ACTIVITY COEFFICIENTS OF ELECTROLYTES & IONIC STRENGTH

September 8, 2022
by Bhoomika Sheladiya

What is Activity?

Activity means solution concentration in terms of Molality. It means moles per kg of the solvent. Activity coefficients are one constant. 

Consider the dissociation of a univalent electrolyte as

\[\displaystyle MA\rightleftharpoons {{M}^{+}}+{{A}^{-}}\]

The law of chemical equilibrium as,

\[\displaystyle K=\frac{{\left( {{{a}_{{{{M}^{+}}}}}} \right)\left( {{{a}_{{{{A}^{-}}}}}} \right)}}{{\left( {{{a}_{{MA}}}} \right)}}-----(1)\]
\[\displaystyle \text{Activity a =}\gamma \text{m --------(2)}\]
\[\displaystyle \gamma =\text{activity coefficient}\]

Now, put the value of equation (1) in equation (2), so we can write as,

\[\displaystyle K=\frac{{\left( {{{\gamma }_{{{{M}^{+}}}}}{{m}_{{{{M}^{+}}}}}} \right)\left( {{{\gamma }_{{{{A}^{+}}}}}{{m}_{{{{A}^{+}}}}}} \right)}}{{{{\gamma }_{{MA}}}.{{m}_{{mA}}}}}\]
\[\displaystyle =\left( {\frac{{{{\gamma }_{{{{M}^{+}}}}}{{\gamma }_{{{{A}^{+}}}}}}}{{{{\gamma }_{{MA}}}}}} \right)\left( {\frac{{{{m}_{{{{M}^{+}}}}}{{m}_{{{{A}^{+}}}}}}}{{{{m}_{{mA}}}}}} \right)-----(3)\]

Activity coefficient of various electrolytes at different concentration can be calculated from above equation.

IONIC STRENGTH

Ionic Strength is the electrical intensity in the solution due to the presence of ions. Mathematically expressed as,

\[\displaystyle I=\frac{1}{2}\left( {{{m}_{1}}Z_{1}^{2}+{{m}_{2}}Z_{2}^{2}+{{m}_{3}}Z_{3}^{2}+......} \right)-----(1)\]

Here, m1, m2, m3 = Molalities, and Z1, Z2, Z3 = Valencies of various ions present in the solution

For single electrolytes, for example, Zinc sulphate, Potassium chloride, and Sodium chloride, equation (1) may be expressed as one for cation and the other for the anion,

\[\displaystyle I=\frac{1}{2}\left( {{{m}_{+}}Z_{+}^{2}+{{m}_{-}}Z_{-}^{2}} \right)-----(2)\]

Here, m+ and m– = molalities and Z+ and Z– = valencies of anion and cation

Consider one example;

The ionic strength of a solution is 0.1 molal in KCl and 0.01 molal CaCl2. Suppose complete ionization, calculated as below,

Molality of K+ ion m1 = 0.1

Molality of Ca+2 ion m2 = 0.01

Total molality of Cl– ion m3 = 0.1 + 0.01 = 0.11

According to the Ionic strength equation,

\[\displaystyle I=\frac{1}{2}\left( {{{m}_{+}}Z_{+}^{2}+{{m}_{+}}Z_{+}^{2}+{{m}_{-}}Z_{-}^{2}} \right)\]
\[\displaystyle =\frac{1}{2}\left( {0.1{{{\left( 1 \right)}}^{2}}+0.01{{{\left( 2 \right)}}^{2}}+0.11{{{\left( 1 \right)}}^{2}}} \right)\]
\[\displaystyle =0.125\]
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About the author

Bhoomika Sheladiya

BSc. (CHEMISTRY) 2014- Gujarat University
MSc. (PHYSICAL CHEMISTRY) 2016 - School of Science, Gujarat University

Junior Research Fellow (JRF)- 2019
AD_HOC Assistant Professor-(July 2016 to November 2021)

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