Ionic strength

Quantifying ionic strength

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

I = \begin{matrix} \frac{1}{2} \end{matrix} \sum_{i = 1}^{n} c_{i} {z_{i}}^{2}

where one half is because we are including both cations and anions, c_i is the molar concentration of ion i (M, mol/L), z_i 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, where each ion is singly-charged, the ionic strength is equal to the concentration. For the electrolyte MgSO₄, however, each ion is doubly-charged, leading to an ionic strength that is four times higher than an equivalent concentration of sodium chloride:

I = \frac{1}{2} [c (+ 2)^{2} + c (- 2)^{2}] = \frac{1}{2} [4 c + 4 c] = 4 c

Multivalent ions, having a large ${z_{i}}^{2}$ , contribute strongly to the ionic strength.

Calculation example

As a more complex example, the ionic strength of a mixed solution containing 0.050 M in Na₂SO₄ and 0.020 M KCl is (assuming complete dissociation):

\begin{matrix} I & = \frac{1}{2} \times [\begin{array}{l} {(concentration of {Na}_{2}^{} {SO}_{4}^{} in M) \times (number of {Na}^{+}) \times (charge of {Na}^{+})^{2}} + \\ {(concentration of {Na}_{2}^{} {SO}_{4}^{} in M) \times (number of {SO}_{4}^{2 -}) \times (charge of {SO}_{4}^{2 -})^{2}} + \\ {(concentration of KCl in M) \times (number of K^{+}) \times (charge of K^{+})^{2}} + \\ {(concentration of KCl in M) \times (number of {Cl}^{-}) \times (charge of {Cl}^{-})^{2}} \end{array}] \\ = \frac{1}{2} \times [{0.050 M \times 2 \times (+ 1)^{2}} + {0.050 M \times 1 \times (- 2)^{2}} + {0.020 M \times 1 \times (+ 1)^{2}} + {0.020 M \times 1 \times (- 1)^{2}}] \\ = 0.17 M \end{matrix}

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Quantifying ionic strength

Calculation example

Non-ideal solutions

Importance

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