Lecture 18 Electrolyte Solutions DebyeHuckel Theory Charge neutrality

Lecture 18 Electrolyte Solutions - Debye-Huckel Theory Ø Charge neutrality Ø Electrostatics effects Ø Charge distribution Ø Activity coefficient Ø Thermodynamics functions

Charge neutrality When ionic material dissociates in the solvent, it has to stay charge neutral Where zi is the charge of an ion and ni is concentration Considering equilibrium between ionic solid and solution, e. g. , for Na. Cl Which means that due to charge neutrality only the sum of the chemical potentials for anions and cations is defined, and not independent chemical potentials

Chemical potential We express chemical potential as This definition is slightly different than before vs But the difference can be absorbed into the definition of For electrostatic problem one can split the activity coefficient into one due to short range interactions and one due to electrostatic (long range) interactions

Electrostatics Electrostatic potential around a single charge in a medium with a dielectric constant With many ions the potential will be modified by the time averaged potential due to other ions. It has to satisfy the Poisson equation Where is the charge density around ion J

Charge distribution In spherical coordinates The charge distribution is connected with potential via Boltzmann distribution Where the sum is over all species. Expanding exponential and inserting to the top equation Note that the first term in the expansion is zero due to charge neutrality

Charge distribution - II Using charge neutrality condition Or Where Is so called ionic strength

Charge distribution - II Equation Has a physical solution Where A is constant that can be evaluated requiring that total charge in the cloud around ion J is negative z. J leading to Where a is the distance of minimum approach between cation and anion

Screening length The inverse of is the Debye screening length over which the ion is neutralized by the cloud of other ions. Remembering that One can see that the Debye length is long at high T and low ion concentrations. Large dielectric constant also promotes long Debye length as the interactions between ions are weaker. When the Debye length is ~ ion size theory does not apply. Why?

Excess chemical potential To find our excess chemical potential we can use so called charging process where initially neutral ion is charged from 0 to its final charge q. J=ez. J. We can calculate the work done during the charging process as With Upon integration