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.