Ionic Equilibrium

1.0What is Ionic Equilibrium?

Ionic equilibrium occurs when the rate at which ions are produced equals the rate at which they are consumed, resulting in a constant concentration of ions in solution.

Ionic equilibrium involves the balance between the concentrations of ions in a solution. This concept is essential in understanding how ions interact and maintain a stable environment in aqueous solutions. 

Example: In a solution of acetic acid (CH₃COOH), an equilibrium is established between the dissociated ions CH₃COO^-     and H⁺ and the undissociated acetic acid.

2.0Basic Concepts

Electrolytes vs. Nonelectrolytes:

• Electrolytes are substances that dissolve in water and separate into ions, allowing the solution to conduct electricity. (e.g., sodium chloride, NaCl).
• Nonelectrolytes: Substances that do not dissociate into ions and do not conduct electricity (e.g., sugar).

Degree of Dissociation:

• Strong Electrolytes: Completely dissociate into ions in solution (e.g.,NaCl,HCl).
• Weak Electrolytes: Partially dissociate in solution (e.g., acetic acid,CH₃COOH).

The degree of ionisation (or dissociation) is the fraction of the total number of molecules that ionise (dissociate) into constituent ions in a solution.

        $\alpha =\frac{\text{ total number of molecules taken }}{\text{ number of molecules ionised or dissociated }}$

• For strong electrolytes,𝛼 =1
• For weak electrolytes,α<1.

The value of the degree of dissociation (α) depends on the following factors:

• Nature of the solute: Different solutes have varying tendencies to dissociate into ions. Strong acids, bases, and salts usually dissociate completely, whereas weak acids and bases only partially dissociate.
• Nature of the solvent: The solvent's ability to stabilize ions affects the degree of dissociation. Solvents with high dielectric constants, such as water, can better stabilize ions, leading to higher degrees of dissociation.
• Concentration of the solute: The degree of dissociation often decreases with increasing concentration due to the common ion effect and other inter-ionic interactions in the solution.
• Temperature: Increasing temperature generally increases the degree of dissociation for most solutes, as higher temperatures provide more energy to overcome the forces holding the ions together.

3.0Ostwald’s Dilution Law

According to Ostwald, the degree of dissociation (α) of a weak electrolyte is inversely related to the square root of the solution's molar concentration.

Let K be the dissociation constant and C be the molar concentration of the solution.

The relationship is given by Ostwald's Dilution Law:

$\alpha =\sqrt{\frac{K}{C}}$

This law indicates that as the concentration C decreases (i.e., the solution is diluted), the degree of dissociation 𝛼 increases. This is particularly applicable to weak electrolytes, which do not fully dissociate in solution.

For a weak electrolyte, the dissociation constant  K_C   can be expressed in terms of the degree of dissociation 𝛼  and the concentration 𝐶:

 $K_{\mathrm{c}}=\frac{C{\alpha }^2}{(1-\alpha )}$

However, for very dilute solutions (where α is much less than 1), this simplifies to:

𝐾≈𝐶𝛼²

Thus, rearranging gives:

$\alpha \approx \sqrt{\frac{K}{C}}$

This simplified version of Ostwald's Dilution Law demonstrates the inverse relationship between the degree of dissociation and the square root of the molar concentration.

Ka​  represents the dissociation constant of an acid and  Kb represents the dissociation constant of a base. The relationship between Ka and Kb is:

Ka × Kb  ​= Kw ​ = 1.0×10⁻¹⁴  ,where Kw ​is the ion-product constant of water.

4.0Dissociation Constants and pK_a Values for Acids at 25°C

5.0Acids and Bases

Arrhenius Concept

• Arrhenius Acid: A substance that furnishes hydrogen ions (H⁺) in an aqueous solution.Example:
• HCl → H⁺ + Cl⁻ (strong acid)
• CH₃COOH ⇌ CH₃COO⁻ + H⁺ (weak acid)
• Arrhenius Base: A substance that furnishes hydroxide ions (OH⁻) in an aqueous solution.Example:
• NaOH → Na⁺ + OH⁻ (strong base)
• NH₄OH ⇌ NH₄⁺ + OH⁻ (weak base)
• The strength of an acid or base depends on its tendency to furnish H⁺ or OH⁻ ions in solution, respectively.
• Water is amphoteric because it can furnish both H⁺ and OH⁻ ions. 
• H₂O ⇌ H⁺ + OH⁻
• The neutralization of an acid and base is a reaction between H⁺ and OH⁻ ions to form water.
• H⁺(aq) + OH⁻(aq) ⇌ H₂O(l)

 Bronsted-Lowry Concept

• A Bronsted-Lowry acid is a proton donor.
• A Bronsted-Lowry base is a proton acceptor.
• The strength of an acid depends on its tendency to donate protons.
• The strength of a base depends on its tendency to accept protons.
• Water is amphoteric because it can both donate and accept protons

              H₂O  +  H₂O  ↔  OH⁻  +  H₃O⁺                  

              Acid_1​   Base₂​     Base₁​     Acid_2​

• The proton donated by an acid does not exist freely and is always solvated.

             CH₃COOH + H₂O ↔ CH₃COO⁻+H₃O⁺

• Each cation behaves as an acid, and each anion behaves as a base. Some can be amphoteric.

              Na⁺+2H₂O ↔ NaOH+H₃O⁺

              Cl⁻+H₂O  ↔  HCl + OH⁻

• In all acid-base reactions, two conjugate acid-base pairs are involved.

              NH₃  +  H₂O  ↔  NH₄⁺  +  OH⁻

             Acid_1​   Base₂​     Base₁​      Acid₂ 

• More examples of Conjugate Acid-Base Pairs:

              HCl ↔ H⁺+Cl⁻

              C₆H₅NH₂+H⁺↔C₆H₅NH₃ ⁺ 

              H₂O+Al(OH)₃↔Al⁺³(𝑎𝑞)+4H₂O

• According to Bronsted-Lowry, all acid-base reactions involve the transfer of protons between two conjugate acid-base pairs.

Lewis Concepts 

Lewis extended the Bronsted concept to include the following:

• Lewis Acid: An electron pair acceptor.
• Lewis Base: An electron-pair donor.
• Acid-base reactions involve sharing an electron pair from the base to the acid, forming a coordinate complex.
• Example:
• • BF₃+NH₃→(H₃N→BF₃)
  • BF₃+F⁻→[BF₄]⁻
  • Ag⁺  + 2CN⁻→[Ag(CN)₂]⁻    
• Lewis acids accept electron pairs, while Lewis bases donate them, forming coordinate complexes in acid-base reactions. The strength of these acids and bases depends on their charge, size, and electronegativity.

Acid Strength and pH

The acid strength is defined by its pH:

pH = −log⁡[H⁺]

Base Strength and pOH

The strength of a base is defined by its pOH:

pOH = −log⁡[OH⁻]

The relationship between pH and pOH is:

pH + pOH =14

6.0Buffer Solution

A buffer solution maintains its pH relatively stable when small quantities of strong acid or base are introduced. It is also called reserve acidity or basicity, demonstrating buffer action.

Features:

• The solution maintains a specific pH.
• The pH remains stable over time.
• pH does not change with dilution.
• Adding small amounts of strong acid or base causes only slight, unnoticeable pH changes.

Henderson-Hasselbalch Equation

By using the Henderson-Hasselbalch equation, the pH of a buffer solution can be determined 

$\alpha \approx \sqrt{\frac{K}{C}}$

Where: A^-   is the concentration of the conjugate base. H_A   is the concentration of the acid.

For a primary  buffer (weak base + conjugate acid), the pOH is calculated as:

$\alpha \approx \sqrt{\frac{K}{C}}$

Where:B⁻ is the concentration of the base. B_H is the concentration of the conjugate acid. 

7.0Salts and Their Ionization

When acids react with bases, salts are generated. Upon ionization in solution, the ions of these salts may subsequently interact with water, resulting in the formation of  acidic, basic, or neutral solutions depending on the properties of the ions involved. 

Common Ion Effect

When equilibrium establishes between an ionic compound and its ions, adding a common ion will shift the equilibrium to consume that ion, according to Le Chatelier’s principle.

The common ion effect is used in:

• Purification of Common Salt: Adding a common ion reduces solubility, helping to purify salt.
• Salting Out of Soap: Enhances precipitation of soap from solution.
• Qualitative Analysis:
• • Group II Radicals: Precipitated in the presence of HCl, which suppresses S₂⁻ ion concentration, sufficient to precipitate only Group II radicals.
  • Group III Radicals:NH₄OH is added in the presence of NH₄Cl to avoid the precipitation of Group V radicals.

Isohydric Solutions

Isohydric solutions are those where the concentration of common ions(e.g.,OH⁻−ions in Ca(OH)₂​    and  Ba(OH)₂​      solutions) is the same. When mixed, the degree of dissociation of either electrolyte does not change.

8.0Solubility and Solubility Product

Solubility: The maximum amount of a substance that dissolves in a fixed amount of a solvent at a specific temperature.

For an ionic compound XY that dissociates in water:

• 𝑋𝑌↔𝑋⁺+𝑌⁻

The solubility product (K_sp) is expressed as:

• K_sp​= [X⁺][Y⁻]

Ionic Product (I.P.): It is the product of the ions' concentrations in the solution.

• Unsaturated Solution:   I.P.< K_sp
• Supersaturated Solution:  I.P.> K_sp​  (precipitate will form)
• Saturated Solution:  I.P.= K_sp​  (no precipitate formation)

9.0SOLVED PROBLEMS

Ques 1. In the reaction equilibrium  P + Q ↔ R + S, what will happen to the concentrations of P, Q, and S if the concentration of R is increased?

Ans When the concentration of R  is increased in the reaction equilibrium P + Q ↔ R + S, the system will respond according to Le Chatelier's Principle. This principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. Equilibrium constant of the reaction can be shown as: 

$\alpha \approx \sqrt{\frac{K}{C}}$

If the concentration of product is increased then the concentration of other components changes which decreases the concentration of R and vice – versa. Thus, increasing the concentration of R shifts the equilibrium to the left, leading to an increase in the concentrations of P and Q and a decrease in the concentration of S.

Ques 2. Write the relationship between molar Solubility (S) and solubility product  K_sp​  for PbI₂ 

Ans The relationship between molar solubility (𝑆) and the solubility product (Ksp​) for  lead(II) iodide(PbI₂):   

Dissociation Equation can be written as:           PbI_2​(s)↔Pb²⁺(aq)+2I⁻(aq)

K_sp​ expression: K_sp​​ = [Pb²⁺][I⁻]²

Molar solubility(𝑆): [Pb²⁺] = S

                              [I⁻] = 2S

Substituting  the values K_sp​ = S⋅(2S)² = 4S³