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Equilibrium

Question
CBSEENCH11006564

The pH of 0·0041M hydrazine solution is 9·7. Calculate the ionisation constant Kb and pKb.

Solution

The reaction is
NH subscript 2 NH subscript 2 space plus space straight H subscript 2 straight O space space rightwards harpoon over leftwards harpoon space space space NH subscript 2 NH subscript 3 superscript plus space plus space OH to the power of minus
But space minus space log space open square brackets straight H to the power of plus close square brackets space equals space pH space equals space 9.7
or space space space log space open square brackets straight H to the power of plus close square brackets space equals space minus 9.7 space equals space minus 9 minus 0.7 space plus 1 space minus 1 space equals space 10 with bar on top. space 3
or space space space space open square brackets straight H to the power of plus close square brackets space equals space antilog space left parenthesis 10 with bar on top.3 right parenthesis space equals space 1.67 space cross times space 10 to the power of negative 10 end exponent straight M
Also comma space open square brackets OH to the power of minus close square brackets space equals space fraction numerator straight K subscript straight w over denominator open square brackets straight H to the power of plus close square brackets end fraction
space space space space space space space space space space space space equals fraction numerator 1 space cross times space 10 to the power of negative 14 end exponent over denominator 1.67 space space cross times space 10 to the power of negative 10 end exponent end fraction space equals 5 space.98 space cross times space 10 to the power of negative 5 end exponent straight M

Also space space space space space straight K subscript straight b space equals space fraction numerator open square brackets NH subscript 2 NH subscript 3 superscript plus close square brackets space open square brackets OH to the power of minus close square brackets over denominator open square brackets NH subscript 2 NH subscript 2 close square brackets end fraction space space space space... left parenthesis 1 right parenthesis
Putting space the space values space in space expression space left parenthesis 1 right parenthesis comma space we space have
straight K subscript straight b space equals space fraction numerator left parenthesis 5.98 space cross times 10 to the power of negative 5 end exponent right parenthesis squared over denominator 0.004 end fraction space equals space 8.96 space cross times space 10 to the power of negative 7 end exponent
pK subscript straight b space equals space minus log space straight K subscript straight b space equals space minus log space left parenthesis 8.96 space cross times space 10 to the power of negative 7 end exponent right parenthesis space equals space 6.04