Hong Life CalculatorsUnderstanding the water potential calculator — concept and principle
Water potential (Ψ) predicts which way water will move between a plant cell and its surroundings. This calculator combines the solute potential of the cell contents with its pressure potential, compares the result with an outside solution and tells you whether water will flow into or out of the cell. It follows the formulas used in AP Biology and introductory plant physiology.
How it is calculated
Ψ = Ψs + Ψp
Ψs = −i × C × R × T
- i is the ionization constant (1 for sucrose or glucose, 2 for NaCl or KCl, 3 for CaCl₂ or MgCl₂).
- C is the molar concentration in mol/L; R = 0.0831 L·bar/(mol·K); T is the temperature in kelvin (°C + 273.15).
- Ψp is the pressure potential inside the cell in bar. A solution in an open beaker has Ψp = 0, so its Ψ equals its Ψs.
- 1 MPa = 10 bar.
The principle
Water moves spontaneously from where its potential is higher to where it is lower, just as a ball rolls downhill. Pure water at atmospheric pressure is set at Ψ = 0. Dissolved particles bind and dilute water, lowering its free energy, so Ψs is always zero or negative; more particles mean a more negative value, which is why salts that split into ions count two or three times. The formula comes from van 't Hoff's relation for osmotic pressure. Pressure pushes the other way: a plant cell's wall resists swelling and builds up positive turgor pressure Ψp, which raises the cell's water potential.
Worked example
Default inputs: inside 0.3 mol/L, i = 1, Ψp = 3 bar, 22 °C; outside 0.1 mol/L, i = 1.
- T = 22 + 273.15 = 295.15 K.
- Cell Ψs = −1 × 0.3 × 0.0831 × 295.15 = −7.36 bar.
- Cell Ψ = −7.36 + 3 = −4.36 bar = −0.436 MPa.
- Outside Ψ = −1 × 0.1 × 0.0831 × 295.15 = −2.45 bar.
- −2.45 is higher than −4.36, so water moves into the cell.
| Solute concentration inside the cell (mol/L) | Cell water potential Ψ (bar) |
|---|---|
| 0.075 | 1.16 |
| 0.15 | -0.68 |
| 0.225 | -2.52 |
| 0.3 | -4.36 |
| 0.375 | -6.2 |
| 0.45 | -8.04 |
| 0.6 | -11.72 |
How to read the result
Water flows towards the more negative value. If the outside is less negative, the cell gains water and turgor pressure rises until the potentials balance or the wall stops expansion. If the outside is more negative, as in salty soil or a concentrated sugar solution, the cell loses water and may plasmolyse. Typical well-watered leaf tissues have water potentials of a few tenths of a megapascal below zero, and they fall during drought.
Common mistakes
- Forgetting the negative sign on solute potential.
- Using °C instead of kelvin.
- Using i = 1 for salts that dissociate.
- Giving an open beaker a pressure potential; it is zero.
Frequently asked questions
Why is pure water's potential zero?
It is the agreed reference point, like sea level for heights.
Can water potential be positive?
Yes, in a cell with high turgor pressure and few solutes, or in pressurised water such as in a pipe.
Why does salt water dehydrate cells?
Its very negative water potential draws water out of the cell.
What is turgor pressure?
The pressure of the cell contents against the cell wall, which keeps non-woody plants rigid.
Sources: College Board, "AP Biology Equations and Formulas" (AP Biology Lab Manual, Appendix A)