A small step. A tenfold change.: sources & model

Compare a hundredfold difference, transfer a tiny aliquot, turn a virtual burette and uncover why a weak acid and a strong acid reach different pH values at equivalence.

What supports the explanation?

What this model assumes

1. Ideal homogeneous aqueous equilibrium at 25°C with additive volumes and analytical totals ≤0.010 mol/L. No activity corrections, gas exchange, minerals, CO₂, precipitation, redox or heat-transfer model.
2. Allowed species are water, HCl, NaOH, acetic acid/acetate and sodium/chloride spectators. Household products and other acids need different composition and equilibrium data.
3. The animation replays prescribed additions; it does not predict mixing speed, reaction rate, electrode delay, a temperature rise or observed indicator color.
4. Source constants have disclosed standard states and rounding. Extra verification digits are mathematical checks, not experimental precision.
5. The two buffer baselines have similar, not identical, pH. Their different inventories must remain visible.
6. Computed molecular conformers are not observed atoms. Colors/radii are display conventions; source coordinates and charges have preserved provenance.
7. No calibrated indicator photograph is supplied. The virtual liquid remains clear; pH colors on the interface are labels, not predicted sample colors.
8. The at-home activity is a paper investigation with fictional sample cards, not chemical mixing.
9. Activity is the definition: pH = −log₁₀ a(H⁺), where a is dimensionless activity. The solver approximates this by −log₁₀([H₃O⁺]/c°), c° = 1 mol/L. Displayed results are ideal-model pH. Neither pH nor the simulator is a chemical hazard scale, and 0–14 is not a universal physical limit.
10. One equilibrium, all the way across: At fixed 25°C, let h=[H₃O⁺], o=[OH⁻], a=[acetate], u=[acetic acid]. Use ho=kW, ha/u=kA, a+u=CT and h+CNa=o+CCl+a. Combining these gives F(h)=h+(CNa−CCl)−kW/h−CTkA/(kA+h)=0. F is strictly increasing for h>0; logarithmic bisection finds its unique positive root.
11. Parameters keep their conventions: The NIST evaluation selects pKa=4.756 at 298.15 K, zero ionic strength and a molal standard state, with nominal pressure 0.1 MPa. This ideal molar model deliberately uses kA=10⁻⁴·⁷⁵⁶ mol/L without its small molar/molal conversion or activity corrections. The concentration water product kW=10⁻¹⁴ (mol/L)² is rounded; thermodynamic constants with standard-state factors are dimensionless.
12. What an input actually adds: HCl adds chloride inventory; NaOH adds sodium inventory. The acid-family total counts HA and A⁻ together. Hydronium is solved after mixing; it is not a separately conserved reagent count. Adding another excess-OH value after solving would double count the base.
13. Neutrality and temperature: In this model neutrality is h=o, giving pH=7 with the rounded kW. IAPWS R11-24 Table 3 gives rounded molal pKw 13.99 at 25°C and 13.26 at 50°C, using liquid density at 0.1 MPa below 100°C. This source comparison does not turn the 25°C acetate solver into a temperature-dependent model.
14. Equivalence versus a familiar shortcut: 25.0 mL of 0.010 M acid contains 0.250 mmol. Adding 25.0 mL of 0.010 M NaOH reaches equivalence for either selected acid. The model gives pH 7.000 for HCl and 8.228 for acetic acid. At acetic half-equivalence it gives 4.760523, close to but not exactly 4.756. Henderson–Hasselbalch is exact here only with the actual equilibrium species ratio.
15. Molecular data have a narrower job: The two PubChem3D conformers provide computed geometry and connectivity. They do not predict pKa, solution snapshots or proton-transfer trajectories. Acid atom 8 is the carboxyl hydrogen; the three methyl hydrogens remain in acetate. An SDF charge assignment is not an MMFF partial charge or a pharmacophore label.
16. Resonance is not alternating bonds: Acetate’s connection table serializes one single and one double C–O bond. Its charge and bonding are delocalized over the carboxylate group. Our symmetric C–O rendering avoids implying a permanently privileged oxygen or rapid switching between separate structures.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

Original offline rendering of PubChem3D computed acetic-acid and acetate conformers, CIDs 176 and 175, National Library of Medicine. Source coordinates and formal charges are preserved in downloadable SDF/JSON records. Colors and sphere sizes are teaching choices; these are computed geometries, not observed solution snapshots or a reaction trajectory.