Lab: Measuring pH and Trusting the Number

Purpose

A pH meter is the only instrument in this course that will give you a confident, stable, precise number that is simply wrong, and give it to you all afternoon. It does not squeak, drift visibly or refuse to settle. It reads 7.42 when the truth is 8.1, and it keeps reading it.

This session is therefore not about learning to dip a probe. It is about learning what the number depends on, how to check it against something whose value is known, and how many of the digits on the display you are entitled to copy into a notebook. You will calibrate a meter against two buffer standards, verify it against a third solution it was not calibrated with, predict the pH of six solutions from the chemistry of the two pages before this one, measure them, and account for every disagreement of more than a couple of tenths.

Learning objectives

By the end of this session you will be able to:

1. Say what a glass electrode actually measures, and why that makes calibration compulsory rather than optional.
2. Perform a two-point calibration, and state what the offset and the slope each correct.
3. Predict the pH of a carbonate, a hydrogencarbonate and an equimolar mixture of the two from cited constants, and explain any measured departure.
4. Give a pH reading with a defensible number of decimal places and a stated uncertainty.
5. Say what an indicator paper can and cannot establish, and name one case where a colour change is the better instrument.
6. Recognise the signs of a tired or dying electrode, and store one so that it lasts.

Prerequisites

• Acids, bases and pH, for the scale itself.
• Buffers and buffer capacity, because three of the six samples are buffers and the standards themselves are buffers.
• Measurement and uncertainty, for the treatment of an instrument reading. This session does not re-derive any of it.
• Laboratory safety and protective equipment, for the controls assumed throughout.
• Concentration and dilution, for making up the sample solutions.

Safety classification

Level A. The criteria of the classification rubric that decided it, taken in order:

• Substances and quantities. Commercial pH buffer standards at pH 4.01 and 7.00, supplied ready to use; household sodium carbonate and sodium hydrogencarbonate as solutions at about 1 per cent w/v; distilled water; tap water; and white vinegar diluted to about 2 per cent w/v acetic acid. All are aqueous, all are dilute, and the most severe classification among them is eye irritation. Sodium carbonate’s Chemical Safety Card records severe eye irritation and mild skin and respiratory irritation for the substance, and a violent reaction with acids generating heat and carbon dioxide.
• Energy. Nothing is heated. Solutions are used at room temperature and their temperature is recorded, which is the whole of the thermal content of the session.
• Electrical. A purchased, battery-powered meter. Nothing is built, wired or modified.
• Waste. Dilute aqueous solutions of carbonate, hydrogencarbonate and acetic acid, plus small volumes of used buffer standard. Nothing silver-bearing, nothing requiring specialist neutralisation.

What is not a hazard here, and why

There is no thiosulfate on this bench, and therefore no sulfur dioxide. The rule that acid samples and thiosulfate samples are never combined in one waste vessel is a real one, because acid on thiosulfate liberates sulfur dioxide — Kodak’s 1928 primer describes the same reaction from the other side, as acid decomposing hypo and precipitating sulfur. That rule does not bite here because no fixer is measured in this session. It will bite in Part XI, and the habit of keeping acid and thiosulfate waste separate is worth forming now, before it matters.

There is no concentrated acid and no caustic alkali. Glacial acetic acid carries H226 and H314 in the aggregated ECHA notifications on PubChem — flammable, and causes severe skin burns and eye damage — and that is a statement about the concentrate. What is handled here is dilute vinegar, which is a food product at the strength it is sold and is diluted further before use. Sodium carbonate is a laundry product handled as a 1 per cent solution. Neither statement transfers to the same substances at strength; the chemical encyclopaedia entries give the difference.

The alkaline buffer standard is deliberately not part of the Level A session. Commercial pH 10 standards are commonly borate-based, and borax as a solid carries H360, may damage fertility or the unborn child, in 93.2 per cent of the aggregated ECHA notifications — a classification that is not among those Level A admits. A supplied dilute standard may well be classified differently, but this course has not verified the safety data sheet of any particular product, so the three-point calibration is placed in Further experiments with the instruction to read your own product’s sheet first and make your own assessment. The two-point session below needs nothing beyond Level A.

What is left is what the Hazards section names: eye irritation from splashes, a fragile glass bulb, and a bench with liquids on it.

Hazards

Eye irritation from splashes. A 1 per cent sodium carbonate solution is an eye irritant; Chemical Safety Card 1135 records severe eye irritation for the substance. Dilute acetic acid stings. Eye protection is worn from the moment the first cap comes off until the bench is cleared.

Broken glass, and a very expensive small piece of it. The sensing element of a glass electrode is a membrane about 50 micrometres thick — one twentieth of a millimetre. It breaks if it is knocked against the bottom of a beaker, and a broken electrode is both a cut hazard and the end of the session. Support the electrode in a stand or clamp; never let it rest on the bottom of a vessel; never stir with it.

Acid meeting carbonate. Card 1135 records that sodium carbonate solution reacts violently with acids, generating heat and carbon dioxide. At the concentrations here that means fizzing rather than anything dramatic, but it is the reason the acid samples and the carbonate samples are rinsed from the electrode separately and are not poured into one another or into one waste vessel.

Slips and spills. Six samples, three standards, a rinse bottle and a waste beaker is a crowded bench. Everything stands in a tray, and the tray is bigger than the largest vessel on it.

Required PPE

• Safety glasses with side protection, to a stated standard, worn throughout. The Level A controls require eye protection whenever solutions are handled, and here the specific reason is the carbonate sample: severe eye irritation is its worst recorded short-term effect, and it is the one that would actually hurt.
• Nitrile gloves. The Level A controls require them whenever solutions are handled. On this page their second job is keeping skin oils and salt off the electrode bulb, which is a measurement control as much as a personal one.

Closed shoes, sleeves clear of the tray, and nothing on the bench that is also food.

Ventilation

Ventilation is not among the controls addressing a chemical hazard on this page, because nothing here produces a vapour, a mist, a dust or a gas in any quantity: every solution is aqueous, cold and dilute, and the only volatile component is the acetic acid in dilute vinegar, whose smell is noticeable and whose concentration at this dilution is not the reason for any control on this page.

Work with a window openable all the same, for two reasons that are not chemical. The vinegar smell in a closed room becomes unpleasant enough to make you hurry, and hurrying is the enemy of a calibration. And opening the window is the first item on the laboratory-opening list, rehearsed here so that it is automatic on a day when it does matter.

Materials

Item	Quantity	Notes
pH buffer standard, pH 4.01	2 sachets or about 100 ml	One for calibration, one kept sealed as a check
pH buffer standard, pH 7.00	2 sachets or about 100 ml	As above
Distilled or deionised water	1 L	For rinsing, and as sample 1
Tap water	as needed	Sample 2, and run the tap for 30 seconds first
Washing soda, or anhydrous sodium carbonate	about 10 g	Samples 3 and 6. Note on your label which form you used
Bicarbonate of soda	about 10 g	Samples 4 and 6
White vinegar, with its acidity stated on the label	100 ml	Sample 5, diluted
Narrow-range pH indicator papers	one pack, or two	Ranges covering about 4 to 7 and 7 to 10 are the useful pair
Lint-free laboratory tissue	a few sheets	For blotting the electrode, never wiping it
Adhesive labels and a waterproof pen	—	Every beaker is labelled before anything goes in it

Chemicals

This session handles buffer standards and household materials only. That is a deliberate departure from the sample list in the course manifest, and the reason is in the callout below.

Chemical id	Quantity	Form	Notes
sodium-carbonate-anhydrous	about 3 g	solid, then 1 % w/v solution	Sold as washing soda, usually as the decahydrate; Chemical Safety Card 1135 records severe eye irritation
sodium-carbonate-decahydrate (entry not yet written)	about 8 g	solid, if that is the form you have	286.14 g/mol against 105.99 for the anhydrous salt: 37.0 % carbonate by mass
sodium-bicarbonate	about 3 g	solid, then 1 % w/v solution	Bicarbonate of soda; 84.01 g/mol
acetic-acid (entry not yet written)	about 4 g as vinegar	dilute aqueous solution, about 2 % w/v	Diluted from white vinegar; the concentrate’s H314 classification does not apply at this strength
borax	none handled	—	Named because the pH 10 buffer standard is commonly borate-based and appears only in Further experiments

Potassium chloride is present but is not a chemical this session handles: it is sealed inside the electrode’s reference compartment, and it is the salt added to pH 4 buffer to make the long-term storage solution described under Storage. If you make your own storage solution you will handle it; that is a purchase decision rather than a step in this procedure.

The buffer standards themselves are purchased products, and their composition varies by supplier. Read the safety data sheet supplied with yours before the session — that is the skill reading an SDS exists for, and a buffer sachet is a good first real use of it.

!Why this session does not measure a developer, a stop bath or a fixer

The course manifest lists a working stop bath, a fixer and a developer among the samples. This page substitutes household analogues, for three reasons, and says so rather than quietly changing the list.

You may not own them yet. Part III comes before the first tray sequence. A reader working through in order has a meter and buffer standards at this point, and no photographic chemistry.

The teaching is not lost. Every obligation this session carries — what the electrode measures, calibration, slope and offset, the honest resolution of indicator papers, uncertainty, alkaline error, the record — is met exactly as well by a carbonate solution as by a print developer, and the carbonate, hydrogencarbonate and equimolar-mixture trio does something the photographic baths cannot: it lets you predict the answer to two decimal places before you measure it.

And one of the substitutions is a genuine electrode question. The Vernier pH sensor manual lists solutions its electrode must not be used in, and silver ions are on that list, alongside sulfide, perchlorate, protein-rich samples and Tris buffers. A used fixer contains dissolved silver. Before you put a probe into any photographic bath, check your own electrode’s manual for the same list; some electrodes are built for it and some are not.

Where the photographic baths are measured is Part VIII, where the developer is the subject, and Part XI, where fixer exhaustion is. Bring this session’s calibration discipline with you.

Equipment

• A pH meter with a combination glass electrode. A pen-type meter is acceptable and its limits are part of what this session teaches. Read its manual before the session, and specifically its calibration procedure, its stated accuracy and its storage instruction.
• A stand or clamp for the electrode, so that it hangs in the solution and does not rest on the bottom.
• Six 100 ml beakers, labelled, plus three more for the standards.
• A wash bottle of distilled water and a waste beaker for rinsings.
• A magnetic stirrer if you own one; otherwise a clean glass rod and the patience to stir gently by swirling the beaker.
• A thermometer, checked at its ice point as the commissioning session taught.
• A balance reading to 0.01 g, a 100 ml graduated cylinder and a 250 ml graduate.
• A timer, the notebook, and the calibration log.

Estimated cost

Cost band ££. The meter and the buffer standards are the whole of it, and both are one-off apart from the standards, which have a shelf life and are consumed. Everything else is Stage 0 equipment or a supermarket item. Dated prices live in the laboratory planner rather than in this page, so that they can be corrected without rewriting the text.

Estimated consumables cost

The meter is an instrument and belongs to the band above. What this session actually consumes is the buffer standards — which have a shelf life and are used up whether or not you use them — a litre of distilled water, and supermarket quantities of three household solids.

Consumed	This session	Sourced price	Cost this session
pH buffer standards at 4.01 and 7.00	2 sachets or about 100 mL of each	None. A named price gap: a pH meter, buffer standards at 4.01 and 7.00, and narrow-range indicator papers	—
Narrow-range pH indicator papers	about a dozen strips from two packs	None. A named price gap: a pH meter, buffer standards at 4.01 and 7.00, and narrow-range indicator papers	—
Distilled or deionised water	1 L	None. distilled-water carries a cost band and no dated figure	—
Sodium carbonate, anhydrous	about 10 g as washing soda	£7.20 per 500 g, anhydrous	£0.14
Bicarbonate of soda and white vinegar	about 10 g and 100 mL	Supermarket items; the planner prices neither	—
Lint-free laboratory tissue	a few sheets	None. glassware carries a cost band and no dated figure	—

The priced rows come to £0.14 for one run of this session, at the retail ranges read on 5 September 2026 and recorded in the laboratory planner. That is a floor, not a total: 4 of the 6 rows carry no dated price, so they are counted as nothing here and are certainly not free. A priced entry is a dated range to plan against, never a quotation.

The electrode itself is the awkward case and is deliberately not in the table: the planner calls it “a consumable measured in months to a couple of years”, which makes it neither a per-session cost nor a one-off purchase. Budget for it once a year or two, not once a session.

Waste streams

Three, all dilute and none silver-bearing.

• Alkaline aqueous waste: the carbonate, hydrogencarbonate and mixed-buffer samples, about 400 ml in total, at 1 per cent w/v or less.
• Acidic aqueous waste: the dilute vinegar sample and the pH 4.01 standard, about 200 ml in total.
• Near-neutral rinse water: everything else, including the pH 7.00 standard and the electrode rinsings.

Keep the first two in separate vessels, for the reason Card 1135 gives: carbonate and acid react, generating heat and carbon dioxide. At these concentrations that means fizzing and an overflowing beaker rather than anything worse, and an overflowing beaker of unlabelled liquid is exactly the mistake this course is trying to make impossible.

Preparation

Read your meter’s manual and your buffer standards’ data sheets. Both, before the session, not during it.

Condition the electrode. If it has been stored dry, or if it is new and arrived dry, soak the bulb in pH 4 buffer or in storage solution for at least eight hours before the session — the Vernier manual gives eight hours as the minimum for a sensor stored dry for a short period. An electrode taken straight from a dry box and used immediately will read slowly, drift, and give you a calibration you cannot trust.

Make up the sample solutions, at least an hour ahead so that they reach room temperature.

Sample	How to make 100 ml	Predicted pH at 25 °C
1. Distilled water	as supplied	see the note below
2. Tap water	run the tap 30 s, then fill	unknown; look up your supplier’s report
3. Sodium carbonate, 1 % w/v	1.00 g anhydrous, or 2.70 g of the decahydrate, to 100 ml	11.6
4. Sodium hydrogencarbonate, 1 % w/v	1.00 g to 100 ml	8.35
5. Acetic acid, about 2 % w/v	dilute white vinegar according to the strength on its label	2.6
6. Equimolar carbonate buffer	1.06 g anhydrous sodium carbonate (or 2.86 g of the decahydrate) and 0.84 g sodium hydrogencarbonate, to 100 ml	10.33

🧮Where those predictions come from, so you can check them

Sample 3. Carbonate is the conjugate base of hydrogencarbonate, whose acid constant OpenStax gives as 4.7 × 10⁻¹¹. Its base constant is therefore Kw ÷ Ka = 1.0 × 10⁻¹⁴ ÷ 4.7 × 10⁻¹¹ = 2.1 × 10⁻⁴. A 1 per cent w/v solution of the anhydrous salt is 10 g/L ÷ 105.99 g/mol = 0.094 mol/L. Solving the hydrolysis equilibrium gives [OH⁻] = 4.4 × 10⁻³ mol/L, so pOH = 2.36 and pH = 11.64.

Sample 4. The hydrogencarbonate ion is amphiprotic: it can give a proton away and take one. For such a salt the pH sits close to the mean of the two constants that bracket it, (6.37 + 10.33) ÷ 2 = 8.35, and — usefully — that result barely depends on concentration.

Sample 5. Acetic acid, Ka 1.8 × 10⁻⁵, at 20 g/L ÷ 60.05 = 0.333 mol/L gives [H₃O⁺] = √(1.8 × 10⁻⁵ × 0.333) = 2.4 × 10⁻³, so pH 2.61.

Sample 6. Equal moles of the acid and its conjugate base means the ratio in the Henderson and Hasselbalch equation is 1, its logarithm is 0, and the pH is exactly the pKa: 10.33. This is the most precisely predictable solution you will make in this course, and it is the one to argue with your meter about.

All four assume 25 °C. Record the actual temperature; you will need it in the Analysis.

Rule up your tables, from the Data to record section, before you switch the meter on.

Procedure

Stage 1: understand what you are about to do

Inside a combination glass electrode

1. 1pH-sensitive glass membrane — the bulb; about 50 µm thick, and the only part that responds to the sample
2. 2Internal reference — a silver/silver chloride wire in 0.1 mol/L hydrochloric acid: a fixed, known inside
3. 3External reference compartment — a second silver/silver chloride wire in potassium chloride solution
4. 4Liquid junction — a porous wick or frit; the salt bridge to the sample, and the source of a small potential of unknown size
5. 5To the meter — which measures the potential difference between the two wires and converts it to pH using a calibration you supply

Drawn to show the arrangement; proportions are not to scale, and the bulb is far thinner in reality than any drawing can show.

The electrode’s response follows a line. At 25 °C, for a good electrode, that line is

E = K + 0.05916 × log₁₀ a(H⁺)   volts

Response of a glass electrode at 25 °C

where E is the potential the meter measures, a(H⁺) is the hydrogen ion activity of the sample — effectively its concentration, for our purposes — and K is a constant that gathers together the potential of the reference electrode, the asymmetry of the glass membrane and the liquid-junction potential. Harvey’s account is blunt about K: all its contributions are subject to uncertainty, and it may change from day to day and from electrode to electrode. That is why you calibrate. Not to make the meter more accurate, but because without a calibration the meter does not know what K is and cannot convert its millivolts into a pH at all.

Two numbers come out of a calibration. The offset is where the line sits — the potential the electrode gives in a solution of known pH, usually 7. The slope is how steeply it responds: 0.05916 volts, or 59.16 mV, per pH unit at 25 °C for a perfect electrode, and somewhat less for a real or ageing one.

What a calibration measures, and what it misses if you only do one point

• Ideal electrode: 59.16 mV per pH unit, offset 0
• Aged electrode: 52 mV per pH unit, offset +20 mV

Show the numbers behind this plot

Two straight lines on axes of electrode potential against pH. The ideal electrode line passes through plus 177 millivolts at pH 4, zero at pH 7 and minus 177 at pH 10, a slope of minus 59.16 millivolts per pH unit. The aged electrode line is shallower and shifted: plus 176 millivolts at pH 4, plus 20 at pH 7 and minus 136 at pH 10, a slope of minus 52 millivolts per pH unit and an offset of plus 20 millivolts. The two lines cross near pH 4, which is the point of the diagram: an electrode calibrated at pH 7 alone, so that only its offset is corrected, assumes the ideal slope and therefore misreads everything away from pH 7. At a true pH of 10 such a meter would display 9.64, and at a true pH of 4 it would display 4.36, an error of 0.36 of a unit in each direction.

Series	pH of the solution	Electrode potential, mV
Ideal electrode: 59.16 mV per pH unit, offset 0	3.00	236.60
Ideal electrode: 59.16 mV per pH unit, offset 0	7.00	0.00
Ideal electrode: 59.16 mV per pH unit, offset 0	11.00	-236.60
Aged electrode: 52 mV per pH unit, offset +20 mV	3.00	228.00
Aged electrode: 52 mV per pH unit, offset +20 mV	7.00	20.00
Aged electrode: 52 mV per pH unit, offset +20 mV	11.00	-188.00

Both lines are arithmetic from the Nernstian response of 0.05916 V per pH unit at 25 °C given by Harvey; the aged electrode's 52 mV per unit is an illustrative value chosen to make the effect visible, not a measurement of any particular electrode. The curve is drawn to show the shape, not measured from a real material. Your own materials will differ, and measuring them is what the sensitometry part of the course is for.

Stage 2: calibrate

1. Rinse the electrode with distilled water from the wash bottle, into the waste beaker.
2. Blot it dry against lint-free tissue. Do not wipe or rub it: rubbing the bulb builds a static charge on the glass that takes minutes to leak away and makes readings wander in the meantime.
3. Place it in the pH 7.00 standard, with the bulb fully covered and clear of the bottom. Stir gently or swirl. Wait for the reading to stop moving — really stop, not slow down — and set the meter’s calibration or standardise control to 7.00. This sets the offset.
4. Rinse, blot, and place it in the pH 4.01 standard. Wait again, and set the meter’s slope control to 4.01. This sets the slope. On an automatic meter both steps are prompted; on a manual one they are two separate knobs, and Harvey’s description of the procedure is exactly this order.
5. Write down the slope if your meter displays it, as a percentage of theoretical or in mV per unit. That single number is the best health indicator an electrode has, and its history in your calibration log is what will tell you the electrode is dying months before it fails outright.

Stage 3: verify against something you did not calibrate with

Calibration is self-fulfilling: a meter always reads 7.00 in the buffer you just told it was 7.00. The check has to be a solution the calibration did not see.

6. Rinse, blot, and measure the second, unopened pH 4.01 sachet — a fresh check standard, not the one you calibrated in, which has now had an electrode in it and a lid off it. Record the reading. If it is not within your meter’s stated accuracy of 4.01, stop and go to Troubleshooting; do not proceed to the samples.

Stage 4: predict, then measure

7. Before measuring anything, write your predicted pH for all six samples in the notebook, and sign the line. This is not ceremony: a prediction written after the fact is not a prediction, and the whole value of the exercise is in the disagreements.
8. Measure the samples in order of increasing pH — 5, 1, 2, 4, 6, 3 — so that carryover on the electrode always moves the next reading in a known direction and never in the direction that would flatter you.
9. For each: rinse with distilled water, blot, immerse, stir gently, wait for a stable reading, and record the pH, the temperature and the time. Take a second reading a minute later without moving anything, and record that too.
10. Test the same sample with indicator paper immediately afterwards: dip a fresh strip, compare against the chart in good light, and record the value you would have written down from the paper alone.

Stage 5: close the loop

11. Return to the pH 7.00 standard and measure it as though it were a sample. The difference between this reading and 7.00 is the meter’s drift across the session, and it is a direct measure of how much of your data you can trust.
12. Rinse the electrode thoroughly and return it to its storage solution before you write anything up. The electrode comes first; the notebook can wait five minutes.

Expected observations

Sample 1, distilled water: the reading will not settle. This is the most instructive result of the session and it is a manufacturer-documented behaviour, not a fault. The Vernier manual states plainly that distilled water can read anywhere from pH 5.5 to 7.0 depending on how much carbon dioxide it has absorbed from the air, and that “due to a lack of ions, the pH values reported with the sensor in distilled water will be erratic.” Two causes, both real: dissolved carbon dioxide makes carbonic acid and genuinely acidifies the water, and the near-absence of ions makes the liquid-junction potential both large and unstable. Watch it wander, record the range you see, and stop treating “pure” as “neutral”.

Sample 2, tap water: somewhere near neutral, and stable, because tap water has ions in it. Where it sits depends on your supply. Thames Water, for instance, publishes hardness bands in milligrams per litre as calcium carbonate — soft up to 100, hard 200 to 300, very hard above 300 — and says all its water is hard because it passes through chalk; carbonate hardness and pH travel together.

Sample 5, dilute vinegar: stable, fast, and close to the predicted 2.6. Acids are the easy end for a glass electrode.

Sample 4, hydrogencarbonate: close to 8.35, and reassuringly independent of exactly how much you weighed.

Sample 6, the equimolar mixture: this should be your best agreement of the day. If your meter reads within 0.05 of 10.33 you have a well-behaved electrode and a good calibration.

Sample 3, 1 per cent carbonate: expect the largest disagreement, and expect the meter to read low. Two effects push the same way. The reading is an extrapolation far beyond the pH 7.00 and 4.01 points you calibrated between. And glass electrodes suffer alkaline error: above about pH 9 the membrane starts responding to sodium and potassium ions as well as to hydrogen ions, so it reports more hydrogen ion than is really there and therefore a lower pH. Harvey works a case at a true pH of 12.7, where the error is −0.5 of a unit. Your carbonate solution at 11.6 is well inside the region where this matters — and it is a sodium carbonate solution, so the interfering ion is the one the classic glass composition responds to most.

The indicator papers: you will find you can place every sample in the right unit and almost none of them in the right tenth.

What is happening chemically

In the electrode. The pH-sensitive glass is a thin membrane with a hydrated gel layer on each face. Hydrogen ions exchange between the solution and that gel layer, and because the activities on the two sides differ, a potential develops across the membrane. The inside is a solution of fixed composition — Harvey gives 0.1 mol/L hydrochloric acid with a silver/silver chloride wire in it — so the inside contributes a constant, and everything that varies is on the outside. That is the whole principle.

Why the response is 59.16 mV per pH unit. It is not an arbitrary calibration factor. A tenfold change in the activity of a singly charged ion produces a potential change of 2.303RT/F, which at 298 K works out at 0.05916 V. Because it contains T, it changes with temperature — which is what automatic temperature compensation exists for.

In sample 3. Carbonate takes a proton from water, leaving hydroxide behind, which is why a solution of a salt with no hydroxide in it is strongly alkaline.

In sample 6. Both members of the conjugate pair are present in equal amounts, so the mixture sits at the pKa and resists being moved. It is also, note, a buffer of exactly the kind used to calibrate meters — you have made a crude standard, which is why it agrees so well.

In sample 1. Carbon dioxide dissolves and forms carbonic acid, whose first ionisation constant is 4.3 × 10⁻⁷. There is almost nothing else in the water to oppose it, so a very small amount of a very weak acid sets the entire pH — and the amount depends on how long the bottle has been open, which is why the number is not reproducible.

Data to record

Four tables. Rule them up before the meter goes on.

Table 1. The calibration entry — this goes in the calibration log, not loose in the notebook.

Field	Value
Date and time
Meter and electrode, make and serial or purchase date
Standards used: nominal value, lot or batch, expiry date
Temperature of the standards
Reading in standard 1 before adjustment
Reading in standard 2 before adjustment
Slope reported by the meter (mV/pH or % of theoretical)
Check standard: nominal value and reading after calibration
Reading in the pH 7.00 standard at the end of the session
Drift across the session
Electrode returned to storage solution?

Table 2. The samples.

Sample	Predicted pH	Temp °C	Reading 1	Reading 2, one minute later	Difference	Indicator paper
5. Acetic acid ~2 % w/v	2.61
1. Distilled water	see notes
2. Tap water	your prediction
4. Sodium hydrogencarbonate 1 %	8.35
6. Equimolar carbonate buffer	10.33
3. Sodium carbonate 1 %	11.64

Table 3. Distilled water, watched.

Time from immersion	Reading
15 s
30 s
1 min
2 min
5 min
Range across all five

Table 4. Your uncertainty budget. One line per contribution, filled in during the Analysis.

Contribution	Estimate, pH units	How you got it
Meter’s stated accuracy		from the manual
Calibration error		check-standard reading minus its nominal value
Drift across the session		end-of-session standard reading minus 7.00
Temperature departure from 25 °C		see the Analysis
Alkaline error, samples above pH 9		see the Analysis
Combined, for a near-neutral sample
Combined, for the carbonate sample

Analysis

1. Account for every miss of more than 0.2 of a unit. Take the six rows of Table 2 and, for each disagreement between prediction and reading, name the cause: an arithmetic error in the prediction, a weighing error, a temperature departure, calibration extrapolation, alkaline error, or an electrode problem. A miss you cannot account for is a result, and it goes in the notebook as one.

2. Decide how many decimal places you are entitled to. Compare your meter’s display resolution with its stated accuracy. A meter that displays 0.01 and specifies plus or minus 0.2 — the figure Vernier publishes for its teaching-laboratory pH sensor — is showing you two digits it cannot support. Then add your own calibration error and drift from Table 4. Write the number of decimal places your budget justifies at the top of Table 2, and round every reading to it.

3. Separate the two things temperature does. Automatic temperature compensation, where your meter has it, adjusts the slope of the calibration line to the Nernstian value at the measured temperature. It does not correct for the sample’s own chemistry changing with temperature, and it cannot, because it does not know what the sample is. The buffer standards make the difference visible, because their own values are certified against temperature:

The certified pH of three NIST primary standard buffers, against temperature

• 0.05 m potassium hydrogen phthalate (nominal 4)
• Equimolal phosphate (nominal 7)
• 0.01 m sodium tetraborate, borax (nominal 9)

Show the numbers behind this plot

Three lines. The 0.05 molal potassium hydrogen phthalate standard is almost flat: 4.003 at 0 degrees C, 3.999 at 5, 3.998 at 10, 4.002 at 20, 4.008 at 25, 4.024 at 35 and 4.060 at 50, a total spread of about 0.06 across fifty degrees. The equimolal phosphate standard falls steadily: 6.984 at 0, 6.923 at 10, 6.881 at 20, 6.865 at 25, 6.844 at 35 and 6.833 at 50, a spread of about 0.15. The 0.01 molal sodium tetraborate, that is borax, standard falls much more steeply: 9.464 at 0, 9.332 at 10, 9.225 at 20, 9.180 at 25, 9.139 at 30 and 9.011 at 50, a spread of about 0.45, roughly ten times that of the phthalate standard. The published table's entry at 35 degrees C is out of sequence with its neighbours and is omitted here. The lesson drawn is that the alkaline standard's own value moves ten times as much with temperature as the acid standard's, so temperature matters most exactly where a photographic developer sits.

Series	Temperature, °C	Certified pH of the standard
0.05 m potassium hydrogen phthalate (nominal 4)	0.00	4.00
0.05 m potassium hydrogen phthalate (nominal 4)	5.00	4.00
0.05 m potassium hydrogen phthalate (nominal 4)	10.00	4.00
0.05 m potassium hydrogen phthalate (nominal 4)	15.00	4.00
0.05 m potassium hydrogen phthalate (nominal 4)	20.00	4.00
0.05 m potassium hydrogen phthalate (nominal 4)	25.00	4.01
0.05 m potassium hydrogen phthalate (nominal 4)	30.00	4.01
0.05 m potassium hydrogen phthalate (nominal 4)	35.00	4.02
0.05 m potassium hydrogen phthalate (nominal 4)	40.00	4.04
0.05 m potassium hydrogen phthalate (nominal 4)	45.00	4.05
0.05 m potassium hydrogen phthalate (nominal 4)	50.00	4.06
Equimolal phosphate (nominal 7)	0.00	6.98
Equimolal phosphate (nominal 7)	5.00	6.95
Equimolal phosphate (nominal 7)	10.00	6.92
Equimolal phosphate (nominal 7)	15.00	6.90
Equimolal phosphate (nominal 7)	20.00	6.88
Equimolal phosphate (nominal 7)	25.00	6.87
Equimolal phosphate (nominal 7)	30.00	6.85
Equimolal phosphate (nominal 7)	35.00	6.84
Equimolal phosphate (nominal 7)	40.00	6.84
Equimolal phosphate (nominal 7)	45.00	6.83
Equimolal phosphate (nominal 7)	50.00	6.83
0.01 m sodium tetraborate, borax (nominal 9)	0.00	9.46
0.01 m sodium tetraborate, borax (nominal 9)	5.00	9.39
0.01 m sodium tetraborate, borax (nominal 9)	10.00	9.33
0.01 m sodium tetraborate, borax (nominal 9)	15.00	9.28
0.01 m sodium tetraborate, borax (nominal 9)	20.00	9.22
0.01 m sodium tetraborate, borax (nominal 9)	25.00	9.18
0.01 m sodium tetraborate, borax (nominal 9)	30.00	9.14
0.01 m sodium tetraborate, borax (nominal 9)	40.00	9.07
0.01 m sodium tetraborate, borax (nominal 9)	45.00	9.04
0.01 m sodium tetraborate, borax (nominal 9)	50.00	9.01

Measured, certified values: the NIST primary standard buffer table reproduced by Harvey from Bates, Determination of pH, second edition, 1973. The borate row's 35 °C entry reads 9.012 in the table as transcribed, which is out of sequence with the 9.139 at 30 °C and 9.068 at 40 °C either side of it; that point is omitted here rather than plotted, because this course does not publish a figure it believes to be a transcription error. If you need it, go to Bates directly. Commercial buffer sachets sold as 4.01, 7.00 and 10.01 are technical buffers formulated to round values rather than these primary standards, and this course has not verified a manufacturer's temperature table for them: use the table printed on your own sachet.

4. Estimate your alkaline error. You cannot measure it without a second method, but you can bound it. Compare your carbonate reading with the predicted 11.64, subtract whatever you can attribute to extrapolation and to temperature, and attribute the remainder to alkaline error. Record it as a bound, not a value: “the reading is 0.3 low, of which at most 0.3 is alkaline error.”

5. Judge the papers honestly. For each sample, write down the pH you would have recorded from the paper alone, and the pH the meter gave. Then answer one question in the notebook: for which of the decisions in this course would the paper have been enough? Checking that a developer is somewhere near 10 and not near 7 — yes. Detecting a 0.15 drift in a fixer — no.

6. Write your own summary line for the electrode, into the calibration log: slope, check-standard error, session drift, and a one-word verdict. Next time you will have two lines, and a trend.

Troubleshooting

The reading will not settle in a buffer standard. Give it two minutes; a slow response is the classic first sign of an electrode that has been stored dry or is nearing the end of its life. If it is still moving, rinse, soak in pH 4 buffer for an hour, and try again. Harvey notes that the average lifetime of a typical glass electrode is several years, so an old one is a plausible diagnosis.

The meter reads 7.00 in the standard, 7.00 in tap water and 7.00 in the stop-bath sample. Work the checks in this order, and note what each rules out.

1. Is the electrode actually in the liquid? The bulb must be fully immersed. This rules out the commonest cause and costs five seconds.
2. Is the protective cap still on? It rules out the second commonest.
3. Measure the pH 4.01 standard. If it also reads 7.00, the electrode is not responding at all and the fault is in the electrode or its connection. If it reads 4.0-something, the electrode is fine and your samples really are all near neutral, which would mean a sample-preparation error.
4. Check the connector. A loose or damp BNC connector gives a dead, stable, plausible mid-scale reading.
5. Try the shock treatment the Vernier manual describes for a sensor that has been stored dry or responds sluggishly, then recalibrate.
6. If it still reads one number everywhere, the electrode is dead. A cracked bulb reads a constant value because the two half-cells are short-circuited through the crack.

The slope is much less than 59 mV per unit. An electrode’s slope falls as it ages, and manufacturers publish an acceptable range for their own products; this course has not verified a specific percentage window and will not invent one, so use your meter’s manual. Falling slope with a good offset usually means an ageing bulb. A large offset with a good slope usually means the reference junction is blocked or the reference solution has been diluted.

Readings drift downwards in every alkaline sample. Suspect carbon dioxide: an alkaline solution standing open absorbs it and genuinely becomes less alkaline. Cover the beakers, and measure the alkaline samples last and promptly.

The reading jumps when you touch the beaker or the bench. Static, usually from wiping the bulb rather than blotting it, or from a synthetic garment. Blot, wait, and keep your hand off the vessel while reading.

Alternative route

If you have no meter, this session is still worth doing with indicator papers alone, provided you are precise about what you get.

What papers can establish. That a solution is acid, near neutral or alkaline. That a print developer is in the region of 10 and not of 7 — which is enough to catch a badly mixed batch, a dilution error by a large factor, or a tray that has been contaminated with stop bath. That a stop bath is acid. That a fixer is on the acid side of neutral. ILFORD’s own process-control guidance treats sticks as a real alternative to a meter and names the useful ranges: pH 7 to 10 for developers, pH 4 to 7 for fixers.

What papers cannot establish. A difference of 0.2 of a unit — which is the difference between ILFORD’s published band for ID-11 stock, 8.60 to 8.70, and a batch that is out of specification. The drift of a working bath over its life. Any comparison you intend to make between two dates. The narrowest-range papers claim finer discrimination than the wide-range ones, and this course has not verified a manufacturer’s resolution figure for any of them — which is precisely why step 10 of the Procedure has you determine it for your own papers, on samples whose pH you predicted from chemistry. That comparison is the honest way to find out what your papers can do.

Do all six samples with papers. Predict, test, and record. You will end the session with a calibrated sense of your own strips, which is worth more than a borrowed number.

Clean-up

Rinse the electrode thoroughly with distilled water, blot it, and return it to its storage solution before anything else. Empty the sample beakers into the correct waste vessel, keeping acid and alkaline streams apart. Rinse all glassware with tap water and then with a little distilled water, and stand it to drain. Wipe the bench and the tray. Wash hands after gloves come off, not instead of.

Used buffer standard is not returned to the bottle. Nothing that has had an electrode in it goes back into a stock container — the same rule as for any sample aliquot in this course.

Storage

The electrode is the thing that will fail if you get this wrong. The Vernier manual is explicit on all three cases:

• Between measurements and up to 24 hours: stand the electrode in pH 4 or pH 7 buffer. It should never be stored in distilled water. The reference compartment is a concentrated potassium chloride solution, and standing in a solution with no ions in it draws that salt out through the junction.
• Longer than 24 hours: store in a pH 4 buffer and potassium chloride solution — the manual’s own recipe is 10 g of potassium chloride in 100 ml of pH 4 buffer — in the cap or bottle it was supplied in, with the bulb immersed. Harvey gives the general principle: the membrane’s outer surface must stay hydrated.
• If it has dried out: soak for at least eight hours in that storage solution before use, and recalibrate.

One manufacturer, not two. The storage rules above are taken from a single manufacturer’s manual, for a sealed gel-filled combination electrode sold to teaching laboratories, together with Harvey’s general statement that a glass electrode is stored in the storage buffer its manufacturer recommends. This course has not cross-checked a second electrode maker’s instructions, and electrodes differ — refillable ones have a fill hole and a fill solution that this one does not. Your own electrode’s manual governs, and where it disagrees with this page, follow it and note the disagreement in the calibration log.

Buffer standards have a shelf life and a once-opened life, both stated on the packaging. A bottle that has had an electrode dipped in it is contaminated and is no longer a standard. Sachets are better than bottles for occasional use, because each one is opened once.

Store the meter with its battery in and its cap on, somewhere it will not be knocked, and put the calibration log with it.

Disposal considerations

Three dilute aqueous streams: an alkaline one of sodium carbonate and hydrogencarbonate at 1 per cent w/v or below, an acidic one of dilute acetic acid and used phthalate buffer, and near-neutral rinse water. There is no silver, no thiosulfate, no developing agent and no heavy metal in any of them.

The chemistry is simple: the two named streams are a weak base and a weak acid, and mixing them in a large excess of water gives a near-neutral solution of sodium acetate, carbon dioxide and water. Doing that deliberately, slowly, in a vessel several times the combined volume, is the general practice for reducing a dilute acid and a dilute alkali to something innocuous — and it fizzes, which is why the vessel is oversized and why the two are not simply tipped together in a beaker.

This course does not give a jurisdiction-specific disposal instruction and will not start here. What it gives you is the description you need in order to ask a specific question: about 600 ml of aqueous solution containing sodium carbonate, sodium hydrogencarbonate, sodium acetate and buffer salts, none above 1 per cent w/v, with no silver, no sulfur compounds and no organic developing agent. Take that description to your local authority’s published guidance, or to your water company’s trade-effluent guidance if you are in any doubt, and follow what it says. Check your local regulations. ILFORD’s own guidance for domestic users makes the same point: find out what applies where you live.

Questions

1. State the pH of your own tap water to the precision your meter and your calibration actually justify, and defend the number of decimal places you used, citing your Table 4.
2. Your meter reads 7.00 in buffer, 7.00 in tap water and 7.00 in the vinegar sample. List the checks in the order you would make them, and say what each rules out.
3. Explain, in terms of ions, why the distilled-water reading wandered and the tap-water reading did not.
4. You calibrated at 4.01 and 7.00 and then measured a solution at a true pH of 11.6. Name the two separate effects that would make your reading low, and say which one a third calibration point would fix and which one it would not.
5. For which of your six samples would an indicator paper have been an adequate instrument, and for which would it not? Answer for a specific decision, not in general.
6. Your equimolar carbonate buffer read 10.33 and your 1 per cent carbonate solution read 11.2 against a prediction of 11.64. What does the good agreement on the first tell you about the disagreement on the second?

Further experiments

The third calibration point. Obtain an alkaline buffer standard, read its safety data sheet first, and satisfy yourself about its classification before you handle it: commercial pH 10 standards are commonly borate-based, and borax as a solid carries H360 in the aggregated ECHA notifications, which is outside the Level A criteria this session was written to. If you are content to proceed, recalibrate at three points and re-measure sample 3. The difference between the two carbonate readings is your extrapolation error, isolated.

The temperature run. Take the equimolar carbonate buffer, whose predicted pH is exactly the pKa, and measure it at 10, 20 and 30 °C, with automatic temperature compensation on and then off. You are watching two different things move at once: the electrode’s slope, which compensation corrects, and the solution’s own pKa, which it does not.

The exhaustion curve. Make 200 ml of the equimolar buffer, and add 2 ml portions of your dilute vinegar, recording the pH after each. Plot pH against millilitres added. You will draw, by hand and from your own kitchen, the buffered curve from the buffers page — including the moment where it stops being flat.

The unbuffered comparison. Do the same to 200 ml of tap water. Count how many drops it takes to move a unit, then compare with the buffer. That ratio is buffer capacity, measured by you.

The carbon dioxide experiment. Boil 200 ml of distilled water for five minutes, cool it covered, and measure its pH; then leave it open and measure again every ten minutes for an hour. Plot it. What you are watching is atmospheric carbon dioxide dissolving, and it is the same mechanism that quietly acidifies an open tray of print developer overnight.

Check your understanding

Question 1. An electrode obeys E = 20 mV − 52 mV per pH unit, referred to pH 7. You calibrate at pH 7.00 only, so the meter records the offset of +20 mV and then assumes the theoretical slope of 59.16 mV per unit. What will it display for a solution whose true pH is 10.00?

• 10.00
• 9.64
• 10.36
• 8.96

Show the answer and why

Answer: 9.64

At true pH 10 the electrode gives E = 20 − 52 × 3 = −136 mV. The meter converts using the slope it assumed: pH = 7 + (20 − (−136)) ÷ 59.16 = 7 + 2.64 = 9.64, an error of 0.36 of a unit. The same arithmetic at true pH 4 gives a displayed 4.36, an error of the same size the other way. A one-point calibration fixes where the line sits and says nothing about how steeply it runs, which is exactly why two points are the minimum and why the slope is the number worth logging.

Question 2. Why should a glass electrode never be stored in distilled water?

• Because distilled water dissolves the glass
• Because the reference compartment holds a concentrated potassium chloride solution, and standing in a solution with essentially no ions in it draws that salt out through the porous junction; the manufacturer’s instruction is short-term storage in pH 4 or pH 7 buffer and long-term storage in pH 4 buffer with potassium chloride added
• Because distilled water is too acidic
• Because the electrode needs to stay dry between sessions

Show the answer and why

Answer: Because the reference compartment holds a concentrated potassium chloride solution, and standing in a solution with essentially no ions in it draws that salt out through the porous junction; the manufacturer’s instruction is short-term storage in pH 4 or pH 7 buffer and long-term storage in pH 4 buffer with potassium chloride added

The Vernier manual states it directly: the electrode should never be stored in distilled water, short-term storage is in pH 4 or pH 7 buffer, and long-term storage is in pH 4 buffer with 10 g of potassium chloride per 100 ml added. Harvey gives the underlying principle from the other side: the membrane’s outer surface must remain hydrated, and a dried electrode has to be reconditioned by soaking. The same lack of ions is why distilled water is also a bad thing to *measure*: the reading is erratic.

Question 3. What does automatic temperature compensation actually correct?

• The sample’s own pH, which changes with temperature
• The slope of the electrode’s calibration line, which is proportional to absolute temperature — and nothing else; it cannot know how the sample’s own chemistry responds to temperature
• Both the slope and the sample’s chemistry
• The drift of the electrode between calibrations

Show the answer and why

Answer: The slope of the electrode’s calibration line, which is proportional to absolute temperature — and nothing else; it cannot know how the sample’s own chemistry responds to temperature

The Nernstian response is 2.303RT/F volts per decade, so it contains the absolute temperature; compensation adjusts the assumed slope to match the measured temperature. The sample’s own behaviour is a separate matter, and the buffer standards prove it: the certified value of the borax standard moves from 9.464 at 0 °C to 9.011 at 50 °C, a change of about 0.45, while the phthalate standard moves only about 0.06 over the same range. Those are the solutions’ own chemistry changing, and no compensation circuit can predict it for an unknown sample. Record the temperature.

Question 4. You make 100 ml containing 0.010 mol of sodium carbonate and 0.010 mol of sodium hydrogencarbonate. What pH do you predict at 25 °C, and why is this the best test of a calibration on the bench?

• pH 7.00, because the acid and base cancel
• pH 10.33, because equal amounts of a conjugate pair put the Henderson and Hasselbalch logarithm at zero, so the pH equals the pKa of the hydrogencarbonate ion
• pH 11.64, the same as a 1 per cent carbonate solution
• It cannot be predicted without knowing the total volume precisely

Show the answer and why

Answer: pH 10.33, because equal amounts of a conjugate pair put the Henderson and Hasselbalch logarithm at zero, so the pH equals the pKa of the hydrogencarbonate ion

pH = pKa + log([A⁻]/[HA]), and with equal amounts the ratio is 1 and its logarithm is 0, so pH = pKa = 10.33 from the second ionisation constant of carbonic acid, 4.7 × 10⁻¹¹. It is the best bench test because the prediction does not depend on the concentration, so a weighing error of a few per cent barely moves it, and because you are in effect making your own alkaline buffer standard — which is exactly what a purchased one is.

Question 5. A meter displays two decimal places and its manual specifies an accuracy of plus or minus 0.2 pH units. Your check standard reads 4.09 against a nominal 4.01, and at the end of the session the pH 7.00 standard reads 7.06. How should you record a sample that displays 8.47?

• As 8.47, because that is what the instrument said
• As about 8.5, with a stated uncertainty of at least 0.2 and probably more once the 0.08 calibration error and the 0.06 session drift are included
• As 8.470, since more figures are more informative
• As 8, because only whole units are ever justified

Show the answer and why

Answer: As about 8.5, with a stated uncertainty of at least 0.2 and probably more once the 0.08 calibration error and the 0.06 session drift are included

Display resolution is not accuracy. The manual’s ±0.2 already exceeds the second decimal place, and your own session adds a calibration error of 0.08 and a drift of 0.06 on top of it. Writing 8.47 claims a precision three of your own measurements contradict. The honest record is one decimal place with the budget written beside it — and the budget is the useful part, because next session’s numbers will tell you whether the electrode is getting worse.

Question 6. Your carbonate sample reads 11.2 against a prediction of 11.64. Which explanation should you rank first, and what would distinguish it?

• The prediction is simply wrong; recompute it
• A combination of calibrating only between pH 4.01 and 7.00, so the reading is an extrapolation, and alkaline error, in which the glass membrane responds to sodium ions as well as hydrogen ions above about pH 9 and therefore reads low; adding a third calibration point near pH 10 removes the first and leaves the second
• The solution absorbed carbon dioxide, which would make it read high
• The electrode is dead

Show the answer and why

Answer: A combination of calibrating only between pH 4.01 and 7.00, so the reading is an extrapolation, and alkaline error, in which the glass membrane responds to sodium ions as well as hydrogen ions above about pH 9 and therefore reads low; adding a third calibration point near pH 10 removes the first and leaves the second

Both effects push the reading the same way, which is why they have to be separated deliberately. Extrapolation error comes from fitting a line to two points and using it far outside them, and a third standard near the sample removes it. Alkaline error is a property of the glass: above roughly pH 9 the membrane responds to sodium and potassium as well as to hydrogen, so it over-reports hydrogen ion and under-reports pH — Harvey works a case at true pH 12.7 where the error is −0.5 of a unit. A sodium carbonate solution is the worst case for it, since the interfering ion is sodium. Carbon dioxide absorption would also lower the true pH, but that is the sample genuinely changing rather than the meter being wrong, and covering the beaker tests it.

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