Water Potential Calculator

Water potential is the free energy of water per unit volume relative to pure free water at atmospheric pressure and the same temperature, which is assigned a value of zero. Because it has the dimensions of pressure it is reported in bars or megapascals, where 1 MPa equals 10 bars, and water moves spontaneously from higher to lower potential. For a plant cell the total is the sum of a solute component and a pressure component. The solute term follows the van t Hoff relation, the negative of the ionization factor times molar concentration times the gas constant of 0.0831 L bar per mol per K times absolute temperature; it is always zero or negative because dissolving anything in water lowers its free energy. The pressure term is positive in a turgid cell, where the protoplast presses against the rigid wall, and strongly negative in xylem conduits, where transpirational tension pulls water upward. Representative values anchor the arithmetic. Cell sap osmotic potential in mesophytes runs about minus 0.5 to minus 3.0 MPa, turgor pressure in a fully hydrated cell about 0.3 to 1.0 MPa, and midday leaf water potential in a well-watered crop about minus 0.5 to minus 1.5 MPa. The conventional permanent wilting point of soil is minus 1.5 MPa, or 15 bars. Two limitations deserve attention. The van t Hoff equation is an ideal dilute-solution law, and above roughly 0.5 molar real solutions deviate appreciably, so an osmotic coefficient is required; sodium chloride is entered with an ionization factor of 2 but behaves nearer 1.8 at moderate concentration because of ion pairing. This calculation also omits matric potential, the binding of water to surfaces and in fine pores, which is negligible in a vacuolate cell but dominates in soils, cell walls and dry seeds.

Quantitative osmosis began with membranes. Moritz Traube produced artificial precipitation membranes in 1867, and Wilhelm Pfeffer, working in Germany in 1877, deposited copper ferrocyanide inside the walls of porous clay pots to make them mechanically strong and semipermeable, then measured the pressures that sugar solutions generated against them. Jacobus Henricus van t Hoff analysed Pfeffer s data in 1887 and showed that the osmotic pressure of a dilute solution obeys a relation formally identical to the ideal gas law, a result central to the work for which he received the first Nobel Prize in Chemistry in 1901. Plant physiology spent the first half of the twentieth century with a confusing vocabulary of suction force, diffusion pressure deficit and osmotic pressure, terms that were not consistently thermodynamic and did not combine cleanly. R. O. Slatyer and S. A. Taylor proposed the unified water potential terminology in 1960, defining the quantity in terms of the chemical potential of water and allowing solute, pressure, matric and gravitational components to be added in the same units; the convention was adopted internationally over the following decade. Measurement caught up in parallel. Thermocouple psychrometers allowed potential to be inferred from equilibrium vapour pressure, and in 1965 Per Scholander and colleagues published the pressure chamber, in which a leafy shoot is sealed with its cut stem protruding and gas pressure is raised until sap returns to the cut surface, giving a rapid field estimate of xylem tension that remains standard practice today.