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Equilibrium

Question
CBSEENCH11008380

The ionisation constant of ammonium hydroxide is 1.77 x 10-5 at 298 K. Hydrolysis constant of ammonium chloride is 

  • 5.65 x 10-10

  • 6.50 x 10-12

  • 5.65 x 10-13

  • 5.65 x 10-12

Solution

A.

5.65 x 10-10

Given comma space straight K subscript straight a space left parenthesis NH subscript 4 OH right parenthesis space equals space 1.77 space straight x space 10 to the power of negative 5 end exponent

NH subscript 4 OH space leftwards harpoon over rightwards harpoon space NH subscript 4 to the power of plus space plus space OH to the power of minus

straight K subscript straight a space equals space fraction numerator left square bracket NH to the power of plus subscript 4 right square bracket left square bracket OH to the power of minus right square bracket over denominator left square bracket NH subscript 4 OH right square bracket end fraction space equals space 1.77 space straight x space 10 to the power of negative 5 end exponent space... space left parenthesis straight i right parenthesis
Hydrolysis of NH4Cl takes place as,
NH4Cl + H2O → NH4OH + HCl
or 
NH4+ +H2O → NH4OH + H+
Hydrolysis constant, Kh

straight K subscript straight h space equals space fraction numerator left square bracket NH subscript 4 OH right square bracket left square bracket straight H to the power of plus right square bracket over denominator left square bracket NH subscript 4 to the power of plus right square bracket end fraction space... space left parenthesis ii right parenthesis

or space straight K subscript straight h space equals space fraction numerator left square bracket NH subscript 4 OH to the power of plus right square bracket left square bracket OH to the power of minus right square bracket over denominator left square bracket NH subscript 4 to the power of plus right square bracket left square bracket OH to the power of minus right square bracket end fraction space... space left parenthesis iii right parenthesis

from space eqs. space left parenthesis straight i right parenthesis space and space left parenthesis iii right parenthesis

straight K subscript straight h space equals space straight K subscript straight w over straight K subscript straight a space left square bracket space because space left square bracket OH to the power of minus right square bracket left square bracket straight H to the power of plus right square bracket space equals space straight K subscript straight w right square bracket
equals space fraction numerator 10 to the power of negative 14 end exponent over denominator 1.77 space straight x space 10 to the power of negative 5 end exponent end fraction
space equals space 5.65 space straight x space 10 to the power of minus to the power of 10