Solubility Equilibria in Water

 

Remember the solubility rules on page 164 of your Moore et al (p. 118 of Brown, Lemay, and Bursten, 9th Ed., p. 111 of 8th Ed.) textbook.  Alkali metal ions, ammonium, nitrates and acetates are soluble, halide compounds are soluble with exceptions.  Phosphates, carbonates, hydroxides and sulfides are insoluble with the exceptions of alkali and ammonium ions.

 

A saturated solution with solid in contact with water will come to equilibrium with ions dissolving and precipitating with equal rates.

 

            AgCl(s) = Ag+(aq) + Cl-(aq)

 

The equilibrium expression for this heterogeneous reaction would be (leaving out the [AgCl] since the concentration of a solid is constant);

 

            Ksp = [Ag+] [Cl-]

 

The constant Ksp is called the solubility product. The reaction showing silver phosphate dissolving and the solubility product expression would be

 

            Ag3PO4 (s) = 3 Ag+ + PO4-3

 

            Ksp = [Ag+]3 [PO4-3]

 

Please note that Ksp calculations work best for solutes that are considered insoluble.  As we get to higher concentrations of solute ions, a lot of non-ideal behavior makes these simple calculations invalid.   Ksp also works better with ions with low charges (+ or -1) and when no other ions are dissolved.  Other dissolved ions can greatly change solubility.

 

Hopefully we learned many chapters ago that solubility is the grams of solute per 100. g of solution.  To convert this into a solubility product we would first determine the molar solubility (moles solute per 1.00 L of solution) and then using the stoichiometry of the equation showing dissolving, determine the ions concentration and calculate the Ksp

 

e.g.   g solute  ® (use molar mass to convert to moles) ® moles solute

      100. g soln.    (use density to convert to V)                      1. L soln.

 

            ®(use stoichiometry to determine [ ] ions in soln.)  then substitute in

 

            Ksp = [Mn+]x [X-m]y

 

Given a solubility of silver chloride of .00019 g/ 100. g solution at 25°C, what is the molar solubility and Ksp?  Since this is a very dilute solution, we can assume the density is close to that of pure water at 25°C 

 

            solubility = .00019 g  X  1mol /143.3209 g AgCl X         1         = 1.325696 X10-5mol/L

                           100. g soln.   1 mL/1g                                    1L/1000 mL

 

So the molar solubility is to 2 significant figures 1.3 X 10-5mol/L (don't round that number yet)

 

Since dissociation of silver chloride will have equal concentrations of silver and chloride

 

            AgCl(s) = Ag+     +    Cl-

 

Initial

0

0

Change

+x

+x

Equilibrium

x

x

 

            Ksp = x2 = (1.325696 X 10-5)2 = 1.8 X 10-10 (if you had squared 1.3 X 10-5 you would get 1.7 X 10-10).

 

To go from Ksp to molar solubility, since x2 = 1.8 X 10-10, the square root of Ksp = molar solubility in this example (it will not always be so easy).

 

The solubility of lead (II) fluoride is 0.0510 g / 100.g solution.  Assuming density = 1.00 g / mL, What is the molar solubility and Ksp? (molar mass = 245.2 g/mol)

You should be able to get

 

            molar solubility = 2.08 X 10-3 M

 

            Now for PbF2 (s) = Pb+2    +    2 F-

Initial

0

0

Change

+x

+2x

Equilibrium

X

2x

 

            Ksp = x (2x)2 = 4x3

            Ksp = 3.6 X 10-8

 

To go backward, Ksp =4x3, and x will = molar solubility.  A common mistake above is to forget to square the 2. 

 

For practice, go backward and forward on these 2 calculations.

 

Factors affecting Solubility

 

1. Temperature – We learned earlier that for most ionic solids, as temperature increases, solubility increases. 

2. Acids and pH

3. Presence of common ions

4. Formation of complex ions

5. Amphoterism

 

Acids and pH (lower pH will increase solubility of basic anions)

 

For salts that contain a basic anion, such as hydroxide, the equilibrium involving that anion will affect solubility.   For example, as pH decreases, ([H+] increases), solubility of a metal hydroxide will increase because the hydrogen ion will consume the hydroxide, shifting the solubility equilibrium reaction to the right to dissolved ions.  A salt with a basic anion (e.g. carbonate, phosphate, cyanide, and sulfides) will show an increased solubility as [H+] increases (pH decreases).  Salts derived from strong acid and bases are negligible conjugates bases and acids, and will not be affected as much by pH changes.

 

e.g. Calculate the molar solubility of Mg(OH)2 in pure water and a buffered pH=9.0 solution. Ksp = 1.8 X 10-11 (page 665)

 

            Mg (OH)2 (s)   =     Mg+2      +    2 OH-

Initial

0

0

Change

+x

+2x

Equilibrium

x

2x

 

            Ksp = [Mg+2] [OH-]2 = x (2x)2 = 4x3

            x = 1.7 X 10-4 M= molar solubility and [OH-] = 2x = 3.3 X 10-4 M and so pH = 10.52

 

            At a pH = 9.0, pOH = 5.0 and [OH-] = 1.0 X 10-5

 

            [Mg+2] = Ksp /  [OH-]2 = 1.8 X 10-11/ (1.0 X 10-5)2

            x = 0.18 M

            molar solubility in pH = 9.0 = 0.18 M

 

Mg(OH)2 is used to neutralize stomach acid without burning your throat on the way down.  In un-buffered liquids, magnesium hydroxide is very insoluble, and so not much dissolves and it doesn’t hurt your throat.  In the stomach where there is lots of acid, it will dissolve and the hydroxide can neutralize some of the stomach acid.

 

In acid base reactions, we have said if one of the reactants is strong the reaction will go to completion.  If both are weak, you will get an equilibrium.  Consider tooth enamel which consists mainly of a mineral called hydroxyapatite, Ca10(PO4)6(OH)2.  Bacteria in your mouth convert sugar into a weak acid such as lactic acid, and this will react completely with the strong base.

 

            Ca10(PO4)6(OH)2 (s) + 2 HLactic Acid (aq) -> 10 Ca2+ (aq) + 6 PO4-3 (aq) + 2 H2O (L) + 2 Lactates-

 

With fluoridated water and fluoride toothpaste, the hydroxide in hydroxyapatite is replaced by the weak base, F.  Instead of reacting completely with lactic acid, you will get an equilibrium, and thus less of your enamel will dissolve, leading to less cavities.

 

 

Common ion effect (decreases solubility)

The presence of a common ion will reduce the solubility by forcing the equilibrium back to the left toward the precipitate (Hip, Hip, Hooray for Le Chatelier).  It will not change the Ksp, but it will change the two solubilities.  This can be used to reduce the concentration of a toxic heavy metal in water.

 

Compare for silver chloride.   Say we had a .010 M NaCl solution. 

            AgCl (s)            =         Ag+   +         Cl-

Initial

0

0.010

Change

x

+ x

Equilibrium

x

0.010 + x

 

            Ksp = 1.8 X 10-10 =  x (.010 + x) ~ 0.010x  (since x will probably be very small compared to 0.010 M)

            x = 1.8 X 10-8 M (see, I told you it would be small)

 

The molar solubility of AgCl in 0.010 M NaCl would be 1.8 x 10-8 M.  Compare this to the molar solubility of AgCl in pure water of 1.3 X 10-5 M.

 

Formation of complex ions (increases solubility)

 

The combination of a metal ion as a Lewis acid and a Lewis base forms a complex ion, such as Ag(NH3)2+ , or Fe(CN)6-4.  The following equilibrium involves an equilibrium constant called the formation constant, Kf.

 

Ag+ + 2 NH3 = Ag(NH3)2+                            Kf = 1.6 X 107

 

The large equilibrium constant tells us this is a favorable reaction.  This will increase the solubility of a compound such as silver chloride by reacting and reducing the dissolved silver ion concentration.

 

Consider the simultaneous equilibrium

 

AgCl(s) = Ag+ + Cl-                                      Ksp = 1.8 X 10-10

Ag+ + 2 NH3 = Ag(NH3)2+                            Kf = 1.6 X 107

 

The sum of the two equilibrium will have an equilibrium expression equal to the product of Ksp and Kf .

 

AgCl(s) + 2 NH3 = Ag(NH3)2+ + Cl-            Kxp x Kf = 2.9 X 10-3

 

This is a much more favorable reaction than the dissolving of silver chloride in pure water.

 

Amphoterism

 

Some metal hydroxides are Amphoteric, they can react as an acid or base.  The metal hydroxide can act as a Bronstead-Lowery base

 

Zn(OH)2 (s) + 2 HCl ZnCl2 + 2 H2O

 

Or the metal can act as a Lewis acid, accepting a pair of electrons from a hydroxide, forming a complex ion.

 

Zn(OH)2 (s) + 2 OH- Zn(OH)4-2