What is the pH difference (△pH)across a membrane at 310 K if the membrane potential is -0.15 V and the overall Gibb's free energy change across the membrane is -19 .0 kJ mol-1? (R = 8.315 J K-1 mol-1;F = 96,485 J V-1 mol-1)
A)5.44
B)2.3
C)0.74
D)1.4

Question

Quizplus · Accepted Answer

The Nernst equation relates the membrane potential and pH difference across a membrane.
ΔV = (RT/zF) * ΔpH
where ΔV = membrane potential, R = gas constant, T = temperature, z = valency of the ion (here, H+), F = Faraday constant, and ΔpH = pH difference.
We can rearrange the equation as:
ΔpH = (ΔV * zF)/(RT)
Given, ΔV = -0.15 V, ΔG = -19.0 kJ/mol
Now, ΔG = -zFΔV
-19.0 * 1000 = (-1) * (96485) *(-0.15)
z = 1
Substitute the values in the Nernst equation:
ΔpH = (0.15 * 1 * 96485)/(8.315 * 310)
= 0.74
Therefore, the pH difference (ΔpH) across the membrane is 0.74. Hence, the correct answer is C.

What Is the PH Difference (△PH)across a Membrane at 310