Osmotic potential and water potential (plant biology)
In plant and cell physiology, water movement depends on water potential, written as
\(\Psi\). Water tends to move from a region of higher \(\Psi\) to lower \(\Psi\).
This calculator uses the classic relation:
\[
\Psi = \Psi_s + \Psi_p
\]
- \(\Psi_s\) = solute (osmotic) potential (usually negative)
- \(\Psi_p\) = pressure potential (can be positive in turgid plant cells)
Key idea: solutes lower water potential (more negative \(\Psi_s\)), while pressure
raises water potential (more positive \(\Psi_p\)).
Solute (osmotic) potential: \(\Psi_s = -iCRT\)
For dilute solutions, a useful approximation for solute potential is:
\[
\Psi_s = - i C R T
\]
- \(i\) = van ’t Hoff factor (number of particles produced per formula unit)
- \(C\) = molar concentration (mol/L)
- \(R\) = gas/pressure constant (used here as \(R = 0.008314\ \text{MPa}\cdot\text{L}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}\))
- \(T\) = absolute temperature (K), with \(T(\text{K}) = T(^{\circ}\text{C}) + 273.15\)
Why is \(\Psi_s\) negative? Because adding solute decreases the “free” energy of water,
reducing its tendency to move into that solution.
Interpreting \(\Psi_p\) (pressure potential)
Pressure potential represents physical pressure on water. In many open containers (beakers),
\(\Psi_p\) is close to 0. In plant cells, turgor pressure can make \(\Psi_p\) positive.
\[
\Psi = \Psi_s + \Psi_p \quad\Rightarrow\quad
\text{pressure can offset a negative } \Psi_s
\]
Comparing two compartments (A vs B)
When comparing a cell and an external solution (or two solutions), compute \(\Psi\) for each:
\(\Psi_A\) and \(\Psi_B\). Then:
\[
\Delta\Psi = \Psi_A - \Psi_B
\]
- If \(\Psi_A > \Psi_B\): water tends to move from A → B
- If \(\Psi_A < \Psi_B\): water tends to move from B → A
- If \(\Psi_A \approx \Psi_B\): no strong net movement (equilibrium)
Direction rule: water moves from higher \(\Psi\) to lower \(\Psi\).
Units used in this calculator
The calculator computes \(\Psi_s\) and \(\Psi\) in MPa internally and can also display
results in bar.
Important limitations
-
The relation \(\Psi_s=-iCRT\) is a dilute-solution approximation.
At high concentrations, real solutions can deviate from ideal behavior.
-
“Water potential” combines multiple effects in real tissues (matric potential, gravity),
but this calculator focuses on the basic form used in many introductory problems:
\(\Psi=\Psi_s+\Psi_p\).
-
The van ’t Hoff factor \(i\) is approximate (e.g., electrolytes may not dissociate perfectly).
