5 Steps to a 5 AP Chemistry 2019

230 ❯ STEP 4. Review the Knowledge You Need to Score High

solids, liquids, and solvents are included in the equilibrium constant.) The Ksp expression

for the PbSO 4 system would be:

Ksp=[Pb]^2 +[SO] 4 2–

For this particular salt, the numerical value of Ksp is 1.6 × 10 -^8 at 25°C. Note that the

Pb^2 + and SO 42 - ions are formed in equal amounts, so the right-hand side of the equation

could be represented as [x]^2. If the numerical value of the solubility product constant is

known, then the concentration of the ions can be determined. And if one of the ion con-

centrations can be determined, then Ksp can be calculated.

For example, the Ksp of magnesium fluoride in water is 8 × 10 -^8. How many grams of

magnesium fluoride will dissolve in 0.250 L of water?

 +

==×

===×

=× =

×

=

+−

+− −

−

−+

−+

+

K

xx x

x

MgF(s) Mg (aq) 2F (aq)

[Mg][F ]8 10

()(2 )4 810

310[Mg ]

(3 10 molMg)

(L)

(0.250L)

(1 molMgF )(62.3gMgF )

(1 mol Mg )(1mol MgF)

0.05 g

2

2

sp

22 8

23 8

32

32

22

2

2

If a slightly soluble salt solution is at equilibrium and a solution containing one of

the ions involved in the equilibrium is added, the solubility of the slightly soluble salt is

decreased. For example, let’s again consider the PbSO 4 equilibrium:

PbSO( 4 s)Pb^2 +−(aq)+SO 42 (aq)

Suppose a solution of Na 2 SO 4 is added to this equilibrium system. The additional

sulfate ion will disrupt the equilibrium, by Le Cha^telier’s principle, and shift it to the

left, decreasing the solubility. The same would be true if you tried to dissolve PbSO 4 in

a solution of Na 2 SO 4 instead of pure water—the solubility would be lower. This applica-

tion of Le Cha^telier’s principle to equilibrium systems of slightly soluble salts is called the

common-ion effect. Calculations like the ones above involving finding concentrations and

Ksp can still be done, but the concentration of the additional common ion will have to be

inserted into the solubility product constant expression. Sometimes, if Ksp is very small and

the common ion concentration is large, the concentration of the common ion can simply

be approximated by the concentration of the ion added.

For example, calculate the silver ion concentration in each of the following solutions:

a. Ag 2 CrO 4 (s) + water

b. Ag 2 CrO 4 (s) + 1.00 M Na 2 CrO 4

Ksp = 1.9 × 10 -^12

a. Ag 24 CrO(s)2Ag(+−aq)C+ rO 42 (aq)

2 x x

Ksp = (2x)^2 (x) = 1.9 × 10 -^12 = 4 x^3

x = 7.8 × 10 -^5

[Ag+] = 2 x = 1.6 × 10 -^4 M