-->

Equilibrium

Question
CBSEENCH11006574

Derive the relation,straight K subscript straight h space equals space straight K subscript straight w over straight K subscript straight b space in the case of hydrolysis of salts of strong acids and weak acids.

Solution
Let the salt of strong acid and weak base (such as CuSO4) be X Y and the hydrolysis reaction represented as:
       straight X to the power of plus space plus space straight H subscript 2 straight O space rightwards harpoon over leftwards harpoon space space space space stack XOH space plus space straight H to the power of plus with left square bracket Cationic space hydrolysis right square bracket below
Applying space the space law space of space chemical space equilibrium comma
space space space space straight K subscript straight b space equals space fraction numerator open square brackets XOH close square brackets space open square brackets straight H to the power of plus close square brackets over denominator open square brackets straight X to the power of plus close square brackets end fraction
space space space space space space space space space equals fraction numerator open square brackets Free space base close square brackets space open square brackets Free space acid close square brackets over denominator open square brackets Unhydrolysed space salt close square brackets end fraction space space space space space space... left parenthesis 1 right parenthesis
[H2O] remains constants as it is taken in large excess. Following equilibrium also occurs:
        space space space space space space space space space space space space space space XOH space space space rightwards harpoon over leftwards harpoon space space space space straight X to the power of plus space plus space OH to the power of minus
space space space space space space space space space space space space space space straight H subscript 2 straight O space space rightwards harpoon over leftwards harpoon space space space straight H to the power of plus space plus space OH to the power of minus
By space the space law space of space chemical space equilibrium comma
space space space space space space space space straight K subscript straight b space equals space fraction numerator open square brackets straight X to the power of plus close square brackets space open square brackets OH to the power of minus close square brackets over denominator open square brackets XOH close square brackets end fraction space space space space space space space space space space... left parenthesis 2 right parenthesis
and space space space straight K subscript straight w space space equals space open square brackets straight H to the power of plus close square brackets space open square brackets OH to the power of minus close square brackets space space space space space space space space space space space... left parenthesis 3 right parenthesis
Dividing space left parenthesis 3 right parenthesis space by space left parenthesis 2 right parenthesis comma
space space space straight K subscript straight w over straight K subscript straight b space space equals space fraction numerator open square brackets straight H to the power of plus close square brackets space open square brackets XOH close square brackets over denominator open square brackets straight X to the power of plus close square brackets end fraction space space space space space space space space space space... left parenthesis 4 right parenthesis space space space space space
Substituting the values from equation (1) in equation (4),
      straight K subscript straight h space equals space straight K subscript straight w over straight K subscript straight b