Question

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. \(8.5\)

Hint:

The output falls by \(60\) mV for every one unit rise in pH from the reference point. Work out how many pH units correspond to a \(150\) mV drop from \(60\) mV to \(-90\) mV.

Answer 1

The Correct Option is D

Step 1: Set up the linear relation between pH and output voltage.
A glass pH electrode gives a straight line output versus pH, so we can write
\[ V = V_{ref} + m(pH - pH_{ref}) \]
where \(V_{ref}\) is the output at the reference pH, and \(m\) is the slope in mV per pH unit.

Step 2: Fix the direction of the slope.
For a glass pH electrode the output voltage falls as the pH rises. This is the usual response of a pH glass electrode, so the slope is negative even though the question gives only its size, \(60\) mV per pH unit. So \(m = -60\) mV/pH.

Step 3: Write the calibration line with the given reference point.
We are told \(V_{ref}=60\) mV at \(pH_{ref}=6\), so
\[ V = 60 - 60(pH - 6) \]

Step 4: Substitute the given output and solve for pH.
We need the pH at which \(V=-90\) mV.
\[ -90 = 60 - 60(pH-6) \]
\[ 60(pH - 6) = 60-(-90) = 150 \]
\[ pH - 6 = 2.5 \]
\[ pH = 8.5 \]

Step 5: Why the other options are wrong.
Options (A) \(3.5\) and (B) \(3\) come from taking the slope as positive (\(m=+60\)) and solving \(-90=60+60(pH-6)\), which lands on the wrong side of the reference pH of \(6\). Option (C) \(8\) comes from an arithmetic slip, such as rounding \(150/60\) down to \(2\) instead of keeping it at \(2.5\). Only \(8.5\) satisfies the calibration line exactly.

Final Answer:
The pH of the solution is \(8.5\). \[ \boxed{pH = 8.5} \]