Ionic Strength

Definition of Ionic Strength:

• Ionic strength (μ) is a measure of total ion concentration in solution.

$\mu = 12 \sum c_i z_i^2$$\mu = \tfrac{1}{2} \sum c_i z_i^2$$\mu = 21 \sum c_i z_i^2$

• Where:
  • ci​ = concentration of ion i
  • zi​ = charge of ion i

Effect:

• Reactions involving charged species are influenced by ionic strengths:
  • Like charges: rate decreases with increasing ionic strength.
  • Opposite charges: rate increases.

Debye–Hückel equation (simplified):

$\log k = \log k^{0} + 1.02 z_{A} z_{B} \sqrt{\mu}$

• Where:
  • z_A​, z_B​: charges of reacting ions
  • μ: ionic strengths
  • k₀: rate constant at zero ionic strengths

Problem: Determining Ionic Strengths

Given:

• Solution contains:
  • 1 M NaCl
  • 05 M CaCl₂
• Find ionic strengths μ

Solution:

$\mu = \tfrac{1}{2} \sum C_i Z_i^2$

• Break down ions:
  • Na⁺ (0.1 M, Z=+1Z = +1Z=+1)
  • Cl⁻ from NaCl (0.1 M, Z=−1Z = -1Z=−1)
  • Ca²⁺ (0.05 M, Z=+2Z = +2Z=+2)
  • 2 Cl⁻ from CaCl₂ → (0.05 M × 2 = 0.1 M)
• Now calculate:

$\mu = \tfrac{1}{2} \Big[ (0.1)(1)^2 + (0.1)(1)^2 + (0.05)(2)^2 + (0.1)(1)^2 \Big]$

$\mu = \tfrac{1}{2}\,[0.1+0.1+0.2+0.1]
= \tfrac{1}{2}\,(0.5)
= \boxed{0.25 \,\text{mol/L}}$

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