Energy that is useful to the cell can be found in ionic concentration gradients. Nernst
formalized this concept in an equation that relates the electrical potential (voltage) across a
membrane to a set of constants and the ratio of the ionic concentration as follows:
E = - RT/nF ln [X] out/ [X] in
where E is the voltage (V) across the membrane; R, the universal gas constant = 2 cal mol-1 \deg K-1;
the absolute temperature, T in \deg K; n, the valence of ion X; and F, the Faraday constant = 2.3 x
104 cal V-1 mol-1 times the ratio of the concentrations of X outside and inside the cell.
Mammalian saline is a phosphate-buffered solution that mimics the extracellular Na+ (140 mM)
and K+ (3 mM) at a pH of about 7.4.
Take an erythrocyte, red blood cell, that is 7 µm in diameter and 2 µm thick that has internal
concentrations of Na+ (10 mM) and K+ (100 mM). Determine the voltage (V) across the
membrane separately for each ionic species.
Now determine the volume of the erythrocyte. Calculate the number Na+ and K+ ions inside the
cell that result in the internal concentrations.