Question #a3dd1

1 Answer
Stefan V.
May 29, 2015

Your solution will have a pH equal to 4.0.

Since you're dealing with a weak acid, you can use an ICE table on its dissociation equilibrium to determine the equilibrium concentrations of the species involved in the reaction

#" "HA_((aq)) + H_2O_((l)) rightleftharpoons H_3O_((aq))^(+) + A_((aq))^(-)#
I.......1.........................................0.................0
C....(-x)......................................(+x).............(+x)
E.....1-x........................................x.................x

The acid dissociation constant, #K_a#, will be equal to

#K_a = ([H_3O^(+)] * [A^(-)])/([HA]) = (x * x)/(1-x) = x^2/(1-x)#

Since #K_a# has such a small value, you ca approximate (1-x) to be equal to 1, which would mean that

#K_a = x^2/1 = x^2 = 10^(-8) => x = sqrt(10^(-8)) = 10^(-4)#

Since#x# is equal to the equilibrium concentration of the hydronium ion, you'll have

#[H_3O^(+)] = 10^(-4)"M"#

Therefore, the pH of the solution will be

#pH_"sol" = -log([H_3O^(+)])#

#pH_"sol" = -log(10^(-4)) = color(green)(4.0)#

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