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,
ci is the
molar concentration of ion i (M, mol/L),
zi 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}[4c + 4c] = 4c
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{align} I & = \tfrac 1 2 \times \left[\begin{array}{l} \{(\text{concentration of }\ce{Na2SO4}\text{ in M}) \times (\text{number of }\ce{Na+}) \times (\text{charge of }\ce{Na+})^2\}\ + \\ \{(\text{concentration of }\ce{Na2SO4}\text{ in M}) \times (\text{number of }\ce{SO4^2-}) \times (\text{charge of }\ce{SO4^2-})^2\} \ + \\ \{(\text{concentration of }\ce{KCl}\text{ in M}) \times (\text{number of }\ce{K+}) \times (\text{charge of }\ce{K+})^2\}\ + \\ \{(\text{concentration of }\ce{KCl}\text{ in M}) \times (\text{number of }\ce{Cl-}) \times (\text{charge of }\ce{Cl-})^2\} \end{array}\right] \\ & = \tfrac 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{align} ==Non-ideal solutions==