Osmotic Potential Calculator
Enter solute molarity, temperature, and dissociation coefficient to compute osmotic (solute) potential Ψs = −iCRT (MPa) via the van't Hoff equation, estimating a solution's water-attracting strength.
Input Data
Results
At a glance:Osmotic potential (Ψs), also called solute potential, is a key component of water potential (Ψ), quantifying how dissolved solutes in water increase the solution's 'water-uptake ability and lower its water potential'. Pure water is defined at 0; once solutes are added, some water molecules are bound by solutes and free water decreases, so the solution tends to take up water from its surroundings and its osmotic potential becomes negative. Quantitatively, for dilute solutions Ψs ≈ − i × C × R × T (van't Hoff relation), where i is the van't Hoff (dissociation) coefficient — how many independently acting particles one solute molecule yields in water: non-dissociating molecular solutes like sucrose or glycerol have i = 1; fully dissociated NaCl splits into Na⁺ and Cl⁻ so i ≈ 2; CaCl₂ splits into three ions so i ≈ 3 (actual i is slightly below the theoretical value due to ion interactions); C is solute molarity (mol/L); R is the gas constant, giving MPa when R = 0.008314 L·MPa·mol⁻¹·K⁻¹; T is absolute temperature (K) = Celsius + 273.15. The negative sign means osmotic potential lowers water potential: higher concentration, more dissociated particles, or higher temperature makes Ψs more negative and the solution's water-uptake drive stronger. In plant physiology Ψs is central to water movement — water always flows from high to low water potential, and solutes (sugars, ions, amino acids like proline) accumulated in cytoplasm and vacuole lower the cell's Ψs, allowing it to keep taking up water from outside or soil and maintain turgor even under drought or salinity; this active solute accumulation to lower Ψs is called 'osmotic adjustment'. Ψs also explains seed and root water uptake, guard-cell turgor changes, and preparing PEG-/mannitol-/salt-based treatment solutions of a set Ψs. Remember van't Hoff is a dilute-solution approximation; very concentrated or non-ideal solutions (e.g. high-MW PEG) deviate and need empirical formulas or direct vapor-pressure/dewpoint osmometry; also molarity refers to the solute itself, with dissociation counted by i — do not double-count.
Formula
van't Hoff osmotic potential: Ψs = − i × C × R × T.
R = 0.008314 L·MPa·mol⁻¹·K⁻¹; T(K) = °C + 273.15.
Water potential (no pressure): Ψ = Ψs + Ψp, with Ψs always ≤ 0.
$$\Psi_s = -\,i\,C\,R\,T$$$$T_{K} = T_{^\circ C} + 273.15$$How to Use
- Enter solute molarity C (mol/L).
- Enter solution temperature (°C, auto-converted to K) and dissociation coefficient i (sucrose 1, NaCl ≈ 2).
- The tool instantly computes Ψs (MPa, negative); more negative means stronger water uptake and lower water potential.
Common solutes: dissociation i and osmotic-potential tendency (25°C dilute approx.)
| Solute | Dissociation i | Note |
|---|---|---|
| Sucrose / mannitol / PEG | 1 | Non-dissociating; Ψs proportional to concentration |
| NaCl (table salt) | ≈ 2 | Splits into Na⁺, Cl⁻; more negative at same concentration |
| KCl | ≈ 2 | Monovalent salt, two particles |
| CaCl₂ | ≈ 3 | Splits into Ca²⁺, 2Cl⁻; most negative Ψs |
Actual i is slightly below theoretical due to ion interactions; concentrated or non-ideal solutions need empirical formulas or direct measurement.
Case Studies
Osmotic potential of a sucrose solution
0.5 mol/L sucrose (i = 1) at 25°C (T = 298.15 K).
Ψs = −1 × 0.5 × 0.008314 × 298.15 ≈ −1.24 MPa.
Means this solution's water potential is pulled down about 1.24 MPa by solutes — the driving force with which it takes up water from surroundings.
Salt solution is more negative due to dissociation
0.15 mol/L NaCl (i ≈ 2) at 25°C.
Ψs = −2 × 0.15 × 0.008314 × 298.15 ≈ −0.74 MPa.
Although only 0.15 mol/L, because each NaCl dissociates into two ions the osmotic potential is still substantial — showing salt stress impacts cell water uptake.
FAQ
Why is osmotic potential negative?
Water potential uses pure water as the 0 baseline. Adding solutes binds some water molecules and reduces free, mobile water, lowering the solution's water potential below pure water, so osmotic potential is negative. Higher concentration binds more water and makes Ψs more negative. The negative sign reminds us solutes always 'pull water potential down and strengthen uptake' — why water flows from pure water (high) to solution (low).
How to choose the dissociation coefficient i?
i is how many independent particles one solute molecule yields in water. Sucrose, mannitol, glycerol, PEG do not dissociate, i = 1; NaCl, KCl split into two ions, i ≈ 2; CaCl₂, MgCl₂ split into three, i ≈ 3. Theoretically i equals the number of ions, but actual observed i (after osmotic-coefficient correction) is slightly below theoretical due to electrostatic ion interactions, closer at low concentration.
How does osmotic potential relate to water potential and turgor?
Ignoring matrix and gravity, cell water potential Ψ = osmotic potential Ψs + pressure potential Ψp (turgor). Ψs is always negative (solutes), Ψp positive in turgid cells. When outside water potential is higher than cell water potential, water enters, turgor rises and Ψp increases until Ψ balances. Osmotic adjustment is the cell actively lowering Ψs so Ψ becomes more negative to keep taking up water and maintain turgor, resisting drought or salinity.
When is the van't Hoff formula inaccurate?
It is an ideal dilute-solution approximation. At very high concentration, for high-MW solutes (e.g. PEG, whose osmolality is non-linear in concentration), or non-ideal solutions (strong ion interactions), actual osmotic potential deviates from −iCRT, usually more negative or flatter than theory. Then use that solute's empirical calibration (e.g. PEG concentration–Ψs relation) or measure directly by vapor-pressure/dewpoint osmometry.
Use Celsius or absolute temperature?
T in the formula must be absolute temperature (kelvin K). This calculator lets you enter Celsius and internally converts T(K) = ℃ + 273.15 before substituting. Because osmotic potential is proportional to absolute temperature, entering Celsius directly is a serious error (e.g. 25°C should be 298.15 K, not 25).
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.