membrane e.g. Na/K+ ATPase (3 Na+-out/2 K+ in).

for Na+ (out - against the gradient)

Co=145 mM

Ci=12 mM

F=2.3x104 cal V-1M-1

E=-70 mM=-0.07 V

R=1.987cal mole-1 T-1

T= 310 K

ΔG = RT ln Ci/ Co+ zFE = 615.97 x ln 0.082 + 2.3 x 104 (-0.07) =

= -1.54+(-1.61) = +3.15 kcal/mole

for K+ (in – against the gradient)

Co=4 mM

Ci=139 mM

ΔG = RT ln Co/ Ci + zFE = 615.97 x ln 0.0287 + 2.3 x 104 (-0.07) =

= -2.187+(-1.61) = +3.79 kcal/mole

Is it correct what I calculated? or maybe it's half way done, and I have to do the calculations for 3 Na and 2 K?

**Calculate the free energy change associated with ATP exiting a cell through one of the ATP permeant transports. Keep in mind the projected concentration gradient for ATP, the plasma membrane voltage, and the charge on the molecule.**The Na+/K+ pump illustrates "active transport" since it moves Na+ and K+ against their concentration gradients. In order to transport the ions against their gradients, energy (ATP) is required. Hydrolysis of 1 ATP under cellular conditions yields -ΔG = 7.3 kcal/mol. ATP hydrolysis is coupled to the pumping of protons across the membrane e.g. Na/K+ ATPase (3 Na+-out/2 K+ in).

for Na+ (out - against the gradient)

Co=145 mM

Ci=12 mM

F=2.3x104 cal V-1M-1

E=-70 mM=-0.07 V

R=1.987cal mole-1 T-1

T= 310 K

ΔG = RT ln Ci/ Co+ zFE = 615.97 x ln 0.082 + 2.3 x 104 (-0.07) =

= -1.54+(-1.61) = +3.15 kcal/mole

for K+ (in – against the gradient)

Co=4 mM

Ci=139 mM

ΔG = RT ln Co/ Ci + zFE = 615.97 x ln 0.0287 + 2.3 x 104 (-0.07) =

= -2.187+(-1.61) = +3.79 kcal/mole

Is it correct what I calculated? or maybe it's half way done, and I have to do the calculations for 3 Na and 2 K?

### Re: The free energy change question

So the total free energy change for the coupled process is deltaG(ATP) + deltaG(Na) + deltaG(K) which is -0.36 kcal/mol. The coupled process can be spontaneous. I think the stoichiometry is implicit. One mole of ATP hydrolyzed antiports 3 Na and 2 K ions is the process and you don't need to calculate a free energy for 3 separate Na and 2 separate K. This calculation makes sense to me, though I can always be wrong. I didn’t check either your arithematic or the inner/outer ion concentrations. Both look reasonable to me.

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