If a 6.03 x 10-6.0 M solution of a weak acid is 20 % ionized, what is the pKa for the acid?

Question

If a 6.03 x 10-6.0 M solution of a weak acid is 20 % ionized, what is the pKa for the acid?

1 Answer

Impact of this question

2162 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-28T10:19:59

$p K_{a} = 6.52$ $pK_a=6.52$

Explanation:

If the formula of a weak acid be reprsented as HA.then its dissociation in aqueous medium can be written as follows:

$H A + H_{2} O ⇌ H_{3} O^{+} + A^{-}$ $HA" "+H_2O""rightleftharpoons""H_3O^+""+" "A^-$

$I 1 m o l 0 m o l 0 m o l$ $color(red)(I)" "1" "mol" " 0" "mol" " 0" " "mol$

$C - α m o l α m o l α m o l$ $color(red)(C)" "-alpha" "mol" " alpha" "mol" " alpha" " "mol$

$E 1 - α m o l α m o l α m o l$ $color(red)(E)" "1-alpha" "mol" " alpha" "mol" " alpha" " "mol$

Where $α$ $alpha$ is the degree of dissociation of $H A$ $HA$

If cM be the initial concentration of the weak acid then the concentrations different species at equilibrium will be as follows

$[H A] = c (1 - α) M$ $[HA]=c(1-alpha)M$

$[H_{3} O^{+}] = c α M$ $[H_3O^+]=calphaM$

$[A^{-}] = c α M$ $[A^-]=calphaM$

The concentration of $H_{2} O$ $H_2O$ is irrelevant as it acts as sovent.

Now the acid dissociation constant

$K_{a} = \frac{[H_{3} O^{+}] [A^{-}]}{{[H A]}^{2}}$ $K_a=([H_3O^+][A^-])/[HA]^2$

$= \frac{(c α) \cdot (c α)}{c (1 - α)}$ $=((calpha)*(calpha))/(c(1-alpha))$

$= \frac{c α^{2}}{1 - α}$ $=(calpha^2)/(1-alpha)$

Given $c = 6.03 \times 10^{- 6} M and α = 20 % = 0.2$ $c=6.03xx10^-6M and alpha=20%=0.2$

$K_{a} = \frac{6.03 \times 10^{- 6} \cdot {(0.2)}^{2}}{1 - 0.2}$ $K_a=(6.03xx10^-6*(0.2)^2)/(1-0.2)$

$= \frac{6.03 \times 10^{- 6} \times 0.04}{0.8}$ $=(6.03xx10^-6xx0.04)/0.8$

$3.015 \times 10^{- 7}$ $3.015xx10^-7$

The $p K_{a}$ $pK_a$ of the weak acid

$p K_{a} = - {log K}_{a} = - log (3.015 \times 10^{- 7})$ $pK_a=-logK_a=-log(3.015xx10^-7)$

$= 7 - log 3.015 = 6.52$ $=7-log3.015=6.52$

Science

Math

Humanities

... and beyond

If a 6.03 x 10-6.0 M solution of a weak acid is 20 % ionized, what is the pKa for the acid?

1 Answer

Explanation:

Related questions

Impact of this question