Question #91010
1 Answer
Here's what I got.
Explanation:
Silver thiocyanate is insoluble in water, which implies that a dissociation equilibrium is established when this salt is dissolved in water.
#"AgCNS"_ ((s)) rightleftharpoons "Ag"_ ((s))^(+) + "CNS"_ ((aq))^(-)#
Your goal here is to figure out the equilibrium concentration of the silver cations and of the thiocyanate anions,
If you take
#["Ag"^(+)] = s#
#["CNS"^(-)] = s#
By definition, the solubility product constant for silver thiocyanate is equal to
#K_(sp) = ["Ag"^(+)] * ["CNS"^(-)]#
which can be rewritten as
#1.16 * 10^(-12) = s * s = s^2#
Solve for
#s = sqrt(1.16 * 10^(-12)) = 1.08 * 10^(-6)#
Since
#color(darkgreen)(ul(color(black)(s = 1.08 * 10^(-6)color(white)(.)"mol L"^(-1))))#
To find the solubility in grams per liter, use the molar mass of the salt
#1.08 * 10^(-6) color(red)(cancel(color(black)("moles")))/"L" * "165.95 g"/(1color(red)(cancel(color(black)("mole AgCNS")))) = color(darkgreen)(ul(color(black)(1.79 * 10^(-4)color(white)(.)"g L"^(-1))))#
The values are rounded to three sig figs.