# 3.1.2 - Osmotic pressure and water potential

How is it that plant cells can have such large turgor pressures? The essential reason is that the cells contain large concentrations of solutes. These solutes attract water into the cells through a process known as osmosis, which involves water flowing in through semipermeable membranes that prevent the passage of solutes but not of water. The inflow of water swells the cells until a hydrostatic pressure is reached at which no more water will flow in. In cells bathed in fresh water, such as algal cells in a pond, this equilibrium hydrostatic pressure is known as the osmotic pressure ($\pi$) of the cell contents, and is commonly about 500 kPa or 0.5 MPa.

This osmotic pressure can be measured directly with an osmometer, or it can be calculated from the solute concentration in the cell ($C$) from the van‘t Hoff relation:

$\pi = RTC \tag{1}$

where $R$ is the gas constant, $T$ is the absolute temperature (in degrees Kelvin) and $C$ is the solute concentration in Osmoles L-1. At 25 ºC, $RT$ equals 2.5 litre-MPa per mole, and $\pi$ is in units of MPa. Hence a concentration of 200 mOsmoles L-1 has an osmotic pressure of 0.5 MPa.

However, land plants are different from algae in a pond. Their leaves are in air, and the water in their cell walls, unlike the water in a pond, is not free. It has a negative hydrostatic pressure (discussed further in the next section). Thus, for a given osmotic pressure ($\pi$) within a cell, the hydrostatic pressure, $P$, will be lower than if the cell were bathed in free water. This difference is known as the water potential ($\psi$) of the cell. It is zero in an algal cell in fresh water, but it is always negative in land plants. Its value is the difference between $P$ and $\pi$, that is:

$\psi=P-\pi \tag{2}$

An alternative notation for equation (2) used commonly by plant physiologists is:

$\psi_w = \psi_p + \psi_s \tag{3}$

In this case, $\psi_w$ is the total water potential, $\psi_s$ is the solute potential and $\psi_p$ is the pressure potential. Thus $\psi_s$ is equal, but opposite in sign, to $\pi$.

The notion of water potential can be applied to any sample of water, whether inside a cell, in the cell wall, in xylem vessels, or in the soil. Water will flow from a sample with a high water potential to one with a low water potential provided the samples are at the same temperature and provided that no solutes move with the water. Water potential thus defined is always zero or negative, for by convention it is zero in pure water at atmospheric pressure.