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Two-point calibration of a pH meter and sample measurement

A glass combination electrode with an unknown zero and slope: calibrate it with pH 4.01, 7.00 and 10.01 buffers, measure acetic acid, an ammonia buffer, a high-sodium caustic solution and an unknown buffer, then reveal the electrode to find which readings were pulled off by extrapolation or by the sodium error.

Difficulty ●○○ ≈ 20 min

Aim Calibrate a pH meter correctly, work out the electrode’s slope efficiency and zero, and measure the pH of an unknown buffer.
Glass/Ag–AgCl combination electrode · 25 °C

Two-point calibration of a pH meter

Put the electrode into
4.01buffer7.00buffer10.01bufferABC?7.14pHSTABLE 25.0 °CCALREADMODE
Stable · −8.6 mV

Factory setting: 0 mV = pH 7, 100 % slope (not calibrated)

Sample readings

—

02468101214pH−400−2000200400Potential / mV
  • The meter’s calibration line
  • Calibration points
The electrode potential follows Nernst, E = E₀ − β·(59.16 mV)·(pH − 7), plus the sodium error (K(H⁺, Na⁺) = 10⁻¹¹); the offset E₀ (±18 mV) and efficiency β (95–99.7 %) come from a deterministic hash of the electrode number and stay hidden until you calibrate. The samples’ true pH values are exact acid–base calculations (ideal solutions). Readings settle exponentially with τ = 0.7 s (illustrative; real electrodes often need 10–30 s); buffer temperature coefficients, junction-potential changes and electrode hysteresis are not modelled.

Procedure

  1. Put the electrode in the pH 7.00 buffer, wait for a stable reading and press “Calibrate on this buffer”; note the zero (mV).
  2. With this one point only, measure samples A (acetic acid) and B (ammonia buffer) and record the displayed pH.
  3. Complete a two-point calibration with the pH 4.01 buffer and read the slope efficiency; measure A and the unknown again. Recalibrate with 7.00 and 10.01 before measuring the basic samples B and C.
  4. Switch to the mV display and watch how the reading settles when the electrode moves between solutions.
  5. Reveal the true pH values and the electrode parameters, compute the error of each reading and explain where it came from.

What to notice

  • With one buffer only, the error grows with distance from pH 7: the meter assumed a 100 % slope.
  • After a two-point calibration, samples lying between the two buffers read within 0.01 of the truth.
  • 0.10 M NaOH + 0.90 M NaCl has a true pH of 13.0, yet the general-purpose glass shows only about 11 — the sodium error, which no calibration can remove.
  • Slope efficiencies lie between 95 and 100 % and zeros between a few and a dozen or so millivolts — every electrode differs.

In a real lab

  • Rinse the electrode with distilled water and blot it gently between solutions; never wipe the bulb, which charges and scratches it.
  • Measure buffers and samples at the same temperature or use automatic temperature compensation; opened buffers absorb CO₂ — the alkaline one especially — and must be replaced regularly.
  • Store the electrode in 3 M KCl storage solution, not distilled water; a clogged junction makes readings drift and respond slowly.
  • Use a low-sodium-error electrode for strongly alkaline, high-sodium samples, and clean the membrane after protein- or oil-rich samples.

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