A cell can shrink immediately after entering a solution and later become larger than it was originally. Calling that solution “concentrated” does not explain both observations. You need to know which particles cross the membrane and how quickly they move compared with water.
The AAMC content outline includes osmosis, osmotic pressure and membrane transport. This lesson connects those concepts through an original model. The quantities describe a fictional compartment, not a normal physiological reference range or a fluid-treatment recommendation.
Count particles before considering permeability
Osmolarity counts osmoles of dissolved particles per litre of solution. One osmole represents one mole of particles. In an ideal calculation, multiply each solute’s molarity by the number of particles it contributes, then add the contributions. Stony Brook’s cellular neurophysiology text explains this particle-count distinction.
For example, a mixture containing 60 mmol/L NaCl and 120 mmol/L urea has an ideal osmolarity of:
(60 × 2) + (120 × 1) = 240 mOsm/L.
NaCl contributes two ions per formula unit under the complete-dissociation approximation; urea does not dissociate. Real solutions can depart from this ideal particle-factor calculation. OpenStax discusses measured versus ideal van’t Hoff factors.
Do not silently replace osmolarity with osmolality, which uses kilograms of solvent rather than litres of solution. Their numerical values can be close in dilute aqueous solutions, but their denominators differ.
Particle counting alone says nothing about whether a particular membrane lets those particles pass.
Tonicity asks what happens to this cell
An external solution is hypotonic, isotonic or hypertonic relative to a cell when it produces, respectively, a larger, unchanged or smaller equilibrium volume under the specified conditions. Nonpenetrating solutes sustain the relevant osmotic imbalance; a freely equilibrating solute eventually has the same concentration on both sides in the ideal passive model. This distinction is discussed in Learning (by) osmosis.
“Permeant” must refer to a membrane and an observation period. A solute that equilibrates eventually may remain effectively trapped during a much shorter experiment. Actual cells also have transporters, metabolism and volume-regulation mechanisms; the problem must tell you which mechanisms to include.
We will call the final passive state below “equilibrium.” We will describe the earlier change separately, so initial shrinkage does not become evidence of a smaller final volume.
Define the model before calculating
Consider a flexible cell-like compartment with initial volume 1.20 pL. Its interior contains 240 mOsm/L nonpenetrating particles and no urea. It is transferred into a large, well-mixed bath containing 160 mOsm/L nonpenetrating particles plus 200 mmol/L urea.
Use these explicit assumptions:
- The bath is sufficiently large that its concentrations remain constant.
- Water crosses much faster than urea. For an early limiting calculation, neglect urea entry during the initial water redistribution; later, allow urea to equilibrate passively.
- The designated nonpenetrating particles cannot cross either way. Urea neither dissociates nor reacts.
- Solutions are ideal and temperature is constant. There is no significant hydrostatic pressure difference, cell wall, elastic resistance, active transport or volume regulation.
- Treat the entire compartment volume as osmotically active; ignore solute partial-volume changes and structural rupture over the calculated range.
The pressure assumption matters: osmotic water redistribution can be opposed by a hydrostatic pressure difference, as OpenStax’s osmotic-pressure model shows. Equal total osmolarities are our equilibrium condition because we have excluded that opposing pressure and assumed ideal behavior.
Follow the same particles through three states
Initially, the bath contains 160 + 200 = 360 mOsm/L, compared with 240 inside. It is hyperosmotic relative to the starting compartment.
In the early water-only limit, water leaves. The trapped particles become more concentrated until the interior approaches 360 mOsm/L. Conservation of their amount gives:
240 × 1.20 = 360 × Vearly, so Vearly ≈ 0.80 pL.
The concentration changes; the amount of trapped particles does not. Using 240 mOsm/L as the internal concentration after shrinkage would violate that distinction.
Later, urea enters. At final passive equilibrium its concentration is 200 mmol/L both inside and outside. To balance the bath’s total 360 mOsm/L, the trapped internal particles must then contribute only 360 − 200 = 160 mOsm/L. Therefore:
240 × 1.20 = 160 × Vfinal, so Vfinal = 1.80 pL.
| State | Internal trapped particles | Internal urea | Internal total | Volume |
|---|---|---|---|---|
| Just after transfer, before redistribution | 240 mOsm/L | 0 mmol/L | 240 mOsm/L | 1.20 pL |
| Early water-only limiting estimate | 360 mOsm/L | Approximately 0 | Approximately 360 mOsm/L | Approximately 0.80 pL |
| Final passive equilibrium | 160 mOsm/L | 200 mmol/L | 360 mOsm/L | 1.80 pL |
The bath is hyperosmotic initially but hypotonic in its final effect: the compartment finishes 50% larger than its starting volume. Urea still contributes particles at equilibrium. Its equal contributions on both sides cancel when determining the remaining osmotic difference; it has not become chemically nonexistent.
The early value is a limiting approximation, not an exact minimum for every real membrane. If appreciable urea enters while water is leaving, the trajectory changes. These data do not provide transport coefficients or enough information to assign a time in seconds.
Change one assumption and test the shortcut
Keep the bath composition but make the membrane impermeable to urea throughout the experiment. All 360 mOsm/L outside are now nonpenetrating. The final volume is 0.80 pL, so this bath is hypertonic for that membrane. Its particle count has not changed; its sustained effect has.
Now restore urea permeability and use a different bath: 160 mOsm/L nonpenetrating particles plus 80 mmol/L urea. Its total is 240 mOsm/L, matching the starting interior. There is no initial osmotic imbalance in our ideal model, but urea entry subsequently leads to a final volume of 1.80 pL. An isoosmotic solution need not be isotonic.
Neither calculation applies unchanged to a small sealed external compartment. Water movement would change its concentrations, and both compartments would require a mass-balance calculation. “Large bath” is doing mathematical work here.
Transfer exercise: the same initial shrinkage, a different ending
Start again with the original 1.20 pL compartment containing 240 mOsm/L trapped particles and no urea. Change the large bath to 240 mOsm/L nonpenetrating particles plus 120 mmol/L urea. Retain all other model assumptions.
Which trajectory follows?
A. Shrink toward 0.80 pL and remain there.
B. Shrink toward 0.80 pL, then return to 1.20 pL.
C. Shrink toward 0.80 pL, then expand to 1.80 pL.
Answer: B. The bath again totals 360 mOsm/L, so the early water-only estimate remains 240 × 1.20/360 = 0.80 pL. At equilibrium, urea is 120 mmol/L on both sides. The trapped internal concentration must equal the bath’s nonpenetrating concentration, 240 mOsm/L. Thus Vfinal = 240 × 1.20/240 = 1.20 pL.
A treats urea as permanently excluded. C carries over the previous bath’s 160 mOsm/L nonpenetrating concentration despite its replacement. The new bath is hyperosmotic initially and isotonic in its final effect. Neither label implies that volume stayed constant throughout.
For your next passage, write four items before choosing a direction: initial particle concentrations, membrane permeability, observation time and whether external concentrations stay fixed. Then preserve solute amounts when volume changes. This is a learning suggestion for exposing assumptions; it does not predict an exam score.
Sources and further reading
- AAMC: What Is on the MCAT Exam? Content Outline
- Stony Brook University: Regulation of Cell Volume
- OpenStax Chemistry 2e: Colligative Properties
- Learning (by) osmosis: an approach to teaching osmolarity and tonicity — relevant indexed excerpts verified; direct full-text retrieval was blocked.