A cell membrane at 25C 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?
Potential difference can be calculated by the following equation:
ECa2+ = (RT/zF) log([X]out/[X]in).
RT/F is approximately 61, therefore the equation can be written as:
ECa2+ = (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:
ECa2+ = (61/2) ln(0.001/0.100) = 30.5 x(-4.605) = -140.45 V
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