Questions: Activity, Ionic Strength, and the Debye–Hückel Equation

Question 1

What is the ionic strength of 0.010 M MgCl₂?

• A. 0.010 M
• B. 0.020 M
• C. 0.030 M
• D. 0.040 M

Answer: (C)

I = ½[(0.010)(2²) + (0.020)(1²)] = ½(0.040 + 0.020) = 0.030 M. The Mg²⁺ ion counts four times per mole because of the z² term.

Question 2

Adding NaNO₃ to a saturated AgCl solution lowers the solubility of AgCl.

• T. True
• F. False

Answer: False

NaNO₃ shares no ion with AgCl, so there is no common-ion effect. It raises the ionic strength, which lowers the activity coefficients of Ag⁺ and Cl⁻, so more AgCl must dissolve to satisfy Ksp written in activities.

Question 3

At the same ionic strength, which ion has the smallest activity coefficient?

• A. Na⁺
• B. Cl⁻
• C. Ca²⁺
• D. Al³⁺

Answer: (D)

In the Debye–Hückel equation, log γ is proportional to z². A 3+ ion is affected nine times as strongly as a 1+ ion, so Al³⁺ has the lowest γ.

Question 4

Use the Debye–Hückel limiting law, log γ = −0.51z²√I (water, 25 °C), to estimate γ for a singly charged ion at I = 0.010 M.

Model answer: About 0.89

log γ = −0.51 × 1 × √0.010 = −0.51 × 0.10 = −0.051, so γ = 10^(−0.051) ≈ 0.89. Even at this low ionic strength, the ion behaves as if it were about 11% less concentrated.