Measuring pH in Thick, Dark Cook Mixtures¶

Version 1 · Disclaimer

A Stage B or C paste at 60–68 °Brix is opaque, dark, viscous and hot when the number matters. A glass bulb will not read it, strips cannot be read against the colour, and the value the base-dose procedure asks for (pH, cold, in the paste) is not quite the value a probe can give (pH of a diluted slurry at room temperature). The bench below plans the sample, corrects the slurry reading back to the paste with an explicit charge balance instead of a guess, and checks the electrode first, because no correction rescues a tired bulb.

The useful fact underneath it: a fruit paste is a real buffer. Its acids are partly neutralised by the potassium the fruit brought with it, so diluting it moves the pH by only a few hundredths (a malic paste at 3.5 reads about 3.54 at 1 + 4, 3.58 at 1 + 9); a jar already based to 6.15 does not move at all. Only an unbuffered acid shifts by the textbook half a unit per decade of dilution. So the honest answer is often "the slurry reading is the paste pH", and the bench says so when that is the case rather than inventing a correction.

The procedure¶

1. Weigh 10 g paste and 40 g distilled or boiled-cooled water (1 + 4 by mass) into a small beaker. Never tap water: its alkalinity reads as base.
2. Stir 60 s until uniform; stand 2 min.
3. Cool to 20–25 °C. Never put the probe in hot paste; glass electrodes drift and age above 60 °C.
4. Read with the probe fully immersed (a bulb needs about 30 mL of slurry). A flat or spear probe can also read a thin cold smear of the paste neat.
5. For a tight figure, titrate a weighed portion of the same slurry with 0.1 M NaOH to pH 8.2 and note the volume: that is Route A below.
6. Log the slurry reading, the dilution and the corrected estimate together.

The bench¶

It also runs on its own at /assets/apps/paste-ph-bench/index.html if the frame above is awkward on a phone.

The model¶

The liquid phase of the paste is described by a total acid concentration \(C\) (mol/L, split equally across the acids in the chosen mix) and a fixed cation load \(K\) (eq/L: the fruit's potassium plus any base dosed). At any dilution \(d\) the pH satisfies the charge balance

with \(\bar z\) the mean negative charge per acid molecule from the same pKa sets the base-dose arithmetic uses (malic 3.40 / 5.13, citric 3.13 / 4.76 / 6.40, tartaric 3.04 / 4.37, quinic 3.39, lactic 3.86; 25 °C, ideal). Mass dilutions are converted to volume with the paste density (default 1.30 g/mL; the water is taken as 1.00).

Two unknowns need two measurements. Route A takes the slurry pH and a titration of the same slurry to pH 8.2: the titration fixes \(C\) directly (it measures \(C\,[\bar z(8.2) - \bar z(\mathrm{pH}_s)]\) plus the free protons), the reading then fixes \(K\), and the balance is re-solved at \(d = 1\). Route B takes readings at two dilutions and solves the two balances for \(C\) and \(K\); it needs no titration but is ill-conditioned whenever the paste is well buffered, which is exactly when the readings differ by less than about 0.05, and the bench then reports "within 0.1" rather than a number. Route C takes one reading and an assumed TA; informational only.

The result is shown as a band. The lower edge applies the Davies equation (\(\log\gamma_1 = -0.51[\sqrt I/(1+\sqrt I) - 0.3 I]\)) to the ionic strength of the paste, which is several times that of the slurry; the upper edge is the ideal solution. Neither edge is the answer; the band is (Med).

Ideal-solution shifts, computed with the bench's own solver; the last row is why an unbuffered acid and a fruit paste behave differently.

The electrode¶

The Nernst slope is \(0.19842\,(T + 273.15)\) mV per pH unit, 59.16 mV at 25 °C. From two buffer readings in mV the bench reports the measured slope, its efficiency against Nernst and the offset at pH 7.

A meter with no mV display gets a read-back check instead: after calibrating on 7.00 and 4.01, read the 4.01 buffer as an unknown; more than 0.05 out fails. Opened pH 7 buffer drifts upward as it takes up CO₂; the pH 4 buffer is stable.

Temperature compensation on the meter corrects the electrode slope, not the sample. Carboxylic acid pKa values move by roughly 0.002 per °C, so a warm slurry reads within about 0.05 of its 20 °C value (Low); the real reasons to read cold are electrode life and that the base procedure is defined cold.