K_sp: Writing the solubility-product constant expression

Solving Ksp Problems: Part One - s2

Solving Ksp Problems: Part Two - 4s3

Solving Ksp Problems: Part Three - 27s4

Solving Ksp Problems: Part Four - 108s5

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This principle was first put forth by Walther Nernst in 1899. It has to do with solid substances usually considered insoluble in water. In each case, we will consider a saturated solution of the insoluble substance that is in contact with some undissolved solid. Important points to consider are:

1) Some of the solid does dissolve. Not very much, but enough.
2) The substance that dissolves will dissociate 100%.
3) There exists an equilibrium between the undissolved solid and ions in solution.

By the way, all of the examples discussed her and elsewhere are all occurring at standard temperature, which is 25.0 °C. Seldom is discussed a K_sp problem at anything other than standard temperature.

Since equilibrium principles can be used, that is where we start. Our first example is silver chloride, AgCl. When it dissolves, it dissociates like this:

AgCl(s) ⇌ Ag⁺(aq) + Cl¯(aq)

An equilibrium expression can be written:

K_c = ( [Ag⁺] [Cl¯] ) / [AgCl]

Now, we come to an important point. When the AgCl is enclosed in square brackets like this − [AgCl] − that means the "molar concentration" of solid AgCl. This value is a constant!! Why?

Answer: The "molar concentration" of a solid (it's not a useful chemistry idea, so it is seldom mentioned) can be directly related to the density, which is also a constant. Here is a short dimensional analysis which summarizes the relationship:

g		mole		1000 cm3
–––––––	x	–––––––	x	–––––––	= mol/L <---molarity
cm3		g		1 L
density		molar mass		convert cm3 to liter

What we do is move the [AgCl] to the other side and incorporate it with the equilibrium constant. We can do this because [AgCl] is a constant.

K_c [AgCl] = [Ag⁺] [Cl¯]

Since K_c [AgCl] is a constant (because it's a constant times a constant which yields a constant), we replace it with a single symbol. Like this:

K_sp = [Ag⁺] [Cl¯]

(Just a side point: as you go on in chemistry, you'll get introduced to the concept of activity. The activity of a solid is defined as equal to the value of one. Since the activity of AgCl(s) = 1, it just drops out of the above expression. However, like I said, activity is for the future. Not right now.)

It turns out that the K_sp value can be either directly measured or calculated from other experimental data. Knowing the K_sp, we can calculate the solubility of the substance in a very straightforward fashion.

Here are three more examples of dissociation equations and their K_sp expressions:

Sn(OH)2(s) ⇌ Sn2+(aq) + 2OH¯(aq)	Ksp = [Sn2+] [OH¯]2
Ag2CrO4(s) ⇌ 2Ag+(aq) + CrO42¯(aq)	Ksp = [Ag+]2 [CrO42¯]
Fe(OH)3(s) ⇌ Fe3+(aq) + 3OH¯(aq)	Ksp = [Fe3+] [OH¯]3

In order to write K_sp expressions properly, you must know how each ionic substance dissociates in water. That means you have to know your chemical nomenclature, polyatomic ions, and the charges associated with each ion.

Also, and this is important, so pardon the shouting:

EACH CONCENTRATION IN THE K_sp EXPRESSION IS RAISED TO THE POWER OF ITS COEFFICIENT IN THE BALANCED EQUATION.

Two more examples:

Hg2Br2(s) ⇌ Hg22+(aq) + 2Br¯ (aq)	Ksp = [Hg22+] [Br¯]2
Zn3(AsO4)2(s) ⇌ 3Zn2+(aq) + 2AsO43¯(aq)	Ksp = [Zn2+]3 [AsO43¯]2

Note how the mercury(I) ion is written. Hg₂²⁺ is correct. Do not write it as 2Hg⁺. Writing [Hg⁺]² in the K_sp expression is wrong.

Here are ten chemical formulas. Write the chemical equation showing how the substance dissociates and write the K_sp expression.

1) AlPO4	2) BaSO4	3) CdS	4) Cu3(PO4)2	5) CuSCN
6) AgCN	7) Mn(IO3)2	8) PbBr2	9) SrCO3	10) Bi2S3

Go to the answers

By the way, a word of warning. You may have done quite well at learning chemical nomenclature. However, in the study of K_sp, there may be some polyatomic ions used that you did not study in the nomenclature section. Thiocyanate (SCN¯) might be one example. Another could be the arsenate ion, (AsO₄^3-). Note that arsenic is just below phosphorous in the periodic table. Compare arsenate with phosphate (PO₄^3-).

Solving Ksp Problems: Part One - s2

Solving Ksp Problems: Part Two - 4s3

Solving Ksp Problems: Part Three - 27s4

Solving Ksp Problems: Part Four - 108s5

Back to Equilibrium Menu