Wize High School Grade 12 Chemistry Textbook > Acids and Bases

Solubility Product Constant, Ksp

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Solubility and Ksp
Recall that a saturated solution is one that has the maximum quantity of solute dissolved. It is at this point that an equilibrium forms between the solid and the dissolved ions. 
Ex: AgCl(s)  ⇌  Ag+(aq) + Cl-(aq)
Increasing temperature can cause the solubility to increase


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Ksp= The solubility product constant
It is the equilibrium constant (K) that is specifically for saturated solutions
Write the Ksp expression for the above reaction in equilibrium:
 

Ksp=[Ag+][Cl-]

Watch Out!
Remember that solids or liquids are never included in any K expression!


For these solids, we can write out ICE tables similar to how we did earlier:

Let's say the Ksp=1.8x10-10 for the AgCl(s) at 25oC and we start with 0.2M of AgCl(s). We could be asked to find the concentrations for the ions at equilibrium.
1) Create an ICE Table 

2) Write out a Ksp expression and solve for x:
Ksp=[Ag+][Cl-]
1.8x10-10=x2
x=1.34x10-5 M = [Ag+]=[Cl-]

Wize Tip
If you are ever asked to solve for the "molar solubility" or "solubility" of a salt, they are asking you to solve for x like we just did! 
Solubility is referring to how much of a solid dissolves to give a saturated solution (at equilibrium)

The solubility of copper(II) arsenate, Cu3(AsO4)2, in pure water is 3.7×10-8 M. Calculate the value of Ksp for copper(II) arsenate from this data. 

6.9×10−386.9\times10^{-38}6.9×10−38

4.2×10−374.2\times10^{-37}4.2×10−37

2.5×10−362.5\times10^{-36}2.5×10−36

3.7×10−363.7\times10^{-36}3.7×10−36

7.5×10−367.5\times10^{-36}7.5×10−36

I don't know

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Q vs K to Predict Solubility
Recall:
There are three possible situations: 
Q = K: The system is at equilibrium. 
Q > K: The [products] is too high compared to [reactants]. The equilibrium will shift left. 
Q < K: The [products] is too low compared to [reactants]. The equilibrium will shift right. 

When asked to predict solubility, we should be able to identify whether a solution is unsaturated, saturated, or supersaturated! 

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Solubility Chart
The following table is a table that many teachers use (on a test this would be provided to you!!)
We can use it to figure out if a precipitate is likely to form or not
Then if we think a precipitate is likely to form, we will solve for Q and compare it to Ksp for that salt and if Q>Ksp we can confirm that a precipitate will form!!



Wize Concept
If a combination of ions is highly soluble, it means that no precipitate will form
If a combination of ions is has low solubility, it means a precipitate MIGHT form, but to see if a precipitate will form we need to make sure Q>K!

Let's see if we understand this table...
Decide whether the following salts could form a precipate or not:

1) NaCl

2) AgCl

3) AgI

4) NaNO3

Extra Practice

For the following reaction, define Ksp.
SrCO3(s) <----> Sr2+(aq) + CO32-(aq)

Given the following values of Ksp for four slightly soluble sulphides at 25 °C. 
  SulphideKspCdS3.6×10–29CuS8.7×10–36PbS8.4×10–28MnS5.1×10–15\def\arraystretch{1.5}
\begin{array}{c}
\rm Sulphide &&K_{sp}  \\ 
\hline
CdS&& 3.6 \times10^{–29}\\
CuS && 8.7 \times10^{–36} \\
PbS&& 8.4 \times 10^{–28} \\ 
MnS&&5.1 \times10^{–15}\\
\end{array}SulphideCdSCuSPbSMnS​​Ksp​3.6×10–298.7×10–368.4×10–285.1×10–15​​
Which one of the following ions exists in the lowest concentration in a solution in which the sulphide ion concentration had been fixed at some (fairly large) constant value at 25°C? 

Solubility Product: Ion Affects

You are trying to dissolve AgBr(s) in an aqueous solution.  Which salt should you add to increase the solubility of silver bromide?

Does a precipitate of PbBr2 form if 50.0 mL of 0.0100 M Pb(NO3)2 is mixed with 50.0 mL of 0.100 M NaBr? (Ksp PbBr2 = 2.1 x 10-6)

A student is adding a saturated solution of lead (II) sulphate (Ksp = 1.3 x 10-8) to a reaction mixture but the label which used to have the concentration given is missing.  Calculate the volume of solution the student needs to add in order to add 2.5 x 10-5 mol of Pb2+ ions.

The Ksp for CuBr is 6.3x10−9. When 1.00 mL of 0.0010 M CuNO3 is mixed with 1.00 mL of 0.0010 M NaBr, will a precipitate form? Assume that any sodium salts or nitrate salts fully dissociate in water.

Solubility

A student is preparing to test the molar solubility of PbHPO4 (s) (Ksp=3.5×10−12) in different aqueous solutions. When this salt dissociates, it produces Pb2+ (aq) and the amphiprotic ion HPO42− (aq).They prepare separate beakers with 100 mL of each of the following solutions to test:
water
0.1 M Pb(NO3)2 (aq) (which fully dissociates in water)