6.13.1. Solubility Product Constant

Let us now have a solid like barium sulphate in contact with its saturated aqueous solution. The equilibrium between the undisolved solid and the ions in a saturated solution can be represented by the equation:

BaSO4(s)  Ba2+(aq) + SO42–(aq),

This chunk introduces the concept of the solubility product constant (Ksp) using barium sulfate as an example. Barium sulfate is a sparingly soluble salt that establishes an equilibrium between the solid form and its ions once dissolved in water. The equation indicates that when solid barium sulfate is in contact with its saturated solution, it dissociates into barium ions (Ba2+) and sulfate ions (SO42–).

Think of barium sulfate like a sweet that barely dissolves in your drink. When you add it, some sweet particles dissolve (the Ba2+ and SO42– ions) while the rest stays at the bottom (the solid BaSO4). Eventually, the amount of dissolved sweet stabilizes, and the flavors balance out, which is similar to how the Ksp indicates the balance between solid and ions in a saturated solution.

The equilibrium constant is given by the equation:

K = {[Ba2+][SO42–]} / [BaSO4]

For a pure solid substance the concentration remains constant and we can write Ksp = K[BaSO4] = [Ba2+][SO42–] (6.43)

In this chunk, the equation for the solubility product constant (Ksp) is defined. It specifies that Ksp is the product of the molar concentrations of the dissolved ions (Ba2+ and SO42–), raised to the power of their respective stoichiometric coefficients. Since barium sulfate is a solid, its concentration remains constant and does not appear in the Ksp expression, simplifying the relationship to just the concentrations of the ions. Ksp itself is a key factor in determining how soluble the salt is in water.

Imagine you have a glass of very salty water. The salt that dissolves (the ions) is what we measure to understand how 'salty' the water is. Ksp acts like a scorekeeper for this salty water: it tells you how much salt can dissolve before the glass can’t hold any more, which means it represents the solubility level.

The experimental value of Ksp in above equation at 298K is 1.1 × 10–10. This means that for solid barium sulphate in equilibrium with its saturated solution, the product of the concentrations of barium and sulphate ions is equal to its solubility product constant. The concentrations of the two ions will be equal to the molar solubility of the barium sulphate. If molar solubility is S, then 1.1 × 10–10 = (S)(S) = S2 or S = 1.05 × 10–5.

This section discusses the relationship between Ksp and molar solubility (S) of barium sulfate. Given that Ksp for barium sulfate is 1.1 × 10–10, you can determine the molar solubility by rearranging the equation. The concentrations of the ions (Ba2+ and SO42–) in a saturated solution are equal to the molar solubility, leading to the calculation of S as approximately 1.05 × 10–5 M. This shows how Ksp helps us quantitatively assess the solubility of a sparingly soluble salt.

Think of it like filling up a bathtub with just a little bit of saltwater. The Ksp tells you how much salt you can add before it stops dissolving and settles at the bottom. Here, S represents the maximum amount of salt water you can have before it can't hold any more salt.