Osmosis and Water Potential
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You should be comfortable with the concept of a concentration gradient and understand that diffusion is the passive movement of molecules from regions of higher to lower concentration, as established in the previous lecture on Fick's Law.
Why this matters
Water potential is the universal currency of water movement in living systems.
While diffusion explains how solutes move, osmosis explains how water moves. This distinction is critical because cells are not open systems; they are bounded by membranes that are selectively permeable. Understanding water potential allows us to predict the direction of water flow in plant cells, animal tissues, and even industrial processes like desalination. Without this framework, we cannot explain why a plant wilts, why red blood cells burst in pure water, or how kidneys concentrate urine. It unifies the physics of pressure and the chemistry of solutes into a single, predictive variable.
The Concept of Water Potential
Imagine two beakers separated by a membrane that allows water to pass but blocks salt. One beaker contains pure water, and the other contains a salt solution. If you place a drop of dye in the pure water, it will eventually spread out, but the water itself will also move. Why? The water molecules in the pure water have more freedom to move than those in the salt solution, where they are partially "tied up" by interactions with the salt ions. This difference in freedom translates to a difference in energy. We call this energy water potential, denoted by the Greek letter psi (\( \psi \)).
Think of water potential as the "thirst" of a system. Pure water at atmospheric pressure is the reference: its water potential is defined as zero. When you add solutes, you lower the water potential because the solute molecules reduce the number of free water molecules available to move. Therefore, water always moves from an area of higher water potential (less negative, more free energy) to an area of lower water potential (more negative, less free energy). This is not magic; it is simply the second law of thermodynamics in action. Systems naturally evolve toward a state of lower free energy. In biological terms, this means water flows from dilute solutions to concentrated solutions until equilibrium is reached, or until a physical barrier, like a cell wall, prevents further movement.
Components of Water Potential
Water potential is not a single, indivisible quantity. It is the sum of two main components: solute potential (\( \psi_s \)) and pressure potential (\( \psi_p \)). The total water potential is given by the equation \( \psi = \psi_s + \psi_p \). Solute potential is always negative or zero because adding solutes reduces the free energy of water. It is also known as osmotic potential. Pressure potential can be positive or negative. In plant cells, the rigid cell wall exerts an outward pressure on the cytoplasm as water enters, creating a positive pressure potential. In xylem vessels, water is under tension, resulting in a negative pressure potential.
The solute potential is calculated using the formula \( \psi_s = -iCRT \), where \( i \) is the van 't Hoff factor (the number of particles each formula unit dissociates into), \( C \) is the molar concentration, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin. For example, a solution of sodium chloride (NaCl) has an \( i \) value of approximately 2 because it dissociates into Na+ and Cl-. A non-dissociating solute like glucose has an \( i \) value of 1. This means that at the same molar concentration, a salt solution has a lower (more negative) water potential than a sugar solution, making it more "thirsty" for water.
Osmosis and Membrane Permeability
Osmosis is the net movement of water across a semipermeable membrane down its water potential gradient. The rate of this movement depends on the difference in water potential between the two sides and the permeability of the membrane to water. A useful rule of thumb is that net water flow is toward the higher solute concentration. This is a simplification that holds true when pressure potential is negligible or equal on both sides. However, in real biological systems, pressure potential often plays a dominant role. For instance, in a turgid plant cell, the pressure potential is high enough to counterbalance the solute potential, preventing further water entry even if the external solution is hypotonic.
The permeability of the membrane is crucial. Biological membranes are not perfectly selective; they allow some water to pass through the lipid bilayer, but the majority of water transport occurs through specialised protein channels called aquaporins. These channels increase the rate of osmosis significantly. Without aquaporins, the movement of water would be too slow to support rapid physiological processes like the reabsorption of water in the kidney tubules or the rapid uptake of water by root hairs. Thus, the biological control of osmosis is not just about creating gradients but also about regulating the permeability of the barrier.
Equilibrium and Turgor Pressure
Equilibrium in an osmotic system is reached when the water potential is equal on both sides of the membrane. At this point, there is no net movement of water, although individual water molecules continue to move randomly in both directions. In animal cells, which lack a cell wall, equilibrium is achieved when the internal and external water potentials are equal. If the external water potential is higher, water enters the cell, causing it to swell and potentially lyse. If the external water potential is lower, water leaves the cell, causing it to shrink (crenate).
In plant cells, the situation is different due to the presence of the cell wall. As water enters the cell, the volume of the protoplast increases, pressing against the cell wall. The cell wall, being elastic to a certain extent, pushes back, generating a positive pressure potential. This pressure potential increases as the cell becomes more turgid. Eventually, the positive pressure potential cancels out the negative solute potential, and the total water potential of the cell equals that of the external environment. At this point, the cell is turgid, and no further net water movement occurs. This turgor pressure is essential for maintaining the structural integrity of non-woody plants and for driving the opening and closing of stomata.
The concept
Diffusion and osmosis
Passive movement of molecules down a gradient.
A common misconception is that water always moves toward the side with more solute. Water moves down the gradient of total water potential, which includes pressure. In the worked example below, the cell holds more solute than the bathing solution (\(\psi_s = -0.8\) against \(-0.6\ \mathrm{MPa}\)), yet its turgor pressure of \(+0.5\ \mathrm{MPa}\) raises its water potential to \(-0.3\ \mathrm{MPa}\), so water leaves the cell. Always add the pressure potential before predicting the direction of flow. C
Worked example
Problem. A plant cell has a solute potential of -0.8 MPa and a pressure potential of 0.5 MPa. It is placed in a solution with a solute potential of -0.6 MPa and a pressure potential of 0 MPa. Calculate the water potential of the cell and the solution, and determine the direction of net water movement.
- Calculate the water potential of the plant cell using the formula \( \psi_{\text{cell}} = \psi_s + \psi_p \). Substituting the values: \( \psi_{\text{cell}} = -0.8\ \mathrm{MPa} + 0.5\ \mathrm{MPa} = -0.3\ \mathrm{MPa} \).
- Calculate the water potential of the external solution. Since it is an open solution, the pressure potential is zero. Thus, \( \psi_{\text{solution}} = -0.6\ \mathrm{MPa} + 0\ \mathrm{MPa} = -0.6\ \mathrm{MPa} \).
- Compare the two water potentials. The cell has a water potential of -0.3 MPa, and the solution has a water potential of -0.6 MPa.
- Recall that water moves from higher water potential (less negative) to lower water potential (more negative). Since -0.3 MPa is greater than -0.6 MPa, the cell has a higher water potential.
- Therefore, the net movement of water will be from the cell to the external solution. The cell will lose water and become less turgid.
Units check. Both potentials are expressed in megapascals (MPa), which is a unit of pressure, consistent with the definition of water potential as a form of energy per unit volume.
What does \(-0.6\ \mathrm{MPa}\) mean as a concentration? From \(\psi_s = -CRT\) for a non-dissociating solute at 298 K, \(C = 0.6 \times 10^{6}/(8.314 \times 298) = 242\ \mathrm{mol\,m^{-3}}\), about \(0.24\ \mathrm{mol\,L^{-1}}\) of sucrose; for NaCl (\(i \approx 2\)) about half that.
Three quick tests
- What is the water potential of pure water at standard temperature and pressure?
Answer
Zero MPa, by definition. - If a cell has a solute potential of -1.0 MPa and a pressure potential of 0.2 MPa, what is its total water potential?
Answer
-0.8 MPa. - Why does a plant cell not burst in a hypotonic solution, whereas an animal cell might?
Answer
The rigid cell wall of the plant cell exerts a counteracting pressure potential, preventing excessive expansion.
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Every lecture and every concept in this unit, with prerequisites and threads.
Lecture notes checked line by line by the editor; every number in the worked example was recomputed.
Concepts cited: T-028 · Threads: regulation, systems