About water potential
Water potential (symbol Ψ, the Greek letter psi) measures the potential energy of water per unit volume relative to pure water at atmospheric pressure. It predicts the direction water will move: water always flows from a region of higher (less negative) water potential to a region of lower (more negative) water potential. Because it is expressed as an energy per volume, water potential is reported in pressure units — most commonly bars or megapascals (1 MPa = 10 bars). Pure water at standard atmospheric pressure has a water potential of exactly 0.
The formula
In plant physiology, water potential is the sum of two components:
Ψ = Ψs + Ψp
- Ψs — solute potential (also called osmotic potential). Dissolved solutes lower the free energy of water, so Ψs is always negative or zero.
- Ψp — pressure potential. Physical pressure such as the turgor pressure exerted by a cell wall. It is usually positive inside a living cell and can be negative (tension) in the xylem.
Solute potential is calculated with the van't Hoff-style relation used throughout introductory biology:
Ψs = −iCRT
- i — ionization (dissociation) constant: the number of particles a solute breaks into. For sucrose i = 1.0; for NaCl i = 2.0; for CaCl₂ i ≈ 3.0.
- C — molar concentration of the solute in mol/L.
- R — the pressure constant, 0.0831 liter·bar / (mol·K).
- T — temperature in Kelvin, found by adding 273 to the Celsius temperature.
The leading minus sign guarantees that adding any solute produces a negative solute potential, which is why solutions always have a lower water potential than pure water.
Why it matters
Water potential explains osmosis without hand-waving. A plant cell placed in distilled water (Ψ = 0) has negative internal water potential from its dissolved solutes, so water moves in until the rising turgor pressure raises Ψp enough to bring the cell's total Ψ up to 0. A cell placed in a strong sugar or salt solution loses water, plasmolyzes, and wilts because the surrounding solution is more negative than the cell interior. The same principle governs how roots pull water from soil and how water climbs a tree.
Common reference points
- Pure water, open to the atmosphere: Ψ = 0 bars.
- 0.15 mol/L NaCl (roughly the salinity of physiological saline) at 25 °C: Ψs = −(2)(0.15)(0.0831)(298) ≈ −7.43 bars.
- 1.0 mol/L sucrose at 20 °C: Ψs = −(1)(1.0)(0.0831)(293) ≈ −24.35 bars.
- Well-watered soil: about −0.1 to −0.3 bars; permanent wilting point for most crops: about −15 bars.