SCIENCE · INVESTIGATE AND EXPLAIN

Analyze a selective membrane through two solvent constraints

The membrane passes solvent but blocks both nonelectrolyte solutes.

Learning outcome: Compare(4,1),(1,4) and(3,3)mM. Track the sign of required left-minus-right pressure and distinguish initial flow direction from an evolving finite-volume state.

Starting recap

Use chemical amount, dimensional ratios and positive interval endpoints. Distinguish original formula units, independently moving species and a chosen thermodynamic standard.

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Try

At298 K, left4 mM and right1 mM give left-minus-right osmotic difference8.314×298×.003=7.432716 kPa.

Open the experiment

Predict

At equal applied pressures, which side initially receives solvent, and what pressure difference would oppose that flow?

Your prediction and reason

Experiment

Compare(4,1),(1,4) and(3,3)mM. Track the sign of required left-minus-right pressure and distinguish initial flow direction from an evolving finite-volume state.

Infer a pressure difference across a selective boundary

Worked teaching model · synthetic values · Both compartments at298 K contain ideal dilute nonelectrolyte in the same solvent; membrane passes solvent but no solute. Δπ=RT(cLeft−cRight), R8.314 kPa L/(mol K). Positive value is left-minus-right pressure needed to halt initial solvent transfer. Reservoir concentrations held fixed; no cell physiology, flow rate or finite-volume equilibration.

Left impermeant-solute concentration: 4 mmol/L Right impermeant-solute concentration: 1 mmol/L

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Calculated evidence under the stated assumptions
Quantity	Value	Unit
Left ideal osmotic pressure	9.910288	kPa
Right ideal osmotic pressure	2.477572	kPa
Required left-minus-right hydrostatic pressure	7.432716	kPa
Initial solvent direction code	1	1 right→left;−1 left→right;0 none

At equal hydrostatic pressures, initial solvent transfer is toward the left higher-solute side.

The membrane is a selective boundary, not an energy source. At osmotic balance a hydrostatic pressure difference can oppose the solvent chemical-potential difference. If solute crosses or concentrations change as finite volumes move, this fixed-reservoir model no longer predicts the evolving state. Osmolarity alone is not a clinical tonicity or treatment claim.

Retain the species, standard state and ideal/nonideal assumptions with every number. This mathematical packet is not a solution-preparation procedure or evidence of observed laboratory technique.

At equal hydrostatic pressures, initial solvent transfer is toward the left higher-solute side.

Observation to attach to a capture

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

Understand

Specify what can cross

The membrane passes solvent but blocks both nonelectrolyte solutes. Both sides have the same solvent and temperature. This selectivity is essential: if the solute crosses, its concentration difference can relax by a different mechanism and the impermeant-solute prediction no longer describes the evolving system.

Compare two osmotic pressures

For ideal dilute solutions π=RTc. Use concentration in mol/L with R=8.314 kPa L/(mol K), not the numerical millimolar value. The pressure difference needed to oppose initial solvent transfer is Δπ=RT(cLeft−cRight). It is a signed left-minus-right comparison, not the sum of the two osmotic pressures.

Calculate and interpret the sign

At298 K, left.004 and right.001 mol/L give Δπ=7.432716 kPa. With equal hydrostatic pressures, solvent initially moves toward the left higher-solute side. Raising left hydrostatic pressure by the predicted difference can balance that ideal chemical-potential tendency. Reversing the concentrations reverses the required pressure sign.

Avoid an unsupported dynamic prediction

The controls stipulate fixed reservoir concentrations. In two finite compartments, solvent transfer changes concentrations and possibly liquid levels, so this initial-state calculation does not determine final volumes or flow rate. No membrane permeability coefficient, area or time law is supplied. A semipermeable boundary does not create energy.

Transfer and preserve the boundary

For left5 mM and right2 mM, predict the same7.432716 kPa difference, even though both absolute osmotic pressures are larger. Equal3 mM concentrations give zero initial difference under the same ideal conditions. These mathematical packets are not clinical tonicity guidance: real cells and tissues have additional permeabilities, regulation and physiological constraints.

Sources and evidence boundary

Conceptual references checked 30 October 2026: Colligative properties. All cases, prose and diagrams are original. Supplied and calculated data are not observed laboratory evidence. No chemical handling, heating, pressurized gas, membrane experiment or clinical application is requested. Retain predictions, contrasting recipes and a changed-case explanation; numerical agreement does not certify independent mastery.

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

Why would a solute-permeable membrane invalidate this impermeant-solute prediction?

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Previous: Separate particle-factor evidence from a unique dissociation claim Next: Bound an apparent molar mass without assuming its identity

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