# Ionic Equilibrium - Ostwald Dilution law

In Ionic equilibrium, the ionic substance dissociates into their ions in polar solvents. The ions formed are always in equilibrium with its undissociated solute in the solution.

⇒ Representation of Ionic Equilibrium: Xa Yb ⇌ aXb+ + bYa-

## Introduction to Ionic Equilibrium

Reactants and products coexist in equilibrium so that reactant conversion to product is always less than 100%. Equilibrium reactions may involve the decomposition of a covalent (non-polar) reactant or ionization of ionic compounds into their ions in polar solvents.

In this section, we will learn about the ionic equilibrium in ionic solutions. Substances in Ionic Equilibrium can be classified into two categories on the basis of their ability to conduct electricity given as under,

### Non-Electrolytes

These are substances that consist of molecules that bear no electric charge, do not dissociate into their constituent ions and thus do not conduct electricity in their aqueous solution or molten state. For example sugar solution.

### Electrolytes

These are substances that dissociate into their constituent ions in their aqueous solution and thus conduct electricity in their aqueous solutions or molten state. Example, salt solution, acid solution, base solution etc.

Electrolytes in ionic equilibrium can be further classified into strong and weak electrolytes.

Strong electrolytes are substances that upon dissociation in their ionic solution ionize completely while in the case of weak electrolytes, the dissociation is partial in nature.

For example, NaCl undergoes complete ionization in its aqueous solution to render sodium ions (Na+) and chloride (Cl) ions, whereas, acetic acid undergoes partial ionization to render some amount of acetate ions(CH3COO) and hydrogen(H+) ions.

• In case of a strong electrolyte, the dissociation reaction is said to be complete, thus moving in the forward direction only, whereas, in case of a weak electrolyte, the reaction is said to be reversible in nature.
• In the case of the weak electrolyte, the equilibrium is established between the ions and the unionized molecules, which can be termed as ionic equilibrium. The same can be understood with the following example.

## Ostwald’s Dilution Law: Degree of Dissociation

Ostwald’s dilution law is the application of the law of mass action to weak electrolytes in solution.

A binary electrolyte AB which dissociates into A+ and B ions.

AB ⇌ A+ + B

(i) For very weak electrolytes, since α <<< 1, (1 – α) = 1

∴ $K=C\alpha^{2}$ $\alpha = \sqrt{KV}$

(ii) Concentration of any ion = Cα = √CK = √K/V

Degree of ionization increases on dilution. Thus, degree of dissociation of a weak electrolyte is proportional to the square root of dilution.

### Limitations of Ostwald’s Dilution law

The law holds good only for weak electrolytes and fails completely in the case of strong electrolytes.

## Ionic Equilibrium Formulas

It becomes necessary to know what fraction of the initial amount of the reactants are converted into products at equilibrium.

The fraction of the initial molecules that are converted at equilibrium is called the degree of Dissociation/ionization.

Degree of dissociation or ionization = α = (Number of reactant molecules dissociated\ionized at the start)/(Number of reactant molecules at the start)

Degree of dissociation in Ionic equilibrium can be expressed in percentage.

% Degree of dissociation or ionization = α = (Number of reactant molecules dissociated or ionized at the start)/(Number of reactant molecules at the start) × 100

## Degree of Ionization

The degree of ionization depends on

• Nature of the electrolyte: strong, weak, insoluble
• Nature of the solvent: High dielectric solvents increase ionization
• Dilution: larger the dilution higher the ionization
• Temperature: higher the temperature, larger the ionization and
• Presence of common ions decreases the ionization of the weak electrolyte.

### Dissociation of Ionic Compounds in Polar Solvents

Ionic compounds dissolve in polar solvents with ionization into cations and anions.

The ionized ions are in equilibrium with the un-dissociated molecules.

AxBy ⇌ xAy+ + yBx-

#### Ionic Solids in Solutions

Strong electrolytes (α ≈100% ionization), Weak electrolytes (α ≈ 10% ionization), Sparingly soluble (α ≈100% ionization)

Example: HCl, NaOH, Salts NH4OH, Organic acids AgCl, BaSO4

### Ionization of Weak Electrolytes

In infinite dilution, all electrolytes are fully ionized. In a concentrated solution, weak electrolytes exist in equilibrium with their unionized molecules. Concentrations of the ions are important in many practical situations like acid-base solubility, and conductance of the solution.

## Common Ion Effect on Degree of Dissociation

Weak electrolytes are poorly ionized in aqueous solution. Their ionization may further be reduced if one of the ions are present from another source. This called a common ion effect.

i) Ammonium hydroxide is a weak base. On addition of ammonium chloride (a salt) ammonium ion from it, will make the ammonium ions to combine with the hydroxide to form unionized ammonium hydroxide.

NH4Cl → NH4+ + Cl

NH4OH ⇌ NH4+ + OH

ii) In the base hydrolysis of oil, the sodium salt of the fatty acid (soap) is in a dissolved state.

When sodium chloride salt is added, the concentration of Na+ ions increases considerably.

CnH2n+1 + COONa ⇌ CnH2n+1 COO + Na+

NaCl ⇌ Na+ + Cl

Hence, the ionic product [CnH2n+1COO] [Na+] exceeds the solubility product of soap and, therefore, soap precipitates out from the solution. This is called salting out of soap.

(iii)  Manufacture of sodium bicarbonate (baking soda):

In Solvay’s soda process. The CO2 gas is passed through ammonical brine to precipitate out NaHCO3.

NH4OH + CO2 → NH4HCO3

NH4HCO3 + NaCl → NH4HCO3 + NH4Cl

NaHCO3 is precipitated first because of its lower solubility product as compared to those of NH4Cl, NH3HCO3 and NaCl.

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