Question

At 298 K, calculate the pH of 0·23 M weak acid (ionisation constant = 7·3 × 10^–6).

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

For the weak acid HX in an aqueous solution,

HX space plus space straight H subscript 2 straight O space space space rightwards harpoon over leftwards harpoon space space straight H subscript 3 straight O to the power of plus space space plus space straight X to the power of minus

If C is the initial concentration of HX and

straight alpha

be its degree of dissociation, then
HX + H₂O

rightwards harpoon over leftwards harpoon

H₃O⁺ + X^-
Initial conc. C mol L^- 0 0
Equilibrium

straight C minus Cα

Cα

Cα

conc
Applying the law of chemical equilibrium,

straight K subscript straight alpha space equals space fraction numerator open square brackets straight H subscript 3 straight O to the power of plus close square brackets space open square brackets straight X to the power of minus close square brackets over denominator open square brackets HX close square brackets end fraction space space space space space equals space fraction numerator Cα space cross times space Cα over denominator straight C minus Cα end fraction space space space space space space equals space fraction numerator straight C squared straight alpha squared over denominator straight C left parenthesis 1 minus straight alpha right parenthesis end fraction space space space space space space equals fraction numerator Cα squared over denominator 1 minus straight alpha end fraction

or space space space straight K subscript straight alpha space equals space Cα squared space space space space space space space space space space space space open square brackets because space space 1 minus straight alpha space asymptotically equal to space 1 close square brackets or space space space space straight alpha space equals space square root of straight K subscript straight alpha over straight C end root space space space space space space space space space equals square root of fraction numerator 7.3 space cross times space 10 to the power of negative 6 end exponent over denominator 0.23 end fraction end root space space space space space space space space equals square root of 31.74 space cross times space 10 to the power of negative 6 end exponent end root space space space space space space space space equals space 5.63 space cross times space 10 to the power of negative 3 end exponent

open square brackets straight H subscript 3 straight O to the power of plus close square brackets space equals space Cα space equals space 0.23 space cross times space 5.63 space cross times space 10 to the power of negative 3 end exponent space space space space space space space space space space space space equals space 1.295 space cross times space 10 to the power of negative 3 end exponent straight M

We space know comma space space space space pH space equals space minus log space open square brackets straight H subscript 3 straight O to the power of plus close square brackets space space space space space space space space equals space minus log space left parenthesis 1.295 space cross times 10 to the power of negative 3 end exponent right parenthesis space space space space space space space space equals negative left square bracket log space 1.295 space minus space 3 space log space 10 right parenthesis space space space space space space space space space space space space equals negative left square bracket 0.1122 minus space 3 right square bracket space space space left square bracket because space log space 10 space equals space 1 right square bracket space space space space space space space space equals negative 0.1122 space plus space 3 space space space space space space space space equals 2.8878 space almost equal to space 2.89 space space space space space

For Daily Free Study Material Join wiredfaculty