Distinguish a pH ratio from a differential amount reserve
Equal buffer ratios need not provide equal resistance to an added amount.
Learning outcome: Hold the pH offset fixed while scaling total concentration, then scan pH to find the capacity maximum. Separate buffer-family and water terms, and reject large-addition claims from a local derivative.
Starting recap
Refresh proton equivalents, conjugate pairs, logarithmic dimensionless activity, analytical amount/volume, mass and charge balances, and bounded observational criteria.
All lessons are open directly. Your saved experiments remain when you leave and return.
Try
At pH=pKa and total .100 M, the buffer-family differential capacity is ln(10)×.100/4≈.0575646 mol/(L pH), before adding the water contribution.
Open the experimentPredict
Can two buffers have equal pH while one needs twice as much small added base for the same pH change?
Experiment
Hold the pH offset fixed while scaling total concentration, then scan pH to find the capacity maximum. Separate buffer-family and water terms, and reject large-addition claims from a local derivative.
Compare buffer ratio with differential capacity
Worked teaching model · synthetic values · Fictional monoprotic ideal buffer, pKa 5, Kw10⁻¹⁴, fixed volume and temperature. Differential strong-base capacity β=ln(10)[C Ka h/(Ka+h)²+h+Kw/h] in mol/(L pH). Local derivative, not a promise about a large finite addition or an unlimited buffer.
Reset keeps your prediction, captures and practice history.
- Buffer-family capacity: solid
Axes rescale. A concentration scan, imposed-pH distribution and titration curve have different horizontal meanings. Read each axis and preserve the difference between an imposed condition and an inferred equilibrium.
All calculated plot coordinates
| pH | buffer-family capacity (mol/(L pH)) |
|---|---|
| 3 | 0.002257215 |
| 3.04 | 0.002470266 |
| 3.08 | 0.002702933 |
| 3.12 | 0.002956925 |
| 3.16 | 0.003234079 |
| 3.2 | 0.003536368 |
| 3.24 | 0.003865903 |
| 3.28 | 0.004224942 |
| 3.32 | 0.004615888 |
| 3.36 | 0.005041293 |
| 3.4 | 0.005503858 |
| 3.44 | 0.006006428 |
| 3.48 | 0.006551987 |
| 3.52 | 0.007143646 |
| 3.56 | 0.007784633 |
| 3.6 | 0.008478267 |
| 3.64 | 0.009227937 |
| 3.68 | 0.01003706 |
| 3.72 | 0.01090906 |
| 3.76 | 0.01184728 |
| 3.8 | 0.01285497 |
| 3.84 | 0.01393515 |
| 3.88 | 0.01509058 |
| 3.92 | 0.01632365 |
| 3.96 | 0.01763624 |
| 4 | 0.01902963 |
| 4.04 | 0.02050432 |
| 4.08 | 0.02205993 |
| 4.12 | 0.02369499 |
| 4.16 | 0.02540684 |
| 4.2 | 0.0271914 |
| 4.24 | 0.02904305 |
| 4.28 | 0.03095446 |
| 4.32 | 0.0329165 |
| 4.36 | 0.0349181 |
| 4.4 | 0.03694623 |
| 4.44 | 0.03898588 |
| 4.48 | 0.04102012 |
| 4.52 | 0.04303026 |
| 4.56 | 0.04499603 |
| 4.6 | 0.04689589 |
| 4.64 | 0.04870739 |
| 4.68 | 0.05040767 |
| 4.72 | 0.05197394 |
| 4.76 | 0.05338411 |
| 4.8 | 0.05461733 |
| 4.84 | 0.05565469 |
| 4.88 | 0.05647973 |
| 4.92 | 0.05707905 |
| 4.96 | 0.05744272 |
| 5 | 0.05756463 |
| 5.04 | 0.05744272 |
| 5.08 | 0.05707905 |
| 5.12 | 0.05647973 |
| 5.16 | 0.05565469 |
| 5.2 | 0.05461733 |
| 5.24 | 0.05338411 |
| 5.28 | 0.05197394 |
| 5.32 | 0.05040767 |
| 5.36 | 0.04870739 |
| 5.4 | 0.04689589 |
| 5.44 | 0.04499603 |
| 5.48 | 0.04303026 |
| 5.52 | 0.04102012 |
| 5.56 | 0.03898588 |
| 5.6 | 0.03694623 |
| 5.64 | 0.0349181 |
| 5.68 | 0.0329165 |
| 5.72 | 0.03095446 |
| 5.76 | 0.02904305 |
| 5.8 | 0.0271914 |
| 5.84 | 0.02540684 |
| 5.88 | 0.02369499 |
| 5.92 | 0.02205993 |
| 5.96 | 0.02050432 |
| 6 | 0.01902963 |
| 6.04 | 0.01763624 |
| 6.08 | 0.01632365 |
| 6.12 | 0.01509058 |
| 6.16 | 0.01393515 |
| 6.2 | 0.01285497 |
| 6.24 | 0.01184728 |
| 6.28 | 0.01090906 |
| 6.32 | 0.01003706 |
| 6.36 | 0.009227937 |
| 6.4 | 0.008478267 |
| 6.44 | 0.007784633 |
| 6.48 | 0.007143646 |
| 6.52 | 0.006551987 |
| 6.56 | 0.006006428 |
| 6.6 | 0.005503858 |
| 6.64 | 0.005041293 |
| 6.68 | 0.004615888 |
| 6.72 | 0.004224942 |
| 6.76 | 0.003865903 |
| 6.8 | 0.003536368 |
| 6.84 | 0.003234079 |
| 6.88 | 0.002956925 |
| 6.92 | 0.002702933 |
| 6.96 | 0.002470266 |
| 7 | 0.002257215 |
| Quantity | Value | Unit |
|---|---|---|
| Selected pH | 5 | pH units |
| Base to acid equilibrium ratio | 1 | ratio |
| Buffer-family differential capacity | 0.05756463 | mol/(L pH) |
| Water differential contribution | 2.302815e-5 | mol/(L pH) |
| Total differential capacity | 0.05758766 | mol/(L pH) |
The same conjugate ratio can have the same pH but a different amount reserve and differential capacity.
At fixed total concentration the buffer-family contribution peaks at h=Ka, or pH=pKa, with value ln(10)C/4. Scaling total concentration scales that contribution but not the ratio-based pH. This is a local fixed-volume derivative; use finite neutralization and a new equilibrium calculation for large additions. Water contributes separately.
These calculated packets are not performed chemical measurements. Keep feasible inventories, activity conventions, fitting observations and independent checks distinct.
The same conjugate ratio can have the same pH but a different amount reserve and differential capacity.
At fixed total concentration the buffer-family contribution peaks at h=Ka, or pH=pKa, with value ln(10)C/4. Scaling total concentration scales that contribution but not the ratio-based pH. This is a local fixed-volume derivative; use finite neutralization and a new equilibrium calculation for large additions. Water contributes separately.
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.
Why does a local differential capacity not replace a finite stoichiometric neutralization table?
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.