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Equilibrium

Question
CBSEENCH11006374

It has been found that the pH of a 0.01 M solution of an organic  acid is 4.15. Calculate the concentration of the anion, the ionisation constant of the acid and its pKa.

Solution
pH equals 4.15 comma space straight c equals 0.01 straight M
pH equals negative log left square bracket straight H to the power of plus right square bracket equals 4.15
left square bracket straight H to the power of plus right square bracket equals antilog left parenthesis negative 4.15 right parenthesis equals 7.08 straight x 10 to the power of negative 5 end exponent space straight M
left square bracket straight H to the power of plus right square bracket equals space cα space equals 7.08 space straight x space 10 to the power of negative 5 end exponent space straight M
equals square root of cK subscript straight alpha space end root space equals square root of 0.01 straight K subscript straight alpha end root
Concentration space of space anion colon
left square bracket straight A to the power of minus right square bracket equals left square bracket straight H to the power of plus right square bracket space equals 7.08 space straight x 10 to the power of negative 5 end exponent space straight M
Ionisation space constant space of space the space acid colon
left square bracket straight H to the power of plus right square bracket space equals square root of 0.01 end root straight K subscript straight alpha space equals 7.08 space straight x 10 to the power of negative 5 end exponent
0.01 straight K subscript straight alpha space equals left parenthesis 7.08 space straight x 10 to the power of negative 5 end exponent right parenthesis squared

straight K subscript straight alpha equals fraction numerator left parenthesis 7.08 space straight x 10 to the power of negative 5 end exponent right parenthesis squared over denominator 0.01 end fraction space equals 5.01 space straight x 10 to the power of negative 7 end exponent
pK subscript straight a space equals negative logK subscript straight a
space equals negative log space 5.01 space straight x 10 to the power of negative 7 end exponent space equals 6.3