# Ionic strength

The ionic strength, I, of a solution is a function of the concentration of all ions present in a solution.

$I_c = \begin{matrix}\frac{1}{2}\end{matrix}\sum_{{\rm B}=1}^{n} c_{\rm B}z_{\rm B}^{2}$

where cB is the molar concentration of ion B (mol dm-3), zB is the charge number of that ion, and the sum is taken over all ions in the solution. For a 1:1 electrolyte such as sodium chloride, the ionic strength is equal to the concentration, but for MgSO4 the ionic strength is four times higher. Generally multivalent ions contribute strongly to the ionic strength.

For example the ionic strength of a mixed 0.0050M Na2SO4 + 0.0020M NaCl solution is :

I= 1/2(2*((+1)2 *0.005) + (+1)2 *0.0020 + (-2)2 *0.005 + (-1)2 *0.002) =0.017M

Because in non-ideal solutions volumes are no longer strictly additive it is often preferable to work with molality (mol/kg H2O ) rather than amount concentration. In that case, ionic strength is defined as:

$I_m = \begin{matrix}\frac{1}{2}\end{matrix}\sum_{{\rm B}=1}^{n} m_{\rm B}z_{\rm B}^{2}$

## Importance

The ionic strength plays a central role in the Debye-Hückel theory that describes the strong deviations from ideality typically encountered in ionic solutions. It is also important for the theory of Double Layer (interfacial) and related Electrokinetic phenomena and Electroacoustic phenomena in colloids and other heterogeneous systems. That is, the Debye length, which is the inverse of the Debye parameter – kappa –, is inversely proportional to the square root of the ionic strength. Debye length is characteristic of the Double layer thickness. Increasing the concentration or valence of the counterions compresses the double layer and increases the electrical potential gradient.

## Ionic replacement

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Main article: Rate equation

The rate coefficient or rate constant of a chemical reaction is the coefficient that precedes reactant concentrations in a simple rate equation. For a chemical reaction n A + m B → n ' C + m ' D, with rate equation: In the study of solution reaction kinetics it is often desirable to change the concentration of an active species without changing the ionic strength, because the latter affects the value of the rate constant k. This can often be done by replacement. If, for example, the [S2O82-] is to be lowered, the solution is diluted with a solution containing the same concentration of a non-active species of equal charge e.g. SO42- rather than just solvent. This produces a solution with a lower [S2O82-] but of the same ionic strength.