How does the ion size affect the conductivity?

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Ion mobility

The conductivity of an ion solution depends on how fast charge carriers move in it. The speed of migration is determined by two competing forces:

  1. The force that the electric field exerts on the ions with the charge:
  2. The force that counteracts the movement through friction due to the interactions of the ions with the radius and the solvent with the viscosity proportional to the speed (Stokes equation): In the equilibrium of the forces one obtains by equating and resolving according to the speed

Since the migration speed decreases with increasing ionic radius, the conductivity should also decrease. In fact, this can only be observed for large ions such as tetraalkylammonium cations or carboxylic acid anions. This contradiction is resolved by taking the hydrodynamic radius into account. This not only takes into account the radius of the bare ion, but also its solvation shell, i.e. the ion including all solvent molecules that it pulls through the solution. Protons are very small, but have a very high conductivity. They conduct according to a different mechanism than other ions, the Grotthuss or chain mechanism: According to this, the protons are not actually transported through the solution, but only bonds and hydrogen bonds are broken and re-established.

The speed of migration is proportional to the applied electric field. The proportionality factor is also called ion mobility, the following applies:

example

For a field of, the speed of migration of a monovalent ion with a hydrodynamic radius in water is about or about water molecule diameter per second.

Since different ions have different migration speeds, they can be separated in this way: An aqueous gel is used as the medium. This increases the viscosity and improves the separation. This process, known as electrophoresis, is used particularly in protein analysis. The molar conductivity of the ions is proportional to the ion mobility: