Skip to content
Science Journaling Club

Volume 1, Issue 3March 2025

Spring 2025

Three pieces of earth science that each break a rule somebody teaches. Gold leaking out of a core that was supposed to be sealed, younger rock sitting underneath older rock across half a basin, and the first video anybody has taken of a fault tearing the ground apart.

This issueSJC 1.3
Published
March 2025
Articles
9
Research
5
Field notes
4
With code
9

Contents

9 articles, in the order the club meant them to be read.

  1. ResearchMethods

    Solving Seawater: A Carbonate Equilibrium Solver and What It Says About Acidification

    The carbonate system in seawater is four coupled equilibria and one conservation law, and substituting them into each other collapses the whole thing into a single quartic in the hydrogen ion concentration with exactly one positive root. We wrote a solver for it. No seawater was sampled at any point: the computation is the experiment. Using published temperature and salinity dependent constants on the total hydrogen ion scale, the solver satisfies the alkalinity definition to 0.849 ulp of total alkalinity at every one of 64 check points, and a safeguarded Newton iteration, a log-space bisection and the roots of the cleared quartic agree to 1.9 × 10−14 relative. At 18 °C, salinity 35 and alkalinity 2300 µmol/kg, the solver returns pH 8.1817 at 280 ppm and 8.0361 at 420 ppm, against accepted figures of 8.17 and 8.05. Between those two atmospheres the hydrogen ion concentration rises by 39.80%, not the 30% that is usually quoted, and we report that plainly rather than rounding toward it. The gap is 51.5 Monte Carlo standard deviations wide, so the published uncertainty in the constants cannot account for it; asked instead the 370 ppm question the quoted figure was originally answering, our solver returns a pH decline of 0.0993 units against the published observational estimate of 0.11 ± 0.03, agreeing to 0.36 standard deviations. Over the full sweep from 180 to 1000 ppm, bicarbonate rises 30.7% while carbonate falls 69.2% and the aragonite saturation state drops from 4.407 to 1.356. Neglecting the second dissociation, the textbook shortcut, costs up to 0.127 pH units and misstates the aragonite saturation state by as much as 79.5%. A 200,000-trial Monte Carlo over the published uncertainties in six equilibrium constants gives 39.80% ± 0.0004% (standard error), with a 95% interval of 39.43% to 40.17%. Seed 20250320. Runtime 1.33 seconds.

    Spring 2025Read 33 minSections 12

  2. ResearchMethods

    Where the Textbook Titration Shortcuts Actually Fail

    Chemistry courses hand out four or five closed-form shortcuts for titration curves and then guard each one with a shrug. We wrote an exact solver instead, built from charge balance and mass balance with nothing thrown away, and used it to audit the shortcuts across a grid of 57 acid strengths and 41 concentrations. The solver was checked first: charge balance holds to a worst relative residual of 4.35×10−15, speciation fractions sum to one within 1.5 machine epsilons, the strong-acid case reproduces its closed form to 2.6×10−12 pH units, and 60-digit decimal arithmetic reproduces the double-precision answer to 8.9×10−16 pH. 3,489,396 exact solutions were computed in all. Henderson-Hasselbalch then turns out to have a sharply defined licence. At 0.1 M it stays inside 0.05 pH only for acids with pKa between 3.92 and 9.84, and that band slides exactly one pKa unit per decade of dilution in each direction, with fitted slopes of −0.9998 and +0.9995 against a closed-form prediction of −1 and +1. The two edges meet at 1.09×10−4 M, below which no acid of any strength keeps the buffer equation inside 0.05 pH. Of 18 real acids at 0.1 M, 8 pass and 10 do not; acetic acid is comfortably in at 0.008 pH, formic acid is out at 0.068, phenol is out at 0.065. A Monte Carlo over the region students actually work in, 200,000 draws from seed 20250411, puts the chance of exceeding 0.05 pH at 2.210% ± 0.033%, against 61.77% ± 0.11% over the full parameter space. The five percent rule fails to protect the square-root formula: of the 1,486 grid cells that obey it, 523 still miss by more than 0.05 pH. And the whole analysis is for an ideal solution: switching on Davies activity corrections moves a 0.1 M half-equivalence point by 0.073 pH, which is larger than the tolerance we spent the article defending.

    Spring 2025Read 31 minSections 12

  3. ResearchOriginal Research

    What a Buffer Is Actually Resisting

    Buffer capacity is introduced as a formula and usually abandoned there. We computed it instead, as the exact derivative β=dCb/dpH\beta = dC_b/d\mathrm{pH} of a full charge-balance solver, across dissociation constants from pKa 2 to pKa 12 and concentrations from 0.1 mM to 1 M. No solution was mixed at any point. The club has no laboratory, so the computation is the experiment. Three independent routes to β\beta agree: the analytic expression, a five-point finite difference, and a simulated titration that adds a measured dose of base and re-solves the nonlinear equilibrium, which match to 1.4×10−10 and 1.8×10−8 respectively. The maximum sits at pH equal to pKa, but not exactly: at 0.100 M and pKa 5 it sits 3.477×10−4 pH units below, a displacement the water term predicts to a ratio of 1.0008, and which is identically zero only at pKa 7.000. Peak height matches ln⁡(10) C/4\ln(10)\,C/4 to 8 parts per million at 0.100 M. Capacity falls to half over a window of 1.531103 pH units, so at one unit from pKa only 33.06% of peak survives and at two units 3.92%. Six of twenty-two tested buffers have no capacity maximum at all. A two-component buffer splits into twin peaks above a separation of 1.143895 pH units, which is 2 arccosh(2)/ln⁡102\,\mathrm{arccosh}(2)/\ln 10. For blood at 37 °C, pH 7.40 and pCO2 40 mmHg, the model produces 24.50 mmol/L bicarbonate without being told to, and gives an open-system capacity of 57.32 against a closed-system 2.940 mmol/L per pH unit, a ratio of 19.50. A Monte Carlo over five uncertain physiological inputs, 200,000 draws, gives 20.162 ± 0.003 with a standard deviation of 1.213. The open system at 1.3 pH units off its own optimum beats the same closed chemistry sitting exactly on that optimum by a factor of 3.85. Seed 20250321.

    Spring 2025Read 27 minSections 12

  4. ResearchMethods

    The Common Ion Effect Is Taught Backwards

    Every general chemistry course states the common ion effect as a rule with no stated exceptions: add an ion the precipitate already contains, and its solubility falls. We built an exact solver for precipitation equilibria, one that carries the solubility product, stepwise complex formation, the anion's own acid-base speciation, and the water equilibrium as a single coupled system with nothing approximated away, and set it against three sparingly soluble salts. For barium iodate and calcium fluoride the rule holds everywhere on the grid we tried, and the solver's own zero-common-ion limit matches closed-form algebra to a few parts in 107. Silver chloride is where it breaks. Added chloride drives AgCl solubility down to a minimum of 3.11 × 10-7 M at 3.01 × 10-3 M added chloride, 223 times below the pure-water value, matching the order of magnitude the analytical-chemistry teaching literature has quoted for this minimum for eighty years [1][2]. Past that point, more chloride does the opposite of what every course says it should: at 5 M NaCl the solver returns 4.96 × 10-3 M dissolved silver, 15,900 times the minimum and 367 times the pure-water solubility, carried almost entirely as AgCl2-, AgCl32- and AgCl43- rather than as free Ag+. A hundred thousand Monte Carlo draws over an assumed ±0.05 log-unit uncertainty in the 1952 stepwise formation constants [4] never once erased the reversal: the location of the minimum moved by a few percent, its existence did not. Every mass balance, complex-formation expression and Ksp, evaluated at the converged solution, closes to a few parts in 1015 (machine precision); an independent full charge balance closes to a few parts in 109, limited by ordinary floating-point cancellation between [H+] and [OH-] near neutral pH, not by the model. Calcium fluoride shows a second, unrelated failure of the naive picture: at fixed added fluoride, dropping the pH from 7 to 0 raises its solubility 816-fold through protonation of F-, a channel the common-ion rule never mentions and one that, for this salt, never reverses. The textbook rule is not false, only incomplete: it is missing a clause. Seed 20250306.

    Spring 2025Read 27 minSections 12

  5. ResearchOriginal Research

    The Reaction That Gives You the Wrong Product Because You Were Impatient

    Two products, one shared starting material, two reversible one-step reactions, and no way for the products to talk to each other directly: this is the standard textbook picture of kinetic versus thermodynamic control, and the textbook almost never tells you how long the experiment takes. We wrote the rate equations, integrated them with a from-scratch fourth-order Runge-Kutta stepper, and separately solved the same linear system exactly by eigendecomposition, then checked the two against each other and against the closed-form single-reaction solution at matching time points. They agree to better than one part in a million everywhere we tested, RK4's global error falls with step size at an observed order of 4.125 against a theoretical 4.000, mass is conserved to 2.0 × 10−14 relative, and the simulated ratio of products reproduces both textbook limits: the kinetic ratio k2/k1k_2/k_1 at short times and the thermodynamic ratio K2/K1K_2/K_1 at long times, each to better than one part in ten thousand once the numerics stop fighting catastrophic cancellation. For a representative pair of channels, 10 kJ/mol apart in barrier height and 25 kJ/mol apart in stability, the faster product claims 98.0% of the mixture within two hours, then loses ground it never gets back: the slower, more stable product does not overtake until 111.7 days at 298.15 K. Across a grid of 676 barrier and stability combinations, only 3.0% cross within a day and 22.5% never cross at all because we gave the "thermodynamic" product no real stability edge; the rest take anywhere from two weeks to millions of years, with almost nothing in between a day and two weeks, because the crossover time is exponential in the barrier gap and exponentials do not fill in the middle. Heating the baseline reaction from 298 K to 400 K divides the wait by 137,000; cooling it to 250 K multiplies the wait by 7,620. No reagent was weighed and no flask was heated for this study. The computation is the experiment, and the club has tried to be honest about what it leaves out.

    Spring 2025Read 25 minSections 12

  6. Field noteOriginal Research

    Why the Periodic Table Is That Peculiar Shape

    Two independent constructions, neither of which involves a beaker. The first builds the periodic table out of nothing but quantum numbers: enumerate every orbital with l<nl<n, give each one 2(2l+1)2(2l+1) seats, and fill them in order of increasing n+ln+l. Run that rule from hydrogen onward and it reproduces the period lengths 2, 8, 8, 18, 18, 32, 32 exactly and lands on all seven noble-gas atomic numbers — 2, 10, 18, 36, 54, 86, 118 — with no chemistry supplied as input anywhere. Laid out honestly, with the f-block left in line rather than cut out, the table is 32 columns wide; the 18-column chart on the classroom wall is that same table with 14 columns lifted out and filed underneath. Checked element by element against measured ground states from Z = 1 to 103, the rule gets 83 of 103 right and misses 20, and every miss sits in the d-block or the f-block — the s- and p-blocks, 44 elements between them, never break it once. The second construction asks how far a much cruder rule, Slater's 1930 electron-screening recipe, can push those same quantum numbers toward numbers you could look up: effective nuclear charge, ionisation energy, atomic radius. It passes the one check with an exact answer — hydrogen predicted at 13.6057 eV against a measured 13.5984 eV — and then degrades on a schedule: a mean ionisation-energy error of 11.9% across period 2 widening to 38.4% across period 3, worst at aluminium (+79.4%), because the rule has no way to ask which orbital an electron actually occupies. The matching radius law does better, landing within 11.2 pm on average of Slater's own 1964 empirical radii from one fitted constant. A last, even cruder relativistic estimate on a single 1s electron is enough to see, in outline, why a gold atom absorbs blue light and a silver one does not.

    Chemistry & PhysicsRead 24 minSections 12

  7. Field notePaper Analysis

    The Core Is Leaking: Ruthenium-100, Hawaiian Lava, and Gold From the Center of the Earth

    Earth's metallic core is supposed to be a sealed room: whatever fell into it 4.5 billion years ago stays there. In May 2025 a Göttingen-led team reported that Hawaiian basalts carry an excess of the isotope ruthenium-100, about nine parts per million, a signature that matches core metal and matches nothing else on the planet. The same rocks carry the tungsten-182 deficit you would expect from that source, an independent clock nobody tuned to match [1]. We re-derive the mixing arithmetic ourselves in a deliberately simple two-component model and get a source containing 0.071% core metal by mass (68% interval 0.044–0.129%), comfortably inside the paper's published upper bound. A mass-flux calculation turns that into roughly 159 kg of core-derived gold a year. One wedding band's worth every thirteen minutes. What follows is a student reconstruction rather than the paper's own analysis, built on seven stated assumptions, one of which (the isotopic composition of a reservoir nobody has ever sampled) could move the answer by a factor of three.

    GeochemistryRead 32 minSections 12

  8. Field noteExplainer

    Younger Rock Beneath Older Rock: The North Sea Layers That Sank Through Time

    A 2025 study of basin-scale 3D seismic data from the northern North Sea reports hundreds of kilometre-wide sand bodies that appear to have liquefied, sunk through a 200–500 m interval of older microfossil ooze, and come to rest beneath it. Rafts of that older ooze went up instead. They built mounds. The authors call the sunken sand sinkites, the risen ooze floatites. Grant the interpretation and the law of superposition has its largest documented breach. We rebuilt the physics with a deliberately simple club model, which puts saturated sand at 40% porosity at 2002 kg/m³ and ooze at 65% porosity at 1404 kg/m³, a contrast of 598 kg/m³ pushing steadily downward at 5861 N/m³. Liquefaction wants a pore-pressure ratio of 1.00 and nothing else. A Stokes-type descent of 200 m takes 2 kyr to 2 Myr for effective viscosities of 1017–1020 Pa s, and nobody has ever measured that viscosity. The mechanism is allowed. What happened is a different question, still open.

    GeologyRead 26 minSections 11

  9. Field notePaper Analysis

    Caught on CCTV: The First Video of a Fault Tearing the Ground Apart

    On 28 March 2025 a security camera twenty metres from Myanmar's Sagaing Fault filmed the ground tearing open. One side slid past the other. Frame-by-frame pixel tracking gives 2.5 ± 0.5 m of slip in 1.3 ± 0.2 s, peaking at 3.2 ± 1.0 m/s. It throws in something nobody ordered. The slip path curves [1]. Nobody had ever filmed a fault rupturing. We rebuild the pulse from the three published numbers. They will not all fit the textbook crack-tip slip function at once. The implied shape factor comes out at k = 0.601. Every regularised Yoffe pulse sits at k ≤ 0.5. Our own smoothed-ramp model hits all three exactly. It puts peak slip acceleration at 1.29 g. Shear strain rate across the mole track: 2.1 per second, roughly 1014.6 times the tectonic loading rate. A rotating slip vector fitted to the paper's rake data bows 19.5 cm off the straight line. At this camera's scale, 2.58 pixels. And nearly all of the turning finishes before peak velocity. Everything past §3 is the club's own simplified forward model rather than the authors' analysis, and we say so every time it matters.

    SeismologyRead 35 minSections 12