KEVOS® MAKEOS · Quality
pH Electrode Two-Buffer Calibration Check (Nernst Slope, Offset, Sample pH)
After a two-buffer calibration, is my pH electrode’s slope and offset within the acceptance limits, and what pH does my sample reading give at its own temperature?
Two-point pH electrode calibration check: the ideal Nernst slope ln 10 × RT/F at the calibration temperature, the measured slope from the two buffer readings and its percentage of ideal, the offset (the reading at pH 7) and the pH at which the electrode reads zero, and the sample pH from its millivolt reading with the slope scaled to the sample’s absolute temperature, against the user’s slope and offset acceptance limits.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| First buffer pH at the calibration temperature | pH | First buffer’s pH at the calibration temperature, from its certificate. |
| Electrode reading in the first buffer | mV | Millivolt reading in the first buffer. |
| Second buffer pH at the calibration temperature | pH | Second buffer’s pH at the calibration temperature. |
| Electrode reading in the second buffer | mV | Millivolt reading in the second buffer. |
| Calibration temperature | °C | Temperature of the buffers during calibration. |
| Acceptance limits | ||
| Lowest acceptable slope | % | Lowest slope your procedure accepts, as a percentage of ideal. |
| Highest acceptable slope | % | Highest slope your procedure accepts. |
| Largest acceptable offset at pH 7 | mV | Largest offset at pH 7 your procedure accepts. |
| Sample | ||
| Electrode reading in the sample | mV | Millivolt reading in the sample. |
| Sample temperature | °C | Temperature of the sample. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: First buffer pH at the calibration temperature
- What it is
- The certified pH of the first calibration buffer at the temperature it was used at, which anchors the electrode’s response line.
- Units and format
- Enter a number in pH: pH. The form accepts 0 pH to 14 pH. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7 pH as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- With the second buffer it sets the slope, the offset and every sample pH.
- Get it right
- Read the buffer’s pH at the calibration temperature from its certificate; buffers change with temperature.
What this means: Electrode reading in the first buffer
- What it is
- The millivolt signal from the electrode once it has settled in the first buffer.
- Units and format
- Enter a number in mV: mV. The form accepts -2000 mV to 2000 mV. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -3 mV as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Shifts the offset directly and changes the slope with the second reading.
- Get it right
- Wait for a stable reading, and rinse and blot the electrode between solutions.
What this means: Second buffer pH at the calibration temperature
- What it is
- The certified pH of the second calibration buffer at the calibration temperature, chosen so the two buffers bracket the samples.
- Units and format
- Enter a number in pH: pH. The form accepts 0 pH to 14 pH. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4.01 pH as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- With the first buffer it sets the measured slope.
- Get it right
- Choose buffers at least 2 pH apart that bracket the samples; the tool rejects buffers closer than 0.5 pH.
What this means: Electrode reading in the second buffer
- What it is
- The millivolt signal from the electrode once it has settled in the second buffer.
- Units and format
- Enter a number in mV: mV. The form accepts -2000 mV to 2000 mV. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 168 mV as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The slope changes in proportion to the difference between the two readings.
- Get it right
- Readings rise as pH falls; acid buffers give positive millivolts on most electrodes.
What this means: Calibration temperature
- What it is
- The temperature of the buffers while the calibration readings were taken, which sets the ideal Nernst slope.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 0 °C to 100 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The ideal slope rises with absolute temperature, so the slope percentage falls slightly.
- Get it right
- Measure the buffer temperature, not the room temperature.
Acceptance limits
What this means: Lowest acceptable slope
- What it is
- The smallest measured slope, as a share of the ideal Nernst slope, that your procedure or the electrode maker accepts.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 50% to 110%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 95% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Moves the slope pass line only.
- Get it right
- Take it from your laboratory procedure or the electrode maker’s instructions.
What this means: Highest acceptable slope
- What it is
- The largest measured slope, as a share of the ideal Nernst slope, that your procedure accepts.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 50% to 120%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 102% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Moves the slope pass line only.
- Get it right
- A slope above ideal usually means a buffer error rather than a better electrode.
What this means: Largest acceptable offset at pH 7
- What it is
- The largest difference from zero millivolts, at pH 7, that your procedure accepts for the electrode.
- Units and format
- Enter a number in mV: mV. The form accepts 0 mV to 200 mV. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mV as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Moves the offset pass line only.
- Get it right
- Take it from your laboratory procedure or the electrode maker’s instructions.
Sample
What this means: Electrode reading in the sample
- What it is
- The settled millivolt signal from the electrode in the sample being measured.
- Units and format
- Enter a number in mV: mV. The form accepts -2000 mV to 2000 mV. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mV as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Each millivolt changes the sample pH by one over the slope.
- Get it right
- Stir the sample the same way as the buffers and wait for a steady reading.
What this means: Sample temperature
- What it is
- The temperature of the sample when its reading was taken, used to scale the electrode slope to that temperature.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 0 °C to 100 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A warmer sample has a steeper slope, moving its pH towards the zero-reading pH.
- Get it right
- Measure the sample itself; this corrects the electrode only, not the sample’s own change of pH with temperature.
Method and formulas
- Ideal slope S = ln 10 × R T ÷ F, from the Nernst relation for the electrochemical potential of the hydrogen ion (Guggenheim ch. 8); R and F are exact SI constants, giving 59.159 mV per pH at 25 °C.
- Measured slope = (E₂ − E₁) ÷ (pH₁ − pH₂); offset = E₁ + S (pH₁ − 7); zero-reading pH = pH₁ + E₁ ÷ S.
- Sample pH = zero-reading pH − E_s ÷ S_s, where S_s = S × T_s ÷ T_c in kelvin (temperature compensation of the slope).
- Example: 171 mV across pH 7.00 and 4.01 is 57.191 mV per pH, 96.672 % of ideal at 25 °C with −3 mV offset; a 50 mV sample reads pH 6.0733.
Limitations
- Straight-line response between and near the buffers; two points cannot show non-linearity.
- The slope is scaled about the zero-reading point; the true isothermal intersection of a real electrode may differ slightly.
- Temperature compensation corrects the electrode slope only, not the real change of the sample’s pH with temperature.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Accept or reject a pH electrode after its routine calibration
- Work out a sample pH from a millivolt reading by hand
- Record calibration evidence for a quality system
Who it is for
- Laboratory and quality technicians
- Water and wastewater operators
- Instrument technicians
What you get
- Ideal and measured slope, and slope percentage
- Offset and zero-reading pH
- Sample pH at its own temperature
Interpreting the result
- A slope well below ideal usually means a dirty, dehydrated or ageing glass membrane; a large offset points to the reference junction or filling solution.
- Bracket the sample: calibrate with buffers either side of the pH you expect.
References
- E. A. Guggenheim, Thermodynamics: An Advanced Treatment for Chemists and Physicists, 5th revised edition (North-Holland, 1967), ch. 8, §8.03 (electrochemical potentials), §8.11 (general treatment of electromotive force), §8.12 (temperature dependence). Method reference; no text, tables or examples are reproduced.
- R. P. Buck et al., Measurement of pH. Definition, standards, and procedures (IUPAC Recommendations 2002), Pure and Applied Chemistry 74(11), 2169–2200.
- BIPM, The International System of Units (SI Brochure), 9th edition (2019): the Boltzmann and Avogadro constants and the elementary charge are exact, so R and F are exact.
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Open the pH Electrode Two-Buffer Calibration Check (Nernst Slope, Offset, Sample pH) calculator