Debye–Hückel equation

The chemists Peter Debye and Erich Hückel noticed that solutions that contain ionic solutes do not behave ideally even at very low concentrations. So, while the concentration of the solutes is fundamental to the calculation of the dynamics of a solution, they theorized that an extra factor that they termed gamma is necessary to the calculation of the activities of the solution. Hence they developed the Debye–Hückel equation and Debye–Hückel limiting law. The activity is only proportional to the concentration and is altered by a factor known as the activity coefficient . This factor takes into account the interaction energy of ions in solution. In order to calculate the activity of an ion C in a solution, one must know the concentration and the activity coefficient: where is the activity coefficient of C, is the concentration of the chosen standard state, e.g. 1 mol/kg if molality is used, is a measure of the concentration of C. Dividing with gives a dimensionless quantity. The Debye–Hückel limiting law enables one to determine the activity coefficient of an ion in a dilute solution of known ionic strength. The equation is where is the charge number of ion species i, is the elementary charge, is the inverse of the Debye screening length (defined below), is the relative permittivity of the solvent, is the permittivity of free space, is the Boltzmann constant, is the temperature of the solution, is the Avogadro constant, is the ionic strength of the solution (defined below), is a constant that depends on temperature. If is expressed in terms of molality, instead of molarity (as in the equation above and in the rest of this article), then an experimental value for of water is at 25 °C. It is common to use a base-10 logarithm, in which case we factor , so A is . The multiplier before in the equation is for the case when the dimensions of are . When the dimensions of are , the multiplier must be dropped from the equation. It is important to note that because the ions in the solution act together, the activity coefficient obtained from this equation is actually a mean activity coefficient.