Ionic Equilibrium, Ostwald’s Dilution Law & Related Concepts - Chemistry

Table of Contents
1. What is Ionic Equilibrium?
2. Classification based on electrical conductivity
3. Ostwald's Dilution Law and Degree of Dissociation
4. Degree of Dissociation (Ionization)
5. Dissociation of ionic compounds in polar solvents
6. Common Ion Effect
7. pH and buffer systems
8. Solubility equilibria and solubility product (Ksp)
9. Conclusion
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What is Ionic Equilibrium?

In a polar solvent an ionic substance or a covalent substance that can ionize dissociates into its constituent ions. At equilibrium the ions formed remain in dynamic balance with the undissociated molecules. The process can be represented generically as a reversible ionization:

Equilibrium characteristics

• Reactants and products coexist: In any chemical equilibrium both the undissociated species and the ions are present; conversion is never 100% in general.
• Dynamic balance: Rates of forward and reverse processes are equal at equilibrium although both processes continue to occur.

Types of ionising reactions

• Ionization of covalent (polar) molecules: Some covalent molecules ionise in polar solvents to give ions (for example, acids and bases that ionize in water).
• Dissociation of ionic compounds in polar solvents: Ionic solids dissolve and separate into cations and anions; the dissolved ions may remain in equilibrium with any undissolved solid or undissociated ion pairs.

Classification based on electrical conductivity

Non-electrolytes

• Description: Consist of neutral molecules which do not produce ions on dissolution.
• Characteristics: Do not conduct electricity in aqueous solution or in molten state because no free ions are present.
• Example: Sugar (sucrose) solution.

Electrolytes

• Description: Substances that dissociate into ions in solution and therefore conduct electricity.
• Characteristics: Conduct electricity in aqueous or molten states due to presence of mobile ions.
• Examples: Salt (NaCl) solution, acid solutions (HCl, CH₃COOH), base solutions (NaOH).

Electrolytes are further classified into:

• Strong electrolytes: Dissociate nearly completely in solution; ionization is effectively one-way (for example, NaCl → Na+ + Cl-; HCl in water).
• Weak electrolytes: Dissociate only partially; a reversible equilibrium is established between the ions and the undissociated molecules (for example, acetic acid CH₃COOH ⇌ CH₃COO- + H+).

Ostwald's Dilution Law and Degree of Dissociation

Ostwald's Dilution Law

This law applies the mass-action principle to weak electrolytes. Consider a binary weak electrolyte AB that ionises in solution according to the equilibrium:

Let:

• C = initial concentration of the electrolyte (mol L-1),
• α = degree of dissociation (fraction of molecules dissociated; 0 ≤ α ≤ 1).

At equilibrium the concentrations are:

• [A+] = Cα
• [B-] = Cα
• [AB] = C(1 - α)

The equilibrium constant (dissociation constant) K is therefore:

\(K = \dfrac{[A^+][B^-]}{[AB]}\)

\(K = \dfrac{C\alpha \times C\alpha}{C(1-\alpha)}\)

\(K = \dfrac{C\alpha^2}{1-\alpha}\)

For very weak electrolytes where \(\alpha \ll 1\), we may approximate \(1 - \alpha \approx 1\). Thus:

\(K \approx C\alpha^2\)

\(\alpha \approx \sqrt{\dfrac{K}{C}}\)

Key point: As the solution is diluted (C decreases), the degree of dissociation α increases. In other words, for a simple 1:1 weak electrolyte α is inversely proportional to the square root of concentration.

Limitations of Ostwald's Dilution Law

• Valid only for weak electrolytes: The law assumes that ionization is partial and that activity coefficients are approximately unity; it is not applicable to strong electrolytes which ionize completely.
• Fails for concentrated solutions: At higher concentrations inter-ionic attractions and deviations from ideality (activity coefficients ≠ 1) are significant and the simple relation does not hold.
• Ion-pairing and multivalent ions: Presence of ion pairs or salts with multiply charged ions leads to deviations from the idealised expression.
• Ionic strength and solvent effects: Changes in ionic strength and solvent dielectric constant affect activity coefficients and therefore limit direct application of the law without corrections.

Degree of Dissociation (Ionization)

The degree of dissociation or degree of ionization (α) is the fraction of the original molecules that dissociate to form ions at equilibrium. It can be expressed as a fraction or as a percentage:

Factors affecting ionization

• Nature of the electrolyte: Strong electrolytes ionize nearly completely whereas weak electrolytes ionize partially. Sparingly soluble salts may appear to ionize completely in the small amount that dissolves.
• Nature of the solvent: Solvents with high dielectric constant (high polarity) reduce electrostatic attraction between ions and favour ionization.
• Dilution: Greater dilution (smaller C) increases α for weak electrolytes (Ostwald's law).
• Temperature: Increased temperature generally favours ionization if the dissociation is endothermic; temperature effects vary with substance.
• Common ion presence: Addition of an ion common to the dissociation equilibrium shifts equilibrium towards the undissociated form (Le Chatelier's principle), reducing ionization.

Dissociation of ionic compounds in polar solvents

When ionic compounds dissolve in polar solvents such as water, they separate into constituent cations and anions. A dynamic equilibrium may exist between dissolved ions and any undissolved solid or ion pairs:

Ionic solids in solution - typical behaviour

• Strong electrolytes: Almost complete ionization in solution (for example HCl, NaOH, NaCl in dilute water).
• Weak electrolytes: Partial ionization (for example acetic acid typically ~1-10% ionised in moderate concentration depending on dilution).
• Sparingly soluble salts: May ionize fully in the small portion that dissolves, but total dissolved amount (solubility) is low (examples: AgCl, BaSO₄).

Ionization of weak electrolytes in practical situations

• Infinite dilution: Even weak electrolytes approach full ionization as dilution tends to infinity.
• Concentrated solutions: Weak electrolytes exist as a mixture of undissociated molecules and ions; properties such as acid-base behaviour and conductance depend strongly on the equilibrium position.

Common Ion Effect

The common ion effect refers to the decrease in the ionization or solubility of a weak electrolyte when a salt containing an ion common to the equilibrium is added. This effect is a direct consequence of Le Chatelier's principle: increasing the concentration of one product ion shifts the equilibrium towards the reactant (undissociated) side.

• When the concentration of a dissociation product ion is increased by addition of a salt that supplies that ion, the equilibrium shifts to reduce the change, suppressing further ionization or decreasing solubility.

Examples of common ion effect

1. Ammonium hydroxide and ammonium chloride: NH₄Cl dissociates to give NH₄+ and Cl-. Addition of NH₄Cl to a solution of NH₄OH increases [NH₄+], shifting the equilibrium to the left and reducing ionization of NH₄OH.
   NH₄Cl → NH₄⁺ + Cl^-
   NH₄OH ⇌ NH₄⁺ + OH^-
2. Salting out of soap: Sodium salts of fatty acids (soap) are soluble because of ionic character. Addition of NaCl increases [Na+], shifting equilibrium and reducing solubility of the soap ion pair. As a result the ionic product exceeds the solubility product and soap precipitates out (salting out).
   C_nH_2n+1 + COONa ⇌ C_nH_2n+1 COO^- + Na⁺
   NaCl ⇌ Na⁺ + Cl^-
3. Manufacture of sodium bicarbonate (Solvay process): In the Solvay process CO₂ is passed through ammoniacal brine. Carbon dioxide reacts with ammonia and water to form ammonium hydrogen carbonate, which reacts with sodium chloride in brine to form sodium bicarbonate that precipitates because of its low solubility product:
   NH₄OH + CO₂ → NH₄HCO₃
   NH₄HCO₃ + NaCl → NH₄HCO₃ + NH₄Cl

pH and buffer systems

Buffers are systems that resist changes in pH on addition of small amounts of acid or base. A typical buffer consists of a weak acid and its conjugate base (or a weak base and its conjugate acid). Addition of the conjugate ion alters the equilibrium due to the common ion effect.

Example: Acetic acid / acetate buffer

The equilibrium for acetic acid is:

On adding sodium acetate the concentration of acetate ion [CH3COO-] increases. According to Le Chatelier's principle the equilibrium CH₃COOH ⇌ H+ + CH₃COO- shifts left, reducing [H+] and thereby increasing the pH (making the solution less acidic).

Henderson-Hasselbalch relation (useful for buffer calculation):

\(\mathrm{pH} = \mathrm{p}K_a + \log\frac{[\mathrm{A}^-]}{[\mathrm{HA}]}\)

This relation links pH to the ratio of conjugate base to weak acid concentrations and shows quantitatively how the common ion controls pH in buffer solutions.

Solubility equilibria and solubility product (Ksp)

Definition of solubility product (Ksp)

The solubility product constant, denoted by Ksp, is the equilibrium constant for the dissolution of a sparingly soluble ionic solid in water. For a salt that dissociates into ions the product of the equilibrium concentrations of the ions (each raised to the power of their stoichiometric coefficients) is constant at a given temperature.

• Ksp is temperature dependent: Its numerical value varies with temperature because solubility generally changes with temperature.
• Solubility: The solubility of an ionic compound is the amount of the compound that dissolves to form a saturated solution under specified conditions (commonly expressed in mol L-1 or g L-1).
• Dependence on lattice and solvation enthalpies: Whether a salt dissolves depends on the balance between lattice enthalpy (energy required to separate ions in the solid) and solvation enthalpy (energy released when ions are solvated by the solvent).
• Some compounds are highly soluble and may even absorb moisture from the atmosphere whereas others are highly insoluble.

Significance of solubility product

Solubility depends on several parameters, chief among them being the lattice enthalpy of the salt and the solvation enthalpy of the ions. The solvation enthalpy is negative (energy is released) and depends on the nature of the solvent. Non-polar solvents have small solvation enthalpies and cannot overcome large lattice enthalpies, so ionic salts are generally insoluble in non-polar solvents.

• The solvation enthalpy must be sufficient: For a salt to dissolve, the energy released by solvation must compensate for the energy needed to break the ionic lattice.
• Solubility varies with solvent: A solvent with higher dielectric constant increases ion separation and solvation, increasing solubility.
• Temperature dependence: Solubility and therefore Ksp vary from salt to salt with temperature.

Common classification of salts by solubility is often presented in tabular form.

Solubility product constant - worked expression

For a sparingly soluble salt such as barium sulphate the equilibrium between the undissolved solid and its saturated solution is:

The equilibrium constant expression (ignoring activity coefficients) is:

Because the activity (apparent concentration) of a pure solid is constant it is omitted from the K expression and the remaining product of ion concentrations defines Ksp:

Thus for BaSO₄:

\( \mathrm{K}_{sp} = [\mathrm{Ba}^{2+}][\mathrm{SO}_4^{2-}] \)

Factors that affect the value of Ksp

Important factors that influence the experimental value of Ksp are:

• Common-ion effect: Presence of a common ion in solution lowers the solubility and hence reduces the equilibrium concentrations of ions-this changes the apparent solubility though the true thermodynamic Ksp at a given temperature remains the same; experimentally measured solubility is reduced.
• Diverse-ion effect: When the ions in solution are from different sources and do not share a common ion, ionic interactions can increase apparent solubility.
• Ion pairs and activity coefficients: Formation of ion pairs or deviation of activity coefficients from unity causes differences between concentration-based calculations and true thermodynamic activities.

Conclusion

Understanding ionic equilibrium, Ostwald's dilution law and the solubility product is essential for predicting and explaining the behaviour of acids, bases, salts and buffer systems. The interplay of ionization, dilution, common-ion effect, solvent properties, lattice and solvation enthalpies and activity effects explains many laboratory and industrial phenomena - from buffer action and precipitation reactions to processes such as the Solvay method for sodium bicarbonate manufacture and salting out in soap technology.