Relation Between Ka And Kb, Common Ion Effect
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Weak acid is related is related to its conjugate base through equilibrium constant expression ka HA +H2O â†” H3O+ +A- Ka = $\frac{\text{[}{{\text{H}}_{\text{3}}\text{O}}^{\text{+}}\text{][}{\text{A}}^{\text{-}}\text{]}}{\text{[HA]}}$                                                                                                                          Weak base is related is related to its conjugate acid through equilibrium constant expression kb BOH + H2O â†” B+ + OH- Kb =  $\frac{\text{[B}{\text{}}^{\text{+}}\text{][}{\text{OH}}^{\text{-}}\text{]}}{\text{[BOH]}}$    As the conjugated base pairs are related through the equilibrium constant we can assume that the equilibrium constant for an acid-base pair also related to each other. Consider the dissociation of weak acid in water HA +H2O â†” H3O+ +A-  Ka = $\frac{\text{[}{{\text{H}}_{\text{3}}\text{O}}^{\text{+}}\text{][}{\text{A}}^{\text{-}}\text{]}}{\text{[HA]}}$     ...........(1) HA being a weak acid it has strong conjugate base A- The dissociation equilibrium of strong conjugate base in water is A-  + H2O â†” HA +OH-  Kb = $\frac{\text{[HA][}{\text{A}}^{\text{-}}\text{]}}{\text{[}{\text{A}}^{\text{-}}\text{]}}$      ...........(2) Multiplying equation 1 & 2 Ka * Kb  = $\frac{\text{[}{{\text{H}}_{\text{3}}\text{O}}^{\text{+}}\text{][}{\text{A}}^{\text{-}}\text{]}}{\text{[HA]}}$ * $\frac{\text{[HA][}{\text{A}}^{\text{-}}\text{]}}{\text{[}{\text{A}}^{\text{-}}\text{]}}$               = [H3O+ ][ OH-] = k w  k w  = Ionic product of water âˆ´  ka * kb = k w Common ion effect:  The common ion effect is defined as the shift in the position of an ionic equilibrium caused by the addition of a solute that provides an ion which is the part of equilibrium. Consider the dissociation of acetic acid in water The equilibrium is represented as  CH3COOH (aq) â†” CH3COO- +H3O+ To this solution add a small amount of sodium acetate. dissociation of sodium acetate is represented as CH3COONa â†’ CH3COO- +Na+ Since the concentration of CH3COO-  ions increased in the solution ,according to Le Chatelier,s principle the equilibrium will be shifted to left. Due to the presence of common ions CH3COO- the equilibrium will be shifted to the left side. And the dissociation of  CH3COOH is suppressed.

#### Summary

Weak acid is related is related to its conjugate base through equilibrium constant expression ka HA +H2O â†” H3O+ +A- Ka = $\frac{\text{[}{{\text{H}}_{\text{3}}\text{O}}^{\text{+}}\text{][}{\text{A}}^{\text{-}}\text{]}}{\text{[HA]}}$                                                                                                                          Weak base is related is related to its conjugate acid through equilibrium constant expression kb BOH + H2O â†” B+ + OH- Kb =  $\frac{\text{[B}{\text{}}^{\text{+}}\text{][}{\text{OH}}^{\text{-}}\text{]}}{\text{[BOH]}}$    As the conjugated base pairs are related through the equilibrium constant we can assume that the equilibrium constant for an acid-base pair also related to each other. Consider the dissociation of weak acid in water HA +H2O â†” H3O+ +A-  Ka = $\frac{\text{[}{{\text{H}}_{\text{3}}\text{O}}^{\text{+}}\text{][}{\text{A}}^{\text{-}}\text{]}}{\text{[HA]}}$     ...........(1) HA being a weak acid it has strong conjugate base A- The dissociation equilibrium of strong conjugate base in water is A-  + H2O â†” HA +OH-  Kb = $\frac{\text{[HA][}{\text{A}}^{\text{-}}\text{]}}{\text{[}{\text{A}}^{\text{-}}\text{]}}$      ...........(2) Multiplying equation 1 & 2 Ka * Kb  = $\frac{\text{[}{{\text{H}}_{\text{3}}\text{O}}^{\text{+}}\text{][}{\text{A}}^{\text{-}}\text{]}}{\text{[HA]}}$ * $\frac{\text{[HA][}{\text{A}}^{\text{-}}\text{]}}{\text{[}{\text{A}}^{\text{-}}\text{]}}$               = [H3O+ ][ OH-] = k w  k w  = Ionic product of water âˆ´  ka * kb = k w Common ion effect:  The common ion effect is defined as the shift in the position of an ionic equilibrium caused by the addition of a solute that provides an ion which is the part of equilibrium. Consider the dissociation of acetic acid in water The equilibrium is represented as  CH3COOH (aq) â†” CH3COO- +H3O+ To this solution add a small amount of sodium acetate. dissociation of sodium acetate is represented as CH3COONa â†’ CH3COO- +Na+ Since the concentration of CH3COO-  ions increased in the solution ,according to Le Chatelier,s principle the equilibrium will be shifted to left. Due to the presence of common ions CH3COO- the equilibrium will be shifted to the left side. And the dissociation of  CH3COOH is suppressed.

#### References

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