Track a protonated anion family under an imposed pH
A protonation equilibrium can change free-ion availability without changing the dissolution constant.
Learning outcome: Compare pH with pKa at fixed constants, recover metal and anion-family totals and free-ion Ksp, then state the reservoir that maintains the imposed condition.
Starting recap
Refresh normalized free-ion activities, charge-balanced stoichiometry, finite analytical inventories, coupled constants and independent versus shared assay errors.
All lessons are open directly. Your saved experiments remain when you leave and return.
Try
At imposed pH4 and pKa5, alphaA=1/11. With Ksp10⁻⁸, s=√(Ksp/alpha)≈.000331662 M and free A≈.0000301511 M.
Open the experimentPredict
Why does lowering the imposed pH increase total dissolution in this particular model?
Experiment
Compare pH with pKa at fixed constants, recover metal and anion-family totals and free-ion Ksp, then state the reservoir that maintains the imposed condition.
Distinguish free anion from protonated dissolved inventory
Worked teaching model · synthetic values · Fictional MA(s)⇌M++A− with ideal Ksp10⁻⁸; HA⇌H++A−, total dissolved M equals total A family. External buffer fixes pH and supplies counterions; no metal hydrolysis, complexation or gas loss. Excess solid, c°1 M. This does not solve the pH of an unbuffered closed packet.
Reset keeps your prediction, captures and practice history.
- Total solubility under imposed pH: solid
Axes rescale. A solubility comparison, depletion constraint and conditional reservoir scan have different horizontal meanings. Read the axes; these are not measured time traces.
All calculated plot coordinates
| externally maintained pH | formula-unit solubility (mol/L) |
|---|---|
| 3 | 0.001004988 |
| 3.066667 | 0.000931502 |
| 3.133333 | 0.0008635058 |
| 3.2 | 0.0008005981 |
| 3.266667 | 0.0007424079 |
| 3.333333 | 0.000688592 |
| 3.4 | 0.0006388327 |
| 3.466667 | 0.0005928363 |
| 3.533333 | 0.0005503312 |
| 3.6 | 0.0005110662 |
| 3.666667 | 0.0004748089 |
| 3.733333 | 0.0004413445 |
| 3.8 | 0.0004104745 |
| 3.866667 | 0.0003820152 |
| 3.933333 | 0.0003557969 |
| 4 | 0.0003316625 |
| 4.066667 | 0.0003094666 |
| 4.133333 | 0.0002890748 |
| 4.2 | 0.0002703622 |
| 4.266667 | 0.0002532133 |
| 4.333333 | 0.0002375203 |
| 4.4 | 0.0002231831 |
| 4.466667 | 0.0002101083 |
| 4.533333 | 0.0001982081 |
| 4.6 | 0.0001874003 |
| 4.666667 | 0.0001776073 |
| 4.733333 | 0.0001687557 |
| 4.8 | 0.000160776 |
| 4.866667 | 0.000153602 |
| 4.933333 | 0.0001471705 |
| 5 | 0.0001414214 |
| 5.066667 | 0.0001362973 |
| 5.133333 | 0.0001317438 |
| 5.2 | 0.0001277089 |
| 5.266667 | 0.0001241438 |
| 5.333333 | 0.0001210024 |
| 5.4 | 0.0001182416 |
| 5.466667 | 0.0001158212 |
| 5.533333 | 0.0001137042 |
| 5.6 | 0.0001118565 |
| 5.666667 | 0.0001102472 |
| 5.733333 | 0.0001088478 |
| 5.8 | 0.0001076331 |
| 5.866667 | 0.0001065803 |
| 5.933333 | 0.0001056689 |
| 6 | 0.0001048809 |
| 6.066667 | 0.0001042003 |
| 6.133333 | 0.0001036129 |
| 6.2 | 0.0001031065 |
| 6.266667 | 0.0001026702 |
| 6.333333 | 0.0001022945 |
| 6.4 | 0.0001019711 |
| 6.466667 | 0.0001016929 |
| 6.533333 | 0.0001014538 |
| 6.6 | 0.0001012482 |
| 6.666667 | 0.0001010715 |
| 6.733333 | 0.0001009197 |
| 6.8 | 0.0001007893 |
| 6.866667 | 0.0001006774 |
| 6.933333 | 0.0001005813 |
| 7 | 0.0001004988 |
| Quantity | Value | Unit |
|---|---|---|
| Free-anion fraction of dissolved family | 0.09090909 | fraction |
| Total dissolved formula units | 0.0003316625 | mol/L |
| Free metal concentration | 0.0003316625 | mol/L |
| Free anion concentration | 3.015113e-5 | mol/L |
| Protonated HA concentration | 0.0003015113 | mol/L |
| Recovered free-ion product | 1.000000e-8 | dimensionless |
Protonating the anion reduces its free fraction and permits more total dissolution in this constrained model.
Because total metal and total anion family each equal s, Ksp=s(alpha s). The external buffer fixes h; it supplies or accepts protons and compensating charge. Without that reservoir, dissolution itself changes pH and this conditional expression is insufficient. A protonation-insensitive anion would not show this mechanism, and real metal hydrolysis could oppose a naive inference.
These calculated packets are not performed chemical measurements or separation procedures. Keep feasible inventories, activity conventions, fitting observations and independent checks distinct.
Protonating the anion reduces its free fraction and permits more total dissolution in this constrained model.
Because total metal and total anion family each equal s, Ksp=s(alpha s). The external buffer fixes h; it supplies or accepts protons and compensating charge. Without that reservoir, dissolution itself changes pH and this conditional expression is insufficient. A protonation-insensitive anion would not show this mechanism, and real metal hydrolysis could oppose a naive inference.
Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.
Understand
Apply
Public practice checks a specific claim. It does not establish independent mastery.
Which omitted metal or anion reaction would invalidate this two-equilibrium expression?
Continue
Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.
Skipping retains experiments and awards no mastery.
Save a science backup or import one
Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.
A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.
Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.
Complete file sets and course backups
A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.
The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.
0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.
Science storage: loading. No account or remote computation is required.