Question

A cell membrane at 25C is found to be permeable to Ca2+ but not to anions, and analysis shows the inside concentration to be 0.100 M and the outside concentration to be 0.001 M in Ca2+ . What potential difference would exist across the membrane for Ca2+ to be in equilibrium at the stated concentrations?

Answer 1

Potential difference can be calculated by the following equation:

E_Ca2+ = (RT/zF) log([X]_out/[X]_in).

RT/F is approximately 61, therefore the equation can be written as:

E_Ca2+ = (61/z) ln([X]_out/[X]_in)

R is the universal gas constant (8.314 J.K^-1.mol^-1).

T is the temperature in Kelvin (°K = °C + 273) = 298 K

z is the ionic charge, for Ca²⁺, z = 2

F is the Faraday's constant (96485 C.mol^-1).

[X]_out is the concentration of the ion outside of the species = 0.001 M

[X]_in is the concentration of the ion inside of the specie = 0.100 M

Substituting the known values we have:

E_Ca2+ = (61/2) ln(0.001/0.100) = 30.5 x(-4.605) = -140.45 V