7.1: The Debye–Hückel Theory of Electrolyte Solutions

The Debye–Hückel theory, established by Peter Debye and Erich Hückel in 1923, is a fundamental concept in physical chemistry. It provides an understanding of the behavior of strong electrolytes in solution, particularly explaining their deviations from ideal behavior.

The theory is based on Coulombic interactions (the attraction or repulsion between charged particles) between ions in solution. In an ionic solution, oppositely charged ions tend to attract each other. This means that cations (positively charged ions) are more likely to be found near anions (negatively charged ions) and vice versa. This attraction creates a spherical haze around each ion, known as an ionic atmosphere.

The counterions have a net charge equal in magnitude but opposite in sign to the central ion. The electrostatic interaction between the central ion and its ionic atmosphere lowers the ion's energy and, therefore, its chemical potential. This decrease in energy manifests as the difference between the molar Gibbs energy (G_m) and the ideal value of the molar Gibbs energy (G_m ^ideal) of the solute.

The Debye–Hückel limiting law provides a method for calculating the activity coefficient at very low concentrations. The activity coefficient accounts for the deviation of a solution from ideal behavior. According to the law, the activity coefficient can be determined if the charge numbers of ions and the ionic strength of the solution are known.

This law is particularly useful for very dilute solutions. However, it may not provide accurate results for solutions with moderate molalities, as their activity coefficients may differ from the values given by this expression.

When the ionic strength of a solution is too high for the limiting law to be valid, the activity coefficient can be estimated using extensions of the Debye–Hückel theory. One such extension is the Truesdell–Jones equation, also known as the extended Debye–Hückel law. Another extension is the Davies equation, proposed by C.W. Davies in 1938.

These extensions allow for more accurate calculations of activity coefficients over a wider range of dilute solutions. However, they still have limitations, especially near 1 mol kg⁻¹.

Current theories for calculating activity coefficients for ionic solutes take an indirect route. They first establish a theory for the dependence of the activity coefficient of the solvent on the solute’s concentration. Then, use the Gibbs–Duhem equation to determine the activity coefficient of the solute. These theories are reasonably reliable for solutions with molalities greater than about 0.1 mol kg⁻¹ and are valuable for discussing mixed salt solutions, such as seawater.