3.3 The Solubility Product Constant, Ksp
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We will now return to an important mathematical relationship we first learned about in our unit on Equilibrium (Unit 3, Section 2.1), the equilibrium constant expression.
Recall that for any general reaction:
aA + bB | cD + dD |
an equilibrium constant expression can be defined as:
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Since saturated solutions are equilibrium systems, we can apply this mathematical relationship to solutions. We will refer to our equilibrium constant as Ksp, where "sp" stands for "solubility product"
For our silver sulfate saturated solution,
Ag2SO4 (s) | 2Ag+(aq) + SO42-(aq) |
we can write our solubility product constant expression as
Ksp | = | [Ag+]2[SO42-] [Ag2SO4] |
But remember from our earlier introduction to the equilibrium constant expression that the concentrations of solids and liquids are NOT included in the expression because while their amounts will change during a reaction, their concentrations will remain constant. Therefore, we will write our solubility product constant expression for our saturated silver sulfate solution as:
Ksp= [Ag+]2[SO42-]
Please note that it is VERY IMPORTANT to include the ion charges when writing this equation.
Try this example:
Write the expression for the solubility product constant, Ksp, for Ca3(PO4)2.
Step 1: Begin by writing the balanced equation for the reaction. Remember that polyatomic ions remain together as a unit and do not break apart into separate elements.
Ca3(PO4)2 (s) | 3 Ca2+(aq) + 2 PO43-(aq) |
Step 2: Write the expression for Ksp:
Ksp= [Ca2+]3[PO43-]2
Solubility Product Tables that give Ksp values for various ionic compounds are available. Because temperature affects solubility, values are given for specific temperatures (usually 25°C).
Recall what we learned about Keq
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Ksp, which again is just a special case of Keq, provides us with the same useful information:
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Iron(II) sulfide, FeS, is an example of a low Ksp : Ksp = 4 ×10-19 In a saturated solution of FeS there would be few Fe2+ or S2- ions. |
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An example of a relatively large Ksp would be for lead(II) chloride, PbCl2 which has a Ksp of 1.8 ×10-4 A saturated solution of PbCl2 would have a relatively high concentration of Pb 2+ and Cl - ions. |
Calculations involving Ksp
There are several types of problems we can solve:
1. | Calculating Ksp when concentration of a saturated solution is known. | |
Example | The concentration of a saturated solution of BaSO4 is 3.90 × 10-5M. Calculate Ksp for barium sulfate at 25°C | |
Solution | Always begin problems involving Ksp by writing a balanced equation: |
BaSO4 (s) Ba2+(aq) + SO42- (aq)
Next, write the Ksp expression:
Ksp= [Ba2+][SO42-]
The question provides us with the concentration of the solution, BaSO4 . We need to find the concentration of the individual ions for our equation.
Recall from Section 2.5 - since 1 mole of BaSO4 produces 1 mole of Ba2+ and also 1 mole of SO42-, then . . .
[BaSO4] = 3.90 × 10-5M
[Ba2+] = 3.90 × 10-5M
[SO42-] = 3.90 × 10-5M
Substitute values into the Ksp expression and solve for the unknown:
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2. | Calculating ion concentrations when Ksp is known. | |
Example | Ksp for MgCO3 at 25°C is 2.0 × 10-8. What are the ion concentrations in a saturated solution at this temperature? | |
Solution | As always, begin with a balanced equation: |
MgCO3(s) Mg2+(aq) + CO32-(aq)
Write the Ksp expression: |
Ksp= [Mg2+][CO32-]
For this example, we are given the value for Ksp and need to find the ion concentrations. We will let our unknown ion concentrations equal x. The balanced equation tells us that both Mg2+ and CO32- will have the same concentration! | |
Substitute values into the equation and solve for the unknown |
Ksp
= [Mg2+][CO32-]
x2 = 2.0 × 10-8
x = √(2.0 × 10-8)
find the square root of 2.0 × 10-8
= 1.4× 10-4M
x = [Mg2+]
= 1.4× 10-4M
Answer
AND x = [CO32-]
= 1.4× 10-4M