What is the solubility of AgBr in a solution of AgBr and AgSCN? Given rarr K_("sp AgSCN") =10^(-12) K_("sp AgBr")=5xx10^(-13) Thank you:)

2 Answers
Oct 15, 2017

x = sqrt((1xx10^(-12)xx12)/18

Explanation:

I would represent the dissociated ions in equal amounts as they are in equilibrium.

"AgSCN" rightleftharpoons "Ag"^+ + "SCN"^-
color(white)(xxxxxxxx)xcolor(white)(xxxxx)x

"AgBr" rightleftharpoons "Ag"^+ + "Br"^-
color(white)(xxxxxxl)ycolor(white)(xxxm)y

K_("sp AgSCN") = ["Ag"^+]["SCN"^-]

K_("sp AgSCN") = (x+y)(x) = 10^(-12)color(white)(xxxxxxl)(1)

K_("sp AgBr") = ["Ag"^+]["Br"^-]

K_("sp AgBr") = (x+y)(y) = 5xx10^(-13)color(white)(xxxmll)(2)

(x+y) = (10^(-12))/xcolor(white)(xxxxxxmmmmmmmll)(1)

(10^(-12))/x xx y = 5xx10^(-13)color(white)(xxxxxxmmmllll)(2)

y/x = 5/12

y = (5x)/12

((5x)/12 + x)(x) = 1xx10^(-12)

(17x^2)/12 = 1xx10^(-12)

x = sqrt((1xx10^(-12)xx12)/17

"solubility of " [Ag^+] " in this solution"= 8.4016805xx10^-7

Dec 27, 2017

Well, if the solution contains both, then since concentration is a state function, we can construct two sequential reactions.

"AgSCN"(s) rightleftharpoons "Ag"^(+)(aq) + "SCN"^(-)(aq)
"AgBr"(s) rightleftharpoons "Ag"^(+)(aq) + "Br"^(-)(aq)

We can define the solubility of "AgBr" as given by ["Ag"^(+)], as it is the ion with a coefficient of 1 and is shared between the two compounds.

Assuming the solution was saturated with "AgSCN"(aq) already, ["Ag"^+]_i ("AgSCN") = sqrt(10^(-12)) = 10^(-6) "M", while ["Br"^(-)]_i = "0 M".

The ICE Table would give for "AgBr" in saturated "AgSCN"(aq):

5 xx 10^(-13) = ["Ag"^+]["Br"^-] = (10^(-6) + s)s

=> color(blue)(s = ["Ag"^(+)])

= color(blue)(3.66 xx 10^(-7) "M")

(The solution with the small s approximation is 5.00 xx 10^(-7) "M", which is 36.6% error, so the approximation would not be good.)

This is in contrast to its solubility by itself:

"Solubility"_("AgBr"(s,"pure")) = sqrt(5 xx 10^(-13))

= 7.07 xx 10^(-7) "M"

So the solubility of "AgBr" in aqueous solution has decreased, in accordance with the common ion effect.