Diffusion Potential

In solution, positively charged particles accumulate around a wire connected to the negative pole the cathode of a battery, whereas negatively charged particles are attracted to a wire connected to the positive pole the anode. This observation gives rise to the names cation (attracted to the cathode) for positively charged ions and anion (attracted to the anode) for negatively charged ions. The battery sets up a gradient of electrical potential (a voltage gradient) in the solution, and the movement of the ions in the solution is influenced by that voltage gradient. Thus, the distribution of ions in a solution depends on the presence of an electric field in that solution. The other side of the coin is that a differential distribution of ions in a solution gives rise to a voltage gradient in the solution. As an example of how an electrical potential can arise from spatial

Figure 4-1 Schematic diagram of an apparatus for measuring the diffusion potential. A voltmeter measures the electrical voltage difference across the barrier separating the two salt solutions.

differences in the distribution of ions, we will consider the origin of diffusion potentials.

Diffusion potentials arise in the situation where two or more ions are moving down a concentration gradient. Examine the situation illustrated in Figure 4-1, which shows a rigid container divided into two compartments by a porous barrier. In the left compartment we place a 0.1 M NaCl solution and in the right compartment a 1.0 M NaCl solution. The porous barrier allows Na+, Cl-, and water to cross, but because of the rigid walls the compartment volume is not free to change and water cannot move. Thus, osmotic factors can be neglected for the moment. However, both Na+ and Cl- will move down their concentration gradients from right to left until their concentrations are equal in both compartments. In aqueous solution, Na+ and Cl- do not move at the same rate; Cl- is more mobile and moves from right to left more quickly than Na+. This is because ions dissolved in water carry with them a loosely associated "cloud" of water molecules, and Na+ must drag along a larger cloud than Cl-, causing it to move more slowly.

In Figure 4-1, then, the concentration of Cl- on the left side will rise faster than the concentration of Na+. In other words, there will be more negative than positive charges in the left compartment, and a voltmeter connected between the two sides would record a voltage difference, E, across the barrier, with the left compartment being negative with respect to the right compartment. This voltage difference is the diffusion potential. Notice that the electrical potential across the barrier tends to retard movement of Cl- and speed up movement of Na+ because the excess negative charges on the left repel Cl- and attract Na+. The diffusion potential will continue to build up until the electrical effect on the ions exactly counteracts the greater mobility of Cl-, and the two ions cross the barrier at the same rate.

Another name for voltage is electromotive force. This name emphasizes the fact that voltage is the driving force for the movement of electrical charges through space; without a voltage gradient there is no net movement of charged particles. Thus, voltage can be thought of as a pressure driving charges in a particular direction, just as the pressure in the water pipe drives water out through your tap when you open the valve. Unlike the pressure in a hydraulic system, however, a voltage gradient can move charges in two opposing directions, depending on the polarity of the charge. Thus, the negative pole of a battery simultaneously attracts positively charged particles and repels negatively charged particles.

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