Cell Osmotic Equilibrium

Osmolarity, tonicity and equilibrium volume of a cell facing an extracellular medium · V_f/V₀ = Osm_imp,in / Osm_imp,out

Parameters

Ideal van't Hoff model

Preset scenarios

Temperature

Only π and Δπ depend on T; osmolarities, classifications and V_f/V₀ do not change.

060

Cell interior

1/6

permeant

Extracellular medium

1/6

permeant

Treated as a reservoir: its composition does not change with whatever the cell exchanges.

Advanced mode (σ coefficient)

Reveals the reflection coefficient σ of every permeant solute. With the switch off, σ is derived from permeability: impermeant → 1, permeant → 0.

Initial volume V₀ (optional)

Leave it empty and the V_f/V₀ ratio and percentage change are still shown, only the absolute final volume is not.

Osmolarity

Pressure

Results

Osmotic classification

Isoosmotic

Total osm

300 300 mOsm/L

Relative tonicity

Isotonic

Imperm. osm

300 300 mOsm/L

Initial water direction

No net movement

Effective osm

300 300 mOsm/L

Equilibrium volume

Volume ratio

V_f / V₀

reaches a stable volume

Volume change0%

Final volume V_f1000µm³

Initial driving force

ΔEffective Osm (out − in)0mOsm/L

Effective Δπ0atm

Osmotic pressure of each solution

π inside7.635atm

π outside7.635atm

Fundamentals & Explanation

Osmolarity, tonicity and three distinct readings

Osmolarity counts dissolved particles; tonicity describes a solution's effect on the volume of a particular cell. They can differ when the membrane passes a solute: an isoosmotic urea bath can be hypotonic because urea equilibrates across the membrane.

Each compartment is therefore summarised by three sums. They are not redundant results: each answers a different question.

Total · osmotic classification

\mathrm{Osm}_{\mathrm{tot}} = \sum_j i_j\,C_j

Effective · initial water direction

\mathrm{Osm}_{\mathrm{eff}} = \sum_j \sigma_j\,i_j\,C_j

Impermeant · tonicity and final volume

\mathrm{Osm}_{\mathrm{imp}} = \sum_{j\ \text{impermeant}} i_j\,C_j

Ideal pressure in Pa · Osmolarity in Osm/L

\pi = 1000\,R\,T\,\mathrm{Osm}_{\mathrm{tot}}

C is in mol/L; i and σ are dimensionless; T is in kelvin and R = 8.314462618 J·mol⁻¹·K⁻¹. The factor 1000 converts litres to cubic metres.

Reflection coefficient and initial flux

Staverman's reflection coefficient σ measures how strongly a solute gradient contributes to osmotic water flow: σ = 1 represents complete reflection and σ = 0 no effective contribution. It is neither a literal fraction of crossing molecules nor a replacement for permeability. In this model, a solute marked impermeant uses σ = 1.

Outside minus inside

\Delta\mathrm{Osm}^{\mathrm{SI}}_{\mathrm{eff}} = \mathrm{Osm}^{\mathrm{SI}}_{\mathrm{eff,out}}-\mathrm{Osm}^{\mathrm{SI}}_{\mathrm{eff,in}}

Flexible cell · no hydrostatic difference

J_v = L_pRT\,\Delta\mathrm{Osm}^{\mathrm{SI}}_{\mathrm{eff}}

J_v> 0 is defined as outward flow: a positive effective difference produces initial water efflux; a negative one produces influx. L_p is the hydraulic permeability of the membrane.

Equilibrium volume

Over time, permeant solutes equalise their concentrations and drop out of the balance. Intracellular impermeant osmoles remain trapped and conserved; at equilibrium their final concentration equals the impermeant concentration in the bath.

Intracellular conservation

\mathrm{Osm}_{\mathrm{imp,in,0}}\,V_0 = \mathrm{Osm}_{\mathrm{imp,in,f}}\,V_f

Result · Osm_imp,in,f = Osm_imp,out

\frac{V_f}{V_0} = \frac{\mathrm{Osm}_{\mathrm{imp,in,0}}}{\mathrm{Osm}_{\mathrm{imp,out}}}

If the outside contains no impermeant osmoles, no finite equilibrium volume exists; if they are absent only from the inside, the model leads to collapse.

Transient reversal

Initial direction depends on effective osmolarity; final volume depends on impermeant osmolarity. Defining both differences as outside minus inside, the two point in opposite directions when:

Reversal condition

\Delta\mathrm{Osm}_{\mathrm{eff}}\,\Delta\mathrm{Osm}_{\mathrm{imp}} < 0

This pattern can arise while loading permeant cryoprotectants: a cell first shrinks and then recovers volume, or vice versa. Only the initial instant and equilibrium are calculated here, not the time course between them.

Declared assumptions

Flexible, wall-less cell: no turgor pressure.
Infinite bath: the outside retains its composition.
Ideal solution: van't Hoff with stoichiometric i.
Fully active volume: osmotically inactive fraction set to zero.
No active transport: no pumps or volume regulation.

Model limitations

Real electrolytes do not behave as independent particles. For physiological NaCl, for example, an osmotic coefficient φ ≈ 0.93 lowers the ideal contribution by about 7 %. The calculator preserves the mathematical classification but warns when the impermeant difference is at most 1 %, a region the model cannot resolve with physical precision.

Osmolarity per litre is used because the inputs are volume-based. Osmolality per kilogram of solvent is preferable for concentrated solutions and freezing-point measurements; conversion between them requires density.

What it does not predict

Lysis: “unbounded swelling” does not say when a membrane ruptures.
Walled cells: no turgor, plasmolysis or cell wall.
Clinical results: no serum osmolality estimate or treatment guidance.

How to read the diagram

Radius scales as (V_f/V₀)^1/3, because the circle represents volume.
“Out of scale” means the drawing reached its visual limit, not that the result changed.
Filled circle = impermeant; hollow diamond = permeant.

Cell Osmotic Equilibrium

Parameters

Cell interior

Extracellular medium

Results

Equilibrium volume

Initial driving force

Osmotic pressure of each solution

Fundamentals & Explanation

Osmolarity, tonicity and three distinct readings

Reflection coefficient and initial flux

Equilibrium volume

Transient reversal

Declared assumptions

Model limitations

What it does not predict

How to read the diagram

References

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Osmolarity, tonicity and three distinct readings

Reflection coefficient and initial flux

Equilibrium volume

Transient reversal

Declared assumptions

Model limitations

What it does not predict

How to read the diagram

References