Debey-Hückel screening length (κ⁻¹) is a measure of size of diffuse ion cloud around an ion, provided (2 e² NA)/(ε₀ kB T) ≈ 30 (nm molkg ⁻¹)⁻¹ at 298 K, which of the following values of κ⁻¹ is true for a 0.03 molal solution for Na₂ SO₄ in water (εr ≈ 100) ?

Q111 · CSIR-NET Chemistry, December 2019

Paper: CSIR-NET December 2019 · Subject: Physical Chemistry · Chapter: Electrochemistry · Topic: Electrochemistry – General · Marks: 2 · Difficulty: Medium

Debey-Hückel screening length $\left(\kappa^{-1}\right)$ is a measure of size of diffuse ion cloud around an ion, provided $\sqrt{\frac{2 e^{2} N_{A}}{\varepsilon_{0} k_{B} T}} \approx 30\left(\mathrm{nm} \sqrt{\text { molkg }^{-1}}\right)^{-1}$ at 298 K , which of the following values of $\kappa^{-1}$ is true for a 0.03 molal solution for $\mathrm{Na}_{2} \mathrm{SO}_{4}$ in water $\left(\varepsilon_{r} \approx 100\right)$ ?

(a)$\frac{10}{9} \mathrm{nm}$

(b)$\frac{9}{10} \mathrm{nm}$

(c)$\frac{10 \sqrt{2}}{9} \mathrm{nm}$

(d)$\frac{9}{10 \sqrt{2}} \mathrm{nm}$

Answer

Answer: A ✓ checked by 4AB · confidence high

Explanation

I(Na₂SO₄) = 3m = 0.09 mol kg⁻¹. κ = 30√(I/ε_r) = 30√(0.09/100) = 0.9 nm⁻¹, so κ⁻¹ = 10/9 nm (a).

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