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pH Electrode Slope and Buffer Calculator

A pH electrode makes about 59 mV per pH unit at 25 °C, less when cold and more when warm. A healthy electrode is close to that ideal. Use these tools to correct buffer values for temperature, grade a two-point calibration by its slope and offset, and see the theoretical slope at your sample temperature.

pH Buffer Value at Temperature

Formula

Linear interpolation between 5 °C steps of the buffer table
pH(t) = pH(low) + (t - t low) / 5 x [pH(high) - pH(low)]
Inputs used
  • Buffer (nominal value at 25 °C)
  • Buffer temperature (°C)

Worked example (fictional plant data)

  1. 7.00 buffer at 12 °C: table gives 7.06 at 10 °C and 7.04 at 15 °C
  2. pH = 7.06 + (12 - 10) / 5 x (7.04 - 7.06) = 7.05

Two-Point Calibration: Slope and Offset

Formula

Theoretical slope, mV/pH = 2.3026 x R x T / F = 0.19842 x (°C + 273.15)   (59.16 at 25 °C)
Measured slope = (mV1 - mV2) / (pH2 - pH1)
Slope % = Measured slope / Theoretical slope x 100
Offset (mV at pH 7) = mV1 - Measured slope x (7 - pH1)
Inputs used
  • Buffer temperature (°C)
  • Buffer 1 value (at temperature) (pH)
  • Electrode mV in buffer 1 (mV)
  • Buffer 2 value (at temperature) (pH)
  • Electrode mV in buffer 2 (mV)

Worked example (fictional plant data)

  1. Calibrating in 7.00 and 4.01 buffers at 25 °C: readings -3 mV and +168 mV
  2. Theoretical slope = 0.19842 x 298.15 = 59.16 mV/pH
  3. Measured slope = (-3 - 168) / (4.01 - 7.00) = 57.19 mV/pH
  4. Slope % = 57.19 / 59.16 x 100 = 96.7%
  5. Offset = -3 - 57.19 x (7 - 7.00) = -3.0 mV

Nernst Slope at Temperature

Formula

Slope, mV/pH = 0.19842 x (°C + 273.15)
pH error per °C, 3 pH units from 7 = 3 x 0.19842 / Slope
Inputs used
  • Temperature (°C)

Worked example (fictional plant data)

  1. Sample at 10 °C
  2. Slope = 0.19842 x 283.15 = 56.18 mV/pH (vs 59.16 at 25 °C)

Cautions

  • Calibrate with fresh buffers that bracket your sample, at about the same temperature as the sample.
  • Rinse between buffers. Carryover is a common cause of a poor slope.
  • A slow response or a low slope usually means a dirty or aging electrode. Clean per the manual before you replace it.
  • Many meters show slope and offset after a calibration; record them to trend electrode health.

References

  • Standard Methods for the Examination of Water and Wastewater, 4500-H+ B (electrometric method).
  • IUPAC Recommendations 2002, Measurement of pH: definition, standards and procedures (Buck and others), for NIST primary buffer values.
  • Buffer supplier temperature tables (4.01, 7.00 and 10.01 values shown are typical).

Results are estimates for operator and technician use. Equations follow the references above; always check against the instrument manual, your calibration procedure and plant data.

This calculator also appears on ActivatedSludge.com, our consulting site. Results are for training and operator use; always follow your plant’s procedures.