Infer a concentration-cell polarity without changing the metal
Two identical electrode materials can differ in reduction potential because their ionic activities differ.
Learning outcome: Compare unequal, equal and reversed activities. Identify oxidation/reduction sides and ionic versus electronic paths while retaining the neglected junction-potential assumption.
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
For left activity10⁻³ and right10⁻¹ in a two-electron cell, Eright−left≈.05916 V; the right electrode is the ideal galvanic cathode.
Open the experimentPredict
What happens to the signed right-minus-left potential when the activities are exchanged?
Experiment
Compare unequal, equal and reversed activities. Identify oxidation/reduction sides and ionic versus electronic paths while retaining the neglected junction-potential assumption.
Determine concentration-cell polarity from two activities
Worked teaching model · synthetic values · Identical pure-metal M/M²+ electrodes at298.15 K; ideal reversible ion activities, negligible liquid-junction potential and no kinetic losses. Signed right-minus-left reduction potential E=RT/(2F) ln(a_right/a_left). Standard reduction potentials cancel; a salt bridge maintains charge continuity but does not carry metal electrons.
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- Right-minus-left potential versus right log activity: 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
| log10 right activity | signed right-minus-left potential (V) |
|---|---|
| -4 | -0.02957967 |
| -3.95 | -0.02810069 |
| -3.9 | -0.02662171 |
| -3.85 | -0.02514272 |
| -3.8 | -0.02366374 |
| -3.75 | -0.02218476 |
| -3.7 | -0.02070577 |
| -3.65 | -0.01922679 |
| -3.6 | -0.0177478 |
| -3.55 | -0.01626882 |
| -3.5 | -0.01478984 |
| -3.45 | -0.01331085 |
| -3.4 | -0.01183187 |
| -3.35 | -0.01035289 |
| -3.3 | -0.008873902 |
| -3.25 | -0.007394919 |
| -3.2 | -0.005915935 |
| -3.15 | -0.004436951 |
| -3.1 | -0.002957967 |
| -3.05 | -0.001478984 |
| -3 | 0 |
| -2.95 | 0.001478984 |
| -2.9 | 0.002957967 |
| -2.85 | 0.004436951 |
| -2.8 | 0.005915935 |
| -2.75 | 0.007394919 |
| -2.7 | 0.008873902 |
| -2.65 | 0.01035289 |
| -2.6 | 0.01183187 |
| -2.55 | 0.01331085 |
| -2.5 | 0.01478984 |
| -2.45 | 0.01626882 |
| -2.4 | 0.0177478 |
| -2.35 | 0.01922679 |
| -2.3 | 0.02070577 |
| -2.25 | 0.02218476 |
| -2.2 | 0.02366374 |
| -2.15 | 0.02514272 |
| -2.1 | 0.02662171 |
| -2.05 | 0.02810069 |
| -2 | 0.02957967 |
| -1.95 | 0.03105866 |
| -1.9 | 0.03253764 |
| -1.85 | 0.03401663 |
| -1.8 | 0.03549561 |
| -1.75 | 0.03697459 |
| -1.7 | 0.03845358 |
| -1.65 | 0.03993256 |
| -1.6 | 0.04141154 |
| -1.55 | 0.04289053 |
| -1.5 | 0.04436951 |
| -1.45 | 0.0458485 |
| -1.4 | 0.04732748 |
| -1.35 | 0.04880646 |
| -1.3 | 0.05028545 |
| -1.25 | 0.05176443 |
| -1.2 | 0.05324341 |
| -1.15 | 0.0547224 |
| -1.1 | 0.05620138 |
| -1.05 | 0.05768037 |
| -1 | 0.05915935 |
| Quantity | Value | Unit |
|---|---|---|
| Left ionic activity | 0.001 | dimensionless |
| Right ionic activity | 0.1 | dimensionless |
| Right minus left electrode potential | 0.05915935 | V |
| Free energy for left oxidation/right reduction | -11.41602 | kJ/mol reaction |
Right electrode is the galvanic cathode and left is the anode under the stated ideal conditions.
The cell tends to reduce the activity difference by dissolving metal at the lower-activity side and depositing it at the higher-activity side. Ionic transport maintains charge continuity; electrons flow through the external electronic path, not through a salt bridge. Nonideal activities and junction potentials can matter in real measurements.
These calculated packets are not performed chemical measurements or separation procedures. Keep feasible inventories, activity conventions, fitting observations and independent checks distinct.
Right electrode is the galvanic cathode and left is the anode under the stated ideal conditions.
The cell tends to reduce the activity difference by dissolving metal at the lower-activity side and depositing it at the higher-activity side. Ionic transport maintains charge continuity; electrons flow through the external electronic path, not through a salt bridge. Nonideal activities and junction potentials can matter in real measurements.
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Why is an observed concentration-cell voltage not necessarily explained by concentration numerals alone in a real electrolyte?
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