1.16.3: Ionic Strength: Ional Concentration
The ionic strength of a salt solution I containing \(\mathrm{i}\)-ionic substances is defined by equation (a); \(\mathrm{m}_{j}\) is the molality of ionic substance-\(j\), charge number \(\mathrm{z}_{j}\) [1].
\[\mathrm{I}=(1 / 2) \, \sum_{\mathrm{j}=\mathrm{i}}^{\mathrm{j}=\mathrm{i}} \mathrm{m}_{\mathrm{j}} \, \mathrm{z}_{\mathrm{j}}^{2} \nonumber \]
The sum is taken over all \(\mathrm{i}\)-ionic substances in the solution. The situation is slightly complicated by the fact some authors use the term ‘ionic strength’ where the concentration \(\mathrm{c}_{j}\) (expressed using the unit, \(\mathrm{mol dm}^{-3}\)) replaces \(\mathrm{m}_{j}\). The substitution is reasonably satisfactory for dilute salt solutions at ambient \(\mathrm{T}\) and \(\mathrm{p}\) where the mass of water, volume \(1 \mathrm{~dm}^{3}\), is approx. \(1 \mathrm{~kg}\).
The ional concentration of a salt solution \(\Gamma\) is defined by equation (b) where \(\mathrm{c}_{j}\) is expressed using the unit, \(\mathrm{mol dm}^{-3}\) [2].
\[\Gamma=\sum_{j=i}^{j=i} c_{j} \, z_{j}^{2} \nonumber \]
Footnotes
[1] An aqueous solution contains \(\mathrm{K}_{2}\mathrm{SO}_{4}\) (\(0.1 \mathrm{~mol}\)) in \(1 \mathrm{~kg}\) of water(\(\ell\)).
\(\mathrm{m}\left(\mathrm{K}_{2} \mathrm{SO}_{4}\right)=0.1 \mathrm{~mol} \mathrm{~kg}^{-1} ; \mathrm{m}\left(\mathrm{K}^{+}\right)=0.2 \mathrm{~mol} \mathrm{~kg}^{-1}\)
and \(\mathrm{m}\left(\mathrm{SO}_{4}{ }^{2-}\right)=0.1 \mathrm{~mol} \mathrm{~kg}^{-1}\)
Hence \(\mathrm{I}=(1 / 2) \,\left[(0.2)+\left(2^{2} \mathrm{X} 0.1\right)\right]=0.3 \mathrm{~mol} \mathrm{~kg}^{-1}\)
[2] H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolytic Solutions, , Reinhold, New York, 2nd. revised edn.1950, p.33.