Question

$Derive space straight K subscript straight h space equals space fraction numerator straight K subscript straight w over denominator straight K subscript straight a space straight K subscript straight b end fraction for space straight a space solution space of space salt space of space weak space acid space and space weak space base.$

Solution

Suppose the salt of weak acid and weak base is BA and its hydrolysis is represented as:

BA with salt below space plus space straight H subscript 2 straight O space space leftwards harpoon over rightwards harpoon space space space BOH with weak below space plus space HA with weak below

or space space straight B to the power of plus space plus space straight A to the power of minus space space plus space straight H subscript 2 straight O space space rightwards harpoon over leftwards harpoon space space space space BOH space plus space HA

It involves both cationic as well as ionic hydrolysis.

Now comma space space space straight K subscript straight h space equals space fraction numerator open square brackets BOH close square brackets open square brackets HA close square brackets over denominator open square brackets straight B to the power of plus close square brackets open square brackets straight A to the power of minus close square brackets end fraction space space space space space space space space... left parenthesis 1 right parenthesis Also space for space weak space acid comma space space space space space space space HA space rightwards harpoon over leftwards harpoon space space straight H to the power of plus space plus space straight A to the power of minus space space space space space space straight K subscript straight a space equals space fraction numerator open square brackets straight H to the power of plus close square brackets open square brackets straight A to the power of minus close square brackets over denominator open square brackets HA close square brackets end fraction space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis For space weak space base comma space space space space space space BOH space leftwards harpoon over rightwards harpoon space space straight B to the power of plus space plus space OH to the power of minus space space space space space straight K subscript straight b space space equals space fraction numerator open square brackets straight B to the power of plus close square brackets open square brackets OH to the power of minus close square brackets over denominator open square brackets BOH close square brackets end fraction space space space space space space space space space space space space space space... left parenthesis 3 right parenthesis

Also comma space space space space straight K subscript straight w 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... left parenthesis 4 right parenthesis

Multiplying equations (1), (2) and (3),

straight K subscript straight h. space straight K subscript straight a space. space straight K subscript straight b 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 plus close square brackets space equals space straight K subscript straight w space space space space left square bracket From space eq. space left parenthesis 4 right parenthesis right square bracket space space therefore space space space space space space straight K subscript straight h space equals space fraction numerator straight K subscript straight w over denominator straight K subscript straight a space straight K subscript straight b end fraction

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Equilibrium

Some More Questions From Equilibrium Chapter

What kind of molecules in a liquid can evaporate?

Name the factors on which vapour pressure of any liquid depends.

Which measurable property becomes constant in water vapour equilibrium?

Give an example from daily life in which there is gas solution equilibrium?

A crystal of common salt of a given mass is kept in its aqueous solution. After 24 hours, its mass remains the same. Is the crystal in equilibrium with the solution?

What is the role of forward and backward reactions at equilibrium of a reversible reaction?

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