Notes On Applications Of Common Ion Effect - CBSE Class 11 Chemistry
In a saturated solution if the concentration of any one of the ions is decreased, then as per the Lechateliers principle, more salt dissolves, and the equilibrium shifts towards the right, untill Ksp = Qsp. And if the concentration of any one of the ions is increased by adding an electrolyte, then the equilibrium shifts towards the left according to the Lechateliers principle, untill Ksp =Qsp. Common ion effect is used for the complete precipitation of one of the ions as its sparingly soluble salt with a very low value of solubility product for gravimetric estimation. Ex: Silver ions are precipitated as silver chloride, Barium ions as Barium sulphate, and Ferric ion as Ferric chloride or Ferric sulphate.  The common ion effect is not only used in the quantitative analysis of compounds, but is also for their purification.  Ex: Sodium chloride, along with impurities such as Sodium sulphate and Magnesium sulphatecan be purified by applying this principle.  When hydrogen chloride gas is passed through a saturated solution of sodium chloride, the precipitation of sodium chloride increases and dissociation of sodium chloride decreases due to the chloride ion, which acts as a common ion.Thus Sodium chloride obtained, is free from impurities.  Relation between the solubilityand H+ ion concentration for a mixture of a weak acid and its salt. Ex: Weak acid HX and its salt MX.      HX + MX  HX = Weak acid  MX = Salt of weak acid  MX ⇌M+ + X-  Ksp = [M+][X-]                          HX(aq)  ⇌ H+ (aq) + X -(aq)                       Ka = $\frac{\text{[H}⁺\text{(aq)}\text{]+[X}⁻\text{(aq)]}}{\text{[HX(aq)]}}$                       $\frac{\text{[X}⁻\text{]}}{\text{[HX]}}=\frac{\text{K}ₐ}{\text{[H}⁺\text{]}}$ Taking inverse of both side and adding 1 we get                                   $\frac{\left[\text{HX}\right]}{\left[{\text{X}}^{\text{-}}\right]}\text{+ 1 =}\frac{\left[{\text{H}}^{\text{+}}\right]}{{\text{K}}_{\text{a}}}\text{+ 1}$                   $\frac{\text{[HX] + [}{\text{X}}^{\text{-}}\text{]}}{\left[{\text{X}}^{\text{-}}\right]}\mathrm{\text{=}}\frac{\mathrm{\text{}}\left[{\text{H}}^{\text{+}}\right]\text{}+\text{}{\text{K}}_{\text{a}}}{{\text{K}}_{\text{a}}}$                   $\frac{\left[{\text{X}}^{-}\right]}{\mathrm{\text{[HX] + [}}{\text{X}}^{-}\mathrm{\text{]}}}\mathrm{\text{=}}\frac{{\text{K}}_{\text{a}}}{\mathrm{\text{}}\left[{\text{H}}^{+}\right]\mathrm{\text{}}+\mathrm{\text{}}{\text{K}}_{\text{a}}}$ = f                 Ksp = [S][fS] = S2f = S2[[Ka] / [Ka]+[H+]  ]   '.' ( [Ka] / [Ka]+[H+]  = f)                                 S = √(Ksp/f) =  $\sqrt{\frac{{\text{K}}_{\text{sp}}\text{}{\text{K}}_{\text{a}}\text{+}{\text{K}}_{\text{sp}}\text{[}{\text{H}}^{\text{+}}\text{]}}{{\text{K}}_{\text{a}}}}$                     or rearranging   S = ${\left\{\frac{{\text{K}}_{\text{sp}}\text{([}{\text{H}}^{\text{+}}\text{] +}{\text{K}}_{\text{a}}\text{)}}{{\text{K}}_{\text{a}}}\right\}}^{\text{2}}$ Thus, solubility increases with decrease in pH and increase in H+ ion concentration.

Summary

In a saturated solution if the concentration of any one of the ions is decreased, then as per the Lechateliers principle, more salt dissolves, and the equilibrium shifts towards the right, untill Ksp = Qsp. And if the concentration of any one of the ions is increased by adding an electrolyte, then the equilibrium shifts towards the left according to the Lechateliers principle, untill Ksp =Qsp. Common ion effect is used for the complete precipitation of one of the ions as its sparingly soluble salt with a very low value of solubility product for gravimetric estimation. Ex: Silver ions are precipitated as silver chloride, Barium ions as Barium sulphate, and Ferric ion as Ferric chloride or Ferric sulphate.  The common ion effect is not only used in the quantitative analysis of compounds, but is also for their purification.  Ex: Sodium chloride, along with impurities such as Sodium sulphate and Magnesium sulphatecan be purified by applying this principle.  When hydrogen chloride gas is passed through a saturated solution of sodium chloride, the precipitation of sodium chloride increases and dissociation of sodium chloride decreases due to the chloride ion, which acts as a common ion.Thus Sodium chloride obtained, is free from impurities.  Relation between the solubilityand H+ ion concentration for a mixture of a weak acid and its salt. Ex: Weak acid HX and its salt MX.      HX + MX  HX = Weak acid  MX = Salt of weak acid  MX ⇌M+ + X-  Ksp = [M+][X-]                          HX(aq)  ⇌ H+ (aq) + X -(aq)                       Ka = $\frac{\text{[H}⁺\text{(aq)}\text{]+[X}⁻\text{(aq)]}}{\text{[HX(aq)]}}$                       $\frac{\text{[X}⁻\text{]}}{\text{[HX]}}=\frac{\text{K}ₐ}{\text{[H}⁺\text{]}}$ Taking inverse of both side and adding 1 we get                                   $\frac{\left[\text{HX}\right]}{\left[{\text{X}}^{\text{-}}\right]}\text{+ 1 =}\frac{\left[{\text{H}}^{\text{+}}\right]}{{\text{K}}_{\text{a}}}\text{+ 1}$                   $\frac{\text{[HX] + [}{\text{X}}^{\text{-}}\text{]}}{\left[{\text{X}}^{\text{-}}\right]}\mathrm{\text{=}}\frac{\mathrm{\text{}}\left[{\text{H}}^{\text{+}}\right]\text{}+\text{}{\text{K}}_{\text{a}}}{{\text{K}}_{\text{a}}}$                   $\frac{\left[{\text{X}}^{-}\right]}{\mathrm{\text{[HX] + [}}{\text{X}}^{-}\mathrm{\text{]}}}\mathrm{\text{=}}\frac{{\text{K}}_{\text{a}}}{\mathrm{\text{}}\left[{\text{H}}^{+}\right]\mathrm{\text{}}+\mathrm{\text{}}{\text{K}}_{\text{a}}}$ = f                 Ksp = [S][fS] = S2f = S2[[Ka] / [Ka]+[H+]  ]   '.' ( [Ka] / [Ka]+[H+]  = f)                                 S = √(Ksp/f) =  $\sqrt{\frac{{\text{K}}_{\text{sp}}\text{}{\text{K}}_{\text{a}}\text{+}{\text{K}}_{\text{sp}}\text{[}{\text{H}}^{\text{+}}\text{]}}{{\text{K}}_{\text{a}}}}$                     or rearranging   S = ${\left\{\frac{{\text{K}}_{\text{sp}}\text{([}{\text{H}}^{\text{+}}\text{] +}{\text{K}}_{\text{a}}\text{)}}{{\text{K}}_{\text{a}}}\right\}}^{\text{2}}$ Thus, solubility increases with decrease in pH and increase in H+ ion concentration.

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