exactly opposes net diffusion of a particular ion through the membrane is called the Nernst potential for that ion. As seen above, the magnitude of the Nernst potential is determined by the ratio of the concentrations of that specific ion on the two sides of the membrane. The greater this ratio the greater the tendency for the ion to diffuse in one direction, and therefore the greater the Nernst potential required to prevent the diffusion. A similar expression exists that includes (the absolute value of the transport ratio). This takes transporters with unequal exchanges into account. See: sodium-potassium pump where the transport ratio would be 2/3, so r equals 1.5 in the formula below. The reason why we insert a factor r = 1.5 here is that current density by electrochemical force Je.c.(Na+) + Je.c.(K+) is no longer zero, but rather Je.c.(Na+) + 1.5Je.c.(K+) = 0 (as for both ions flux by electrochemical force is compensated by that by the pump, i.e. Je.c. = −Jpump), altering the constraints for applying GHK equation. The other variables are the same as above. The following example includes two ions: potassium (K+) and sodium (Na+). Chloride is assumed to be in equilibrium. When chloride (Cl−) is taken into account, Derivation Using Boltzmann factor For simplicity, we will consider a solution of redox-active molecules that undergo a one-electron reversible reaction and that have a standard potential of zero, and in which the activities are well represented by the concentrations (i.e. unit activity coefficient). The chemical potential of this solution is the difference between the energy barriers for taking electrons from and for giving electrons to the working electrode that is setting the solution's electrochemical potential. The ratio of oxidized to reduced molecules, , is equivalent to the probability of being oxidized (giving electrons) over the probability of being reduced (taking electrons), which we can write in terms of the Boltzmann factor for these processes: Taking the natural logarithm of both sides gives If at = 1, we need to add in this additional constant: Dividing the equation by to convert from chemical potentials to electrode potentials, and remembering that , we obtain the Nernst equation for the one-electron process : Using thermodynamics (chemical potential) Quantities here are given per molecule, not per mole, and so Boltzmann constant and the electron charge are used instead of the gas constant and Faraday's constant . To convert to