GATE 2026 IN Q.26: solution and answer

GATE 2026 · INQ.26 · 1 mark · MCQ

A glass pH electrode behaves linearly with an output change of 60 mV per unit change in pH. The measurement reference is set such that a solution of pH 6 produces an output of 60 mV. The pH of a solution that results in an output of −90 mV is ________ .

(A)
3.5
(B)
3
(C)
8
(D)
8.5

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Answer and solution

ANSWER

The pH is 8.5, option (D). A glass electrode's output falls by 60 mV for each unit rise in pH, so a drop of 150 mV from the pH 6 reference means a rise of 2.5 pH units.

Official answer: DSource: Official answer key, GATE 2026 IN (IIT Guwahati)

A glass pH electrode follows the Nernst equation. Its potential depends on the hydrogen-ion activity: $E = E_{0} + \frac{2.303 R T}{F} lo g_{10} a_{H^{+}} = E_{0} - \frac{2.303 R T}{F} pH$ So the output falls as pH rises. The slope is negative.
The question gives the size of the slope as $60 mV$ per pH unit, so the sensitivity is $S = - 60 mV/pH$ . The linear model about the reference point is $V = V_{ref} - 60 (pH - pH_{ref})$ in mV.
Reference point: at $pH = 6$ the output is $60 mV$ , so $V = 60 - 60 (pH - 6) mV$
Set the output to $- 90 mV$ : $- 90 = 60 - 60 (pH - 6)$
Rearrange: $60 (pH - 6) = 150$ , so $pH - 6 = 2.5$ .
Result: $pH = 6 + 2.5 = 8.5$ .
Check: going from $60 mV$ to $- 90 mV$ is a change of $- 150 mV$ , which is $2.5$ pH units at $60 mV/pH$ . A more negative output means a less acidic solution, so the pH rises from 6 to 8.5. The answer is (D).

KEY IDEA

By the Nernst equation, a glass electrode's potential is $E = E_{0} - (2.303 R T / F) pH$ , so its slope against pH is negative (about $- 59 mV/pH$ at $2 5^{\circ} C$ ). A more negative output means a higher pH, i.e. a more alkaline solution.

WATCH OUT FOR

Taking the slope as $+ 60 mV/pH$ just because the question says "60 mV per unit change in pH" gives $pH = 3.5$ , option (A). That sign is the wrong way round for a glass electrode: its output drops as pH rises, so a fall from $60 mV$ to $- 90 mV$ means the pH goes up.

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