If the difference in pH across a membrane is 0.60 and the membrane potential is -0.10 V,about what percent of the Gibbs free energy change,△G,is from the pH difference at 37 oC? (R = 8.315 J K-1 mol-1;F = 96,485 J V-1 mol-1)
A)15%
B)27%
C)73%
D)85%

Question

Quizplus · Accepted Answer

The Gibbs free energy change for a reaction can be calculated using the Nernst equation:

△G = -nF△E

where n is the number of electrons transferred, F is the Faraday constant, and △E is the difference in membrane potential.

We can calculate the contribution of the pH difference as follows:

△GpH = -RTln(10)zF△pH

where z is the charge of the solute, and △pH is the difference in pH.

Plugging in the values given:

△GpH = -(8.315 J K-1 mol-1)(310 K)ln(10)(1)(96,485 J V-1 mol-1)(0.60)

△GpH = -13,635 J/mol

Now, we can calculate the total Gibbs free energy change:

△Gtotal = △GpH + △Gmembrane

where △Gmembrane is the contribution from the membrane potential:

△Gmembrane = -nF△E = -(1)(96,485 J V-1 mol-1)(-0.10 V) = 9,649 J/mol

△Gtotal = -13,635 J/mol + 9,649 J/mol = -3,986 J/mol

Finally, we can calculate the percent contribution of the pH difference:

Percent contribution = (△GpH / △Gtotal) x 100%

Percent contribution = (-13,635 J/mol / -3,986 J/mol) x 100%

Percent contribution = 27%

Therefore, the answer is B, 27%.

If the Difference in PH Across a Membrane Is 0