Question

The voltage across a cell membrane due to the transport of ions is ~100 mV. What is the concentration gradient, ie, the ratio of the ions in the cell to those outside the cell, at 37 C?

Answer 1

We will use Nernst equation to solve for concentration gradient.

V = - (RT/zF) ln ci/co

Where, V is voltage across membrane = 100 mV = 0.1 V

R is gas constant = 8.314 J/(mol.K)

T is temperature in K = 37C = 310.15 K

z is valence of ion = we will consider as 1 (not mentioned in Question)

F is Faraday’s constant = 9.646*10^4 C/mol

ci/co is ratio of inside and outside concentration = ?

Let us put the values in equation.

0.1 V = - (8.314*310.15/1*9.645*10^4) ln ci/co

               = - (2578.6/9.645*10^4) ln ci/co

0.1 V = - 0.0267 ln ci/co

Ci/co = 0.0236

Ratio of concentrations is 0.0236 which may be ≈ 0