GATE 2023 CY – Question 62

Physical Chemistry · Electrochemistry: Standard electrode potential and electrochemical cells. Nernst Equation and its application, relationship between electrode potential and thermodynamic quantities, Potentiometric and conductometric titrations. Ionic mobility and conductivity. Kohlrausch’s law, Debye-Hückel limiting law. Debye-Hückel- Onsager equation. · 2 marks · Numerical answer

By the Debye–Hückel limiting law, the mean molal activity coefficient of 0.87 g $K_2SO_4$ (molar mass 174 g/mol) in 1 kg water at 25 °C is ______ (two decimal places).

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Correct answer: 0.74 to 0.76

Explanation

The salt molality is (0.87/174)/1=0.005 mol/kg. Complete dissociation gives 0.010 mol/kg K+ and 0.005 mol/kg SO4²−. Ionic strength weights each ion by the square of its charge: I=½[0.010×1²+0.005×2²]=0.015 mol/kg. The Debye–Hückel limiting law gives log10 γ±=−0.509|z+z−|√I=−1.018√0.015≈−0.12468. Taking the base-10 antilogarithm gives **γ±≈0.75**. Using the salt molality directly in place of ionic strength would miss the sulfate charge contribution.