Water Potential — Comprehensive Study Notes

Overview

• Water potential (Ψ) is the potential energy of water per unit area relative to pure water, used to predict the direction of water movement.
• It determines water flow due to osmosis, gravity, pressure, and surface tension, and helps decide whether water will enter or leave a cell.
• Measured in bars, represented by the symbol Ψ (psi). A memory cue mentioned: Poseidon (god of the ocean) and the trident resemble the water-potential symbol.
• Pure water has Ψ = 0 bars.
• Water moves from high water potential (less negative or more positive) to low water potential (more negative). This is equivalent to movement from high water concentration to low water concentration.

Key Concepts and Components

• Water potential equation: \Psi = \Psis + \Psip where:
  • \Psi_s = solute potential (osmotic component)
  • \Psi_p = pressure potential (physical pressure component)
• Solute potential, \Psi_s = -iCRT
  • i = ionization constant (dimensionless; varies with solute, typically between 1 and 2)
  • C = molar concentration (mol L⁻¹)
  • R = gas constant, typically around 0.0831\ \text{L bar mol}^{-1}\text{K}^{-1}
  • T = absolute temperature in Kelvin (K)
• Temperature must be in Kelvin: TK = T{°C} + 273
• Solute potential gets more negative as solute concentration (C) or ionization (i) increases; more solutes mean fewer free water molecules, lowering Ψ_s.
• Pressure potential, \Psip, is the physical pressure exerted by surroundings or by the cell wall in plant cells. It can be positive (pushing water inward) or negative (tension). In many open-system examples, \Psip = 0.
• Practical interpretation: When the sum of solute and pressure potentials is higher on one side than another, water moves toward the side with the lower total water potential (more negative value).

Osmosis and Practical Examples

• Osmosis concept: adding solutes (like salt) to water lowers the solute potential on that side, creating a gradient that drives water movement across membranes.
• Slug example (salt exposure):
  • Dissolving NaCl in water dissociates into Na⁺ and Cl⁻. The ions become hydrated by water molecules.
  • This dissociation increases effective solute presence (higher i) and lowers Ψ_s on that surface, creating a gradient that pulls water out of the slug’s cells, potentially causing dehydration.
  • In a membrane scenario, outside solution might have Ψ ≈ -40 bars and inside ≈ -5 bars, so water flows from the higher Ψ (inside) to the lower Ψ (outside) across the membrane (direction depends on the actual Ψ values on both sides).
• Plant context and water movement:
  • Distilled water in soil has Ψ ≈ 0 bars.
  • Plant roots typically have Ψ around Ψ_r ≈ −2 bars due to solutes (ions, organic compounds).
  • Stems and leaves usually have more negative Ψ (lower Ψ) than roots, and the atmosphere can drive further negative Ψ at the leaf surface due to evaporation (transpiration).
  • Water moves up a plant along a root-to-leaf gradient—from higher Ψ (less negative) to lower Ψ (more negative) as it travels toward regions where water vapor is being lost to the atmosphere.
• Summary: Water potential gradients drive the movement of water in organisms and ecosystems, with osmosis and physical pressure being the main driving forces.

Solute Potential: Derivation and Significance

• Formula:
  \Psi_s = -iCRT
• Components:
  • i: ionization constant (e.g., NaCl ≈ 2 because it dissociates into two ions; sucrose ≈ 1 because it does not dissociate)
  • C: molar concentration (mol L⁻¹)
  • R: gas constant, ≈ 0.0831 L bar mol⁻¹ K⁻¹
  • T: absolute temperature in Kelvin (K)
• Conceptual notes:
  • Higher i or higher C lowers Ψ_s (more negative).
  • Temperature effects: increasing T typically lowers Ψ_s (more molecular motion), reflected in the term iCRT.
• Practical takeaway: Solute potential is the osmotic component; the more solutes present, the lower (more negative) the solute potential becomes.

Pressure Potential (Ψp)

• Definition: physical pressure acting on water, often produced by turgor pressure in plant cells or by external forces.
• Positive Ψ_p: forces water into the cell or area (turgor pressure). In plant cells, the cell wall resists expansion, generating positive pressure.
• Negative Ψ_p: tension or suction, as can occur in xylem when water is pulled upward under tension.
• Example scenario: If water continually enters a plant cell, Ψp increases until cell wall tension balances inflow; the resulting Ψ = Ψs + Ψ_p describes the net potential.

Worked Example: 0.2 M Sugar at 22°C

• Given:
  • Solute: sugar (sucrose), i = 1 (does not ionize)
  • Concentration: C = 0.2\ \text{mol L}^{-1}
  • Temperature: T = 22^{\circ}\text{C}
• Convert to Kelvin:
  T_K = 22 + 273 = 295\ \text{K}
• Constants:
  R = 0.0831\ \text{L bar mol}^{-1}\text{K}^{-1}
• Compute solute potential:
  \Psi_s = -iCRT = -(1)(0.2)(0.0831)(295) \approx -4.9049\ \text{bars} \approx -5\ \text{bars}
• If the beaker is open (no external pressure): \Psi_p = 0\ \text{bars}
• Overall water potential:
  \Psi = \Psis + \Psip \approx -5\ \text{bars}
• Takeaway: For a 0.2 M sugar solution at 22°C in an open beaker, Ψ_w ≈ -5 bars; the sign indicates a tendency to draw water in from surroundings with higher Ψ.

Quick Scenarios and Flow Directions

• Scenario 1: External solution Ψ ≈ -40 bars; internal solution Ψ ≈ -5 bars across a membrane.
  • Water moves from the side with higher Ψ (less negative, here -5 bars) to the side with lower Ψ (more negative, here -40 bars).
  • Result: water would tend to move from the interior toward the exterior across the membrane (toward lower Ψ).
• Scenario 2: Plant root Ψr ≈ −2 bars; leaf Ψleaf is more negative due to transpiration; atmosphere has very low Ψ (highly negative).
  • Water moves from roots up the shoot through the xylem toward leaves, driven by the gradient from higher to lower Ψ along the pathway.
• Scenario 3: Open beaker with distilled water (Ψ ≈ 0) in contact with a plant tissue with Ψ ≈ −3 bars.
  • Water moves from the beaker (0 bars) into the plant tissue (−3 bars).

Real-World Relevance and Applications

• Plant physiology: understanding water uptake, turgor pressure, stomatal function, and responses to drought or salinity.
• Agriculture: managing soil salinity and irrigation to maintain favorable Ψ gradients for crop water uptake.
• Medicine and biology: osmotic stress, cell swelling/plasmolysis in cells exposed to hypertonic or hypotonic solutions.
• Ecology: water potential gradients guide water movement in soils, trees, and ecosystems, affecting nutrient transport and plant distribution.

Practical Tips for Problems

• Always identify the two components of Ψ and their signs: Ψ = Ψs + Ψp.
• Check the sign convention: energy and flow considerations depend on whether Ψ is more or less negative.
• For Ψ_s calculations:
  • Determine i for the solute (1 for non-dissociating solutes like sucrose; ~2 for salts like NaCl).
  • Use C in mol L⁻¹, R = 0.0831 L bar mol⁻¹ K⁻¹, T in Kelvin.
  • Convert Celsius to Kelvin before plugging in.
• When solving problems:
  • Cancel units carefully to end with bars for Ψ_s.
  • For solutions in open containers, Ψ_p is typically 0.
  • Round to appropriate significant figures consistent with the given data (e.g., 0.2 M with one significant figure → Ψ ≈ −5 bars).

Summary of Core Takeaways

• Water potential is a measure of the potential energy of water guiding water movement; water flows from high Ψ (less negative) to low Ψ (more negative).
• Ψ = Ψs + Ψp, where Ψs becomes more negative with more solutes or higher i, and Ψp reflects physical pressure (positive in turgid cells, can be zero in open systems).
• The solute potential is given by \Psi_s = -iCRT, with i depending on ionization, C the molarity, R = 0.0831\ \text{L bar mol}^{-1}\text{K}^{-1}, and T in Kelvin.
• Everyday examples (slugs with salt; plant water transport from roots to leaves) illustrate how these principles govern water movement in biology and ecosystems.