SCIENCE · INVESTIGATE AND EXPLAIN

Why does net movement slow down—even while particles keep crossing?

Follow both directions of particle exchange and check conservation.

Learning outcome: Distinguish net movement from the continuing motion of particles at equilibrium.

Starting recap

Concentration is amount per volume. Here both volumes are equal and fixed, so comparing amounts also compares concentrations.

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Try

The left compartment holds 80 expected particles and the right holds 20. Both sides exchange 20% of their particles each step.

Open the experiment

Predict

Predict both amounts after one step. Does the right side send any particles back?

Your prediction and reason

Experiment

Set 80 particles left and zero steps. Increase to one step, then two, then ten. Capture at least two settings. Repeat from a 50/50 split and explain what remains unchanged.

Physical diffusion · expected amounts

Both ways. One net change.

Step 0 / 10

If exchange happens in both directions, why do the amounts become more equal?

Left compartment80.00expected particles

Right compartment20.00expected particles

Bar length shows expected amount on the same 0–100 scale, not compartment size. Both volumes stay equal and fixed.

Left sends to right16.00 20% × 80.00

Right sends to left 4.0020% × 20.00

Net transfer: 12.00 left → right. Subtract the smaller opposing exchange from the larger.

Initial left amount 80Initial right amount = 20. Recalculates the selected step.Exchange step 0Discrete model updates, not measured time

Conserved total100.00expected particles

Inspect every computed step

Expected amounts; each row comes from the existing diffusion model.
Step	Left	Right	Total
0	80.00	20.00	100.00

After 0 steps: left 80.000, right 20.000 expected particles.

Where does randomness fit?

For an integer number of particles, one possible interpretation gives each particle an independent 0.2 probability of crossing during a step. Expected outgoing count is then 0.2 × current count; an actual random count must be an integer and can differ from its expectation.

This model calculates expected amounts only. It does not sample random crossings or simulate microscopic trajectories. A value such as 60.8 means an expected count, never part of a particle.

Review probability and return

Idealized physical exchange, not AI denoising diffusion. No active transport, reactions, electrical potential, measured time or microscopic physics is modeled. Equal amounts correspond to equal concentrations only because the two volumes are equal.

Observation to attach to a capture

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

CONNECTED IDEAS · SMALL PILOT CLUSTER

Find the idea you need

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Selected idea

Physical diffusion

Particle motion can produce net transport down a concentration gradient; the pilot uses expected exchange between two equal fixed volumes, not individual random trajectories.

Explain diffusion through opposing flows

Concentration
Physical diffusion can review Concentration.
Compare amount per volume to interpret a concentration difference. This lab uses equal fixed volumes, so amount differences also indicate concentration differences.
Explain diffusion through opposing flows Explore these connections
Probability and randomness
Physical diffusion can review Probability and randomness.
The displayed fractional particle counts are expected amounts under a fixed exchange rule. They are not literal fractional particles or one sampled random trajectory.
Averages, probability, and expectation Explore these connections

Open the full local map and resource list

11 concepts in this cross-subject pilot, not a complete curriculum graph. The existing AI lesson map and progress records remain separate and available below or through AI discovery.

Understand

Count both directions

Begin with 80 expected particles left and 20 right. In one step, 0.2 × 80 = 16 leave the left, while 0.2 × 20 = 4 arrive from the right. The new left amount is 80 − 16 + 4 = 68. The new right amount is 20 − 4 + 16 = 32. Their total is still 100.

For the next step use the new amounts on both sides: 68 − 13.6 + 6.4 = 60.8 on the left. Using an updated left amount to compute the right side in that same step would mix two different times and break the intended model.

Net flow is not all motion

At 50 on each side, 10 move in each direction per step. Net flow is zero even though exchange continues. Passive transport can redistribute a permeant substance down its concentration gradient without a cell supplying metabolic energy directly to that transfer. Membrane selectivity determines which substances can pass. Background: OpenStax, passive transport.

The two compartments here have equal fixed volumes. With unequal volumes, equal particle counts would not imply equal concentrations. An electrical gradient can also matter for charged particles; this model omits it.

Inspect the approximation

The fractional counts are expected amounts from a deterministic rule. They are not a single microscopic trajectory. Starting at 80, the distance from 50 becomes 30, 18, 10.8 and so on: each step multiplies the imbalance by 0.6. The model approaches equal amounts smoothly without random fluctuations.

Choose a new initial amount and verify conservation at two successive steps. Then state what additional information would be needed to interpret a step as seconds: geometry, permeability and the substance’s transport properties would matter. The slider alone does not supply a real diffusion rate.

The boundary determines what can cross

Membrane phospholipids have water-interacting heads and nonpolar tails. In a bilayer, the tails face inward. That interior impedes ions and many polar solutes; small nonpolar molecules such as oxygen can cross more readily. Channels provide selective passages, while carrier proteins bind substances and change shape. A protein-assisted crossing can still be passive: facilitated diffusion follows the relevant gradient without directly spending ATP. Background: OpenStax, passive transport.

For an ion, concentration and electrical effects must be considered together. “More concentrated outside” alone cannot establish its direction of passive movement if the voltage is unknown.

Keeping a gradient requires a coupled process

Primary active transport couples movement to an energy source such as ATP hydrolysis. In a standard sodium-potassium pump cycle, three sodium ions leave and two potassium ions enter per ATP used. Secondary active transport instead couples one substance moving down its electrochemical gradient to another moving uphill. Maintaining the driving gradient ultimately requires energy. Background: OpenStax, active transport.

The lab’s two-way exchange has no pump. Its approach to equal amounts cannot explain how a cell maintains unequal concentrations.

Repair a model: start with 80 particles left and 20 right. Passive exchange gives 68 and 32. Suppose an external energy source then powers transfer of five particles from right to left. Predict the resulting amounts and whether this restores the starting distribution. This is a separate hypothetical arithmetic extension, not a feature of the lab or a sodium-potassium pump simulation.

Check the proposed repair

The amounts become 73 and 27, still totaling 100. Five pumped particles offset only part of the passive net transfer of twelve. Restoring 80 and 20 in this one-step example requires pumping twelve back. A steady gradient depends on rates balancing; conserving particles alone does not establish that enough energy or transport capacity is available.

In your reflection, compare a closed channel, an open passive channel and a powered pump. Identify which changes permeability, which can move material uphill, and why disabling ATP supply need not stop all molecular motion immediately.

Apply

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

Explain why equal final amounts do not mean particle motion has stopped. Identify why this model cannot predict diffusion time in a real cell.

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: Connect cell structures to the work they do Next: Track water while solute stays behind

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