Track passive diffusion without an infinite reservoir assumption
Passive transport moves a permeating substance down its relevant chemical or electrochemical potential gradient. In the neutral-solute model here, a concentration difference drives net flux. Individual molecules can cross in both directions even when net movement is toward the lower-concentration compartment.
Learning outcome: Compare outside8 atP1 andP2. At several displayed times reconstruct inside amount plus outside amount. Then set outside below2 to reverse the initial flux. Explain the difference between concentration and amount at equilibrium.
Starting recap
Connect calibrated dimensions, cell organization, material balance and membrane energetics. State the model boundary before interpreting a changed condition.
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Try
With outside8mmol/L, total amount is2×1+8×4=34mmol. Equal equilibrium concentration is34/5=6.8mmol/L. Initial inward flux atP=1L/min is6mmol/min; doublingP doubles that initial flux but leaves6.8mmol/L unchanged.
Open the experimentPredict
If permeability doubles in a closed system, should the final equilibrium concentration double, or should only the approach speed change?
Experiment
Compare outside8 atP1 andP2. At several displayed times reconstruct inside amount plus outside amount. Then set outside below2 to reverse the initial flux. Explain the difference between concentration and amount at equilibrium.
Follow a solute between two finite compartments
Worked teaching model · synthetic values · Closed, well-mixed compartments: inside1L starts at2mmol/L; outside4L starts at the selected value. Neutral permeating solute, fixed volumes, no reactions. Flux=P×(cout−cin); P includes area. Exponential mixing is an idealized supplied solution, not measured membrane kinetics.
Reset keeps your prediction, captures and practice history.
Permeability changes approach speed, not the closed-system equilibrium inventory.
Balance d(cin)/dt=P(cout−cin)/1L and conserve cin×1L+cout×4L. At equilibrium concentrations match, but amounts remain in the1:4 volume ratio. Molecules continue microscopic exchange even when net flux is zero.
Solid: Inside concentration. Dashed: Outside concentration. Axes rescale to the current range; use labeled values rather than comparing graph heights across settings.
| Elapsed model time(min) | Inside concentration (Concentration(mmol/L)) | Outside concentration (Concentration(mmol/L)) |
|---|---|---|
| 0 | 2.000000 | 8.000000 |
| 0.1 | 2.564015 | 7.858996 |
| 0.2 | 3.061756 | 7.734561 |
| 0.3 | 3.501011 | 7.624747 |
| 0.4 | 3.888653 | 7.527837 |
| 0.5 | 4.230745 | 7.442314 |
| 0.6 | 4.532641 | 7.366840 |
| 0.7 | 4.799062 | 7.300234 |
| 0.8 | 5.034179 | 7.241455 |
| 0.9 | 5.241668 | 7.189583 |
| 1 | 5.424777 | 7.143806 |
| 1.1 | 5.586370 | 7.103408 |
| 1.2 | 5.728975 | 7.067756 |
| 1.3 | 5.854824 | 7.036294 |
| 1.4 | 5.965885 | 7.008529 |
| 1.5 | 6.063896 | 6.984026 |
| 1.6 | 6.150391 | 6.962402 |
| 1.7 | 6.226722 | 6.943320 |
| 1.8 | 6.294084 | 6.926479 |
| 1.9 | 6.353530 | 6.911617 |
| 2 | 6.405992 | 6.898502 |
| Quantity | Value | Unit |
|---|---|---|
| Initial inward solute flux | 6 | mmol/min |
| Conserved total solute | 34 | mmol |
| Equilibrium concentration in each compartment | 6.800000 | mmol/L |
| Inside concentration at2min | 6.405992 | mmol/L |
| Outside concentration at2min | 6.898502 | mmol/L |
Retain prior predictions, settings and quantities in the notebook. These are original supplied/calculated comparisons, not physical specimen observations or laboratory participation.
Permeability changes approach speed, not the closed-system equilibrium inventory.
Balance d(cin)/dt=P(cout−cin)/1L and conserve cin×1L+cout×4L. At equilibrium concentrations match, but amounts remain in the1:4 volume ratio. Molecules continue microscopic exchange even when net flux is zero.
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.
A closed1L inside compartment starts at3mmol/L and a4L outside compartment at8mmol/L. Find the shared equilibrium concentration for a neutral permeating solute with no reaction.
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