Design an independent constraint before spending the sample
Two apparently different assays can share the same calibration ambiguity.
Learning outcome: Retain two compatible gain hypotheses, freeze a six-of-eight virtual mL allocation and predict an electrode result before revealing it. Explain why a ratio is robust to common multiplicative gain but not an additive offset.
Starting recap
Reconstruct species, calibration, equilibrium, rate and thermodynamic boundaries before combining evidence.
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Try
Signals .040 and .010 have ratio4. With unknown common gain, both total .020/free .005 at gain2 and total .040/free .010 at gain1 fit. An independent ideal electrode against .001 M gives E=(RT/2F)ln5≈.020675 V for the first pair, resolving gain2 under the declared assumptions.
Open the experimentPredict
Will repeating both assays identify the common gain?
Experiment
Retain two compatible gain hypotheses, freeze a six-of-eight virtual mL allocation and predict an electrode result before revealing it. Explain why a ratio is robust to common multiplicative gain but not an additive offset.
Break a shared assay calibration ambiguity
Worked teaching model · synthetic values · Fictional dilute metal system at298.15 K with total/free ratio F imposed by a ligand reservoir. Total-specific and free-specific assays both have unknown common gain g=2 in the synthetic generator and zero offsets. A separate ideal two-electron electrode calibrated against free concentration .001 M has known activity coefficients1 and no junction offset. Assays are not chemical procedures. Six virtual mL of an8 mL sample support the disclosed package; no real sampling.
Reset keeps your prediction, captures and practice history.
- Compatible total concentration before electrode evidence: solid
- Compatible free concentration before electrode evidence: long dashes
Axes rescale. A compatible-parameter family is not a time trajectory. Read each axis and do not treat a computed curve as additional measured evidence.
All calculated plot coordinates
| hypothesized shared gain | compatible concentration (mol/L) |
|---|---|
| 1 | 0.04 |
| 2 | 0.02 |
| 3 | 0.01333333 |
| 4 | 0.01 |
| hypothesized shared gain | compatible concentration (mol/L) |
|---|---|
| 1 | 0.01 |
| 2 | 0.005 |
| 3 | 0.003333333 |
| 4 | 0.0025 |
| Quantity | Value | Unit |
|---|---|---|
| Total-specific signal | 0.04 | signal units |
| Free-specific signal | 0.01 | signal units |
| Identifiable total/free ratio | 4 | ratio |
| Independent electrode potential | 0.02067531 | V |
| Electrode-inferred free concentration | 0.005 | mol/L |
| Recovered common gain | 2 | signal units/(mol/L) |
| Recovered total concentration | 0.02 | mol/L |
| Committed virtual sample | 6 | mL |
| Remaining virtual sample | 2 | mL |
The signal ratio identifies partitioning, but an independent calibrated reference is needed for absolute concentration.
A repeat of either assay or a second signal derived from the same gain cannot identify that gain. The electrode breaks the ambiguity only under its independently established standard, activity and offset assumptions. A shared offset would also invalidate the ratio cancellation. The6 mL ledger reserves2 each for total/free assays,1 for electrode packet and1 for a withheld consistency packet;2 mL remain. This is a virtual allocation, not an apparatus protocol.
The signal ratio identifies partitioning, but an independent calibrated reference is needed for absolute concentration.
A repeat of either assay or a second signal derived from the same gain cannot identify that gain. The electrode breaks the ambiguity only under its independently established standard, activity and offset assumptions. A shared offset would also invalidate the ratio cancellation. The6 mL ledger reserves2 each for total/free assays,1 for electrode packet and1 for a withheld consistency packet;2 mL remain. This is a virtual allocation, not an apparatus protocol.
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 independent calibration evidence must be retained before claiming an absolute concentration?
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