SCIENCE · INVESTIGATE AND EXPLAIN

Convert charge to a product only after electron and efficiency accounting

Passed charge counts electron equivalents, not automatically the desired product.

Learning outcome: Vary current and duration, close desired plus competing charge, convert through F and the electron coefficient, and verify remaining initial metal inventory.

Starting recap

Refresh state-function boundaries, absolute temperature, dimensionless logarithms, written reaction/electron equivalents, conserved charge and formal orbital/identity bookkeeping.

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Try

At2 A for300 s, Q600 C. With85% desired-current efficiency and two electrons per hypothetical64 g/mol metal, amount≈.002643 mol and mass≈.16915 g.

Open the experiment

Predict

Would a theoretical electrode potential alone establish85% product current efficiency?

Your prediction and reason

Experiment

Vary current and duration, close desired plus competing charge, convert through F and the electron coefficient, and verify remaining initial metal inventory.

Separate electron charge from product current efficiency

Worked teaching model · synthetic values · Hypothetical reduction M²++2e−→M with molar mass64.0 g/mol, initial available M²+ .0200 mol.85% of total current produces this metal,15% goes to explicitly unspecified competing reactions. Constant current/efficiency are supplied; all allowed recipes retain enough inventory. No physical electrolysis or operating voltage/protocol.

Constant current: 2 A Virtual duration: 300 s

Reset keeps your prediction, captures and practice history.

Desired product mass versus time: solid

Axes rescale. A multiplicity distribution, inverse-temperature relation and charge-budget graph have different meanings. Read each axis and do not treat a computed curve as additional measured evidence.

All calculated plot coordinates

Desired product mass versus time
virtual duration (s)	hypothetical product mass (g)
0	0
8.333333	0.004698469
16.66667	0.009396938
25	0.01409541
33.33333	0.01879388
41.66667	0.02349234
50	0.02819081
58.33333	0.03288928
66.66667	0.03758775
75	0.04228622
83.33333	0.04698469
91.66667	0.05168316
100	0.05638163
108.3333	0.0610801
116.6667	0.06577856
125	0.07047703
133.3333	0.0751755
141.6667	0.07987397
150	0.08457244
158.3333	0.08927091
166.6667	0.09396938
175	0.09866785
183.3333	0.1033663
191.6667	0.1080648
200	0.1127633
208.3333	0.1174617
216.6667	0.1221602
225	0.1268587
233.3333	0.1315571
241.6667	0.1362556
250	0.1409541
258.3333	0.1456525
266.6667	0.150351
275	0.1550495
283.3333	0.1597479
291.6667	0.1644464
300	0.1691449
308.3333	0.1738433
316.6667	0.1785418
325	0.1832403
333.3333	0.1879388
341.6667	0.1926372
350	0.1973357
358.3333	0.2020342
366.6667	0.2067326
375	0.2114311
383.3333	0.2161296
391.6667	0.220828
400	0.2255265
408.3333	0.230225
416.6667	0.2349234
425	0.2396219
433.3333	0.2443204
441.6667	0.2490189
450	0.2537173
458.3333	0.2584158
466.6667	0.2631143
475	0.2678127
483.3333	0.2725112
491.6667	0.2772097
500	0.2819081

Calculated under the declared model
Quantity	Value	Unit
Total passed charge	600	C
Total electron amount	0.006218562	mol electrons
Charge assigned to desired reduction	510	C
Charge assigned to other reactions	90	C
Deposited hypothetical metal amount	0.002642889	mol
Deposited hypothetical metal mass	0.1691449	g
Remaining available metal-ion amount	0.01735711	mol

Charge counts electron equivalents; product amount also depends on reaction stoichiometry and current efficiency.

Q=It and electron amount Q/F are distinct from product amount: two electrons are required per deposited metal and only85% of the current follows that path. The model explicitly leaves sufficient starting inventory for every recipe. Current efficiency is supplied, not inferred from a cell voltage or a theoretical electrode potential; no real deposition or gas-producing procedure is instructed.

These calculated packets are not performed chemical measurements or separation procedures. Keep feasible inventories, activity conventions, fitting observations and independent checks distinct.

Charge counts electron equivalents; product amount also depends on reaction stoichiometry and current efficiency.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Count electron amount from charge

Constant current I over time t supplies Q=It coulombs. Divide by the Faraday constant F to obtain electron moles. For the fictional reaction M²++2e−→M, two electron moles are needed for one mole of metal, so an ideal fully selective product would be Q/(2F).

The supplied current efficiency is .85, meaning only85% of passed charge drives this reduction. The rest belongs to competing reactions left unspecified. At2 A for300 s, total Q600 C, desired charge510 C and competing charge90 C. Desired product is510/(2F)≈.00264289 mol, or about.169145 g for the fictional64.0 g/mol metal.

Check the finite supply and what was assumed

The starting available metal-ion amount is .0200 mol, sufficient for every allowed control recipe. If an extrapolation exceeded that inventory, the constant-efficiency product law could not continue unchanged. A neat linear charge graph does not supply missing reactant.

Current efficiency is not the same as energy efficiency and cannot be read from an equilibrium potential. A real product assay, competing-reaction evidence and charge calibration would be needed to test it. No actual electrolysis, wiring or operating-voltage procedure is provided.

Transfer and check

For a separate three-electron reduction, Q900 C and current efficiency .80 give product720/(3F)≈.00248740 mol. Explain why using the two-electron divisor from the first packet would overstate product by50%, even if the current and timer were perfectly measured.

Source and evidence boundary

Conceptual reference checked 30 October 2026: OpenStax Chemistry 2e. All prose, cases, graphs and questions are original. These supplied thermodynamic, electrical, nuclear or orbital models are not actual measurements, apparatus instructions, synthesis protocols or practical certification. Retain conventions, independent constraints, changed-case reasoning and limits. No heating, wiring, electrolysis, source handling or chemical manipulation is requested.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Which independent product measurement would test the supplied current-efficiency assumption?

Your explanation and limitations

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.

Previous: Infer a concentration-cell polarity without changing the metal Next: Distinguish cell charge capacity, loaded energy and internal conversion

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