Question

The mean ionic activity coefficient of 0.004 molal CaCl$_2$ in water at 298 K (rounded off to three decimal places) is ________. (Given: Debye–Hückel constant for an aqueous solution at 298 K is 0.509 kg$^{1/2}$ mol$^{-1/2}$)

Hint:

The Debye–Hückel limiting law is valid for dilute electrolyte solutions ($I<0.01$). The ionic strength depends on both charge and molality.

Answer 1

Correct Answer: 0.772

Step 1: Use the Debye–Hückel limiting law.

ρlog _γ± = -A z₊ z_- √I

Step 2: Calculate ionic strength. For CaCl₂:

I = ¹⁄₂[m₊(z₊)² + m_-(z_-)²] = ¹⁄₂[0.004(2)² + 0.008(1)²] = 0.006

Step 3: Apply Debye–Hückel law.

ρlog _γ± = -0.509 × 2 × 1 × √0.006 = -0.509 × 0.1548 × 2 = -0.1576

γ± = 10^-0.1576 = 0.696

Step 4: Conclusion. Mean ionic activity coefficient γ± = 0.696 (≈ 0.68).