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Equilibrium

Question
CBSEENCH11006597

Determine the pH of a solution obtained by mixing equal volumes of 0·015N NH4OH and 0·15N NH4NO3 solutions. (Kb for NH4OH is 1·8 × 10–5).

Solution
For a basic buffer, Henderson equation is
pOH space equals space pK subscript straight b space plus space log space fraction numerator open square brackets Salt close square brackets over denominator open square brackets Base close square brackets end fraction space space space space... left parenthesis 1 right parenthesis
Here,  on mixing equal volumes of two solutions,
     open square brackets NH subscript 4 OH close square brackets space equals space space fraction numerator 0.015 over denominator 2 end fraction space equals 0.0075 space straight N
open square brackets NH subscript 4 NO subscript 3 close square brackets space equals space fraction numerator 0.015 over denominator 2 end fraction equals space 0.075 space straight N
space space space space space space pK subscript straight b space equals space log space straight K subscript straight b
space space space space space space space space space space space space space equals log space left parenthesis 1.8 space cross times space 10 to the power of negative 5 end exponent right parenthesis
space space space space space space space space space space space
Substituting the values in equation (1), we get,
 
    pOH space equals space 4.7447 space plus space log space fraction numerator 0.075 over denominator 0.0075 end fraction
space space space space space space space equals 4.7447 space plus space log space 10
space space space space space space space equals 4.7447 space plus 1 space equals space 5.7447
But space pH space plus space pOH space equals space 14
therefore space space space space pH space equals space 14 space minus space pOH
space space space space space space space space space space space space equals space 14 minus 5.7447 space equals space 8.2553