GATE 2026 CY – Question 63

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

A calibrated glass-electrode/standard-calomel pH meter measures 0.814 V for pH 4.01 at 25 °C. Its potential for 0.0040 M acetic acid in V (three decimal places) is _____. Given $K_a=1.75\times10^{-5}$, $2.303RT/F=0.059$ and $a_{H^+}=[H^+]$.

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Correct answer: 0.836 to 0.842

Explanation

The glass-electrode/calomel pH meter responds linearly to the pH:
$$E=E^0-0.059\,\text{pH}\quad(25\,^\circ\text{C}).$$

**Step 1: calibrate** with the buffer: $0.814=E^0-0.059(4.01)$, so $E^0=0.814+0.2366=1.0506$ V.

**Step 2: pH of 0.0040 M acetic acid.** With $K_a=1.75\times10^{-5}$ and $C=0.0040$ M, solve the weak-acid equilibrium exactly:
$$[H^+]^2+K_a[H^+]-K_aC=0\;\Rightarrow\;[H^+]=\frac{-K_a+\sqrt{K_a^2+4K_aC}}{2}=2.5597\times10^{-4}\text{ M},$$
$$\text{pH}=-\log(2.5597\times10^{-4})=3.592 .$$

**Step 3: potential.**
$$E=1.0506-0.059\times3.592=1.0506-0.2119=\mathbf{0.839\ V}.$$

Official GATE 2026 answer key: https://gate2026.iitg.ac.in/doc/download/2026/Keys/CY_Keys.pdf