Ionic Equilibrium: Relation Between Solubility (S) & Ksp | CHEMCA

Ionic Equilibrium: Relation Between Solubility (S) & K_sp

Published by Abhishek Sengar | CHEMCA India

One of the most intimidating topics for students in the Ionic Equilibrium chapter is calculating the Solubility Product Constant (K_sp) for complex salts.

It's easy when dealing with simple salts like AgCl, but what happens when you get a monster molecule like Magnesium Phosphate? If you don't know the master formula, you will spend precious minutes doing complex algebra. Let's decode the ultimate shortcut.

Video Tutorial: The Master Formula

Watch Abhishek Sengar sir from CHEMCA break down the exact mathematical relationship between Molar Solubility (S) and K_sp, ending with a universal formula that works for every electrolyte!

1. Defining the Terms

Molar Solubility (S): The number of moles of solute that can dissolve in 1 Liter of solution before it becomes saturated. (Units: mol/L)
Solubility Product Constant (K_sp): The equilibrium constant for a solid substance dissolving in an aqueous solution.

Crucial Note:
When a solid electrolyte dissociates, its active mass (concentration) is considered constant (taken as 1). Therefore, the solid reactant NEVER appears in the final K_sp equation!

2. The Simple Case: AB Type Electrolyte

Let's take a simple 1:1 salt like Silver Chloride (AgCl).

AgCl_(s) ⇌ Ag⁺_(aq) + Cl^-_(aq)

If the solubility of AgCl is S, then at equilibrium:
[Ag⁺] = S
[Cl^-] = S

K_sp = [Ag⁺] × [Cl^-] = (S) × (S)
K_sp = S²
Or, S = √K_sp

3. The Complex Case: Magnesium Phosphate

Now let's tackle the monster: Mg₃(PO₄)₂.

Mg₃(PO₄)_2(s) ⇌ 3 Mg²⁺_(aq) + 2 PO₄^3-_(aq)

If the solubility is S, then:
[Mg²⁺] = 3S
[PO₄^3-] = 2S

K_sp = [Mg²⁺]³ × [PO₄^3-]²
K_sp = (3S)³ × (2S)²
K_sp = (27S³) × (4S²)
K_sp = 108 S⁵

4. The Universal Shortcut Formula

To avoid doing this algebra during a timed exam, Abhishek Sir derived a general formula for ANY electrolyte of the form A_xB_y:

Fig: Just identify the stoichiometric coefficients 'x' and 'y' and plug them straight into the formula!

K_sp = x^x · y^y · S^(x+y)

Practice Questions for JEE & NEET

Let's test this universal formula on some classic examiner favorites!

Question 1: Using the universal formula, calculate the mathematical relationship between K_sp and S for Aluminum Sulfate: Al₂(SO₄)₃.

Answer: K_sp = 108 S⁵

Reasoning:

The salt is Al₂(SO₄)₃.
This is an A_xB_y type where x = 2 and y = 3.

Plug into the formula: K_sp = x^x · y^y · S^(x+y)
K_sp = (2)² · (3)³ · S⁽²⁺³⁾
K_sp = (4) · (27) · S⁵
K_sp = 108 S⁵.
(Notice it gives the exact same result as Magnesium Phosphate, because both have x=2, y=3 or x=3, y=2!)

Question 2 (The Units Trap): In a numerical problem, the examiner gives you the solubility of AgCl as 1.435 × 10^-3 g/L. Can you plug this number directly into the formula K_sp = S²?

Answer: NO! You must convert it to Molar Solubility first.

Reasoning:

The "S" in all K_sp formulas strictly stands for Molar Solubility, which must be in units of moles per liter (mol/L).

If the examiner gives you solubility in grams per liter (g/L), you must divide that number by the Molar Mass of the salt before using the formula.
Molar Solubility (S) = Solubility in g/L ÷ Molar Mass (g/mol).

For AgCl (Molar mass = 143.5 g/mol): S = (1.435 × 10^-3) / 143.5 = 10^-5 mol/L.
Now you can plug 10^-5 into the formula!

Search This Blog