Tonicity & water potential

Osmosis is about water, not solutes

Osmosis is the net movement of water across a selectively permeable membrane, one that lets water through but blocks some dissolved substances (solutes). In Pfeffer's pot, sugar couldn't get out, so only water moved.

Which way does the water go? Toward the side with more solute. That can sound backwards, so think about it from the water's point of view. Dissolved particles lower water's tendency to move (chemists call this its free energy), so water in a concentrated solution is less "free" to leave. Water keeps crossing both ways, but more of it crosses from the side where it's freer to the side where it's less free.

Water potential: one number to predict the direction

Biologists measure water's tendency to move with a quantity called water potential, written Ψ (the Greek letter psi). It's measured in units of pressure: megapascals (MPa) or bars, where 1 MPa = 10 bar. Water always moves from higher water potential to lower water potential.

By definition, pure water at normal atmospheric pressure has Ψ = 0. Water potential has two main parts, which you add together:

Ψ = Ψs + Ψp

• Solute potential (Ψs): the effect of dissolved solutes. Adding solute always makes Ψs more negative. Pure water has Ψs = 0; any solution has Ψs below zero.
• Pressure potential (Ψp): the effect of physical pressure. Pushing on water raises its potential, so Ψp is positive when a solution is squeezed. In an open beaker, Ψp = 0. In a plant cell pressing against its wall, Ψp is positive and is called turgor pressure.

In whole plants and soil, gravity and water clinging to surfaces add extra terms (they matter in tall trees and dry soil), but for cells and solutions Ψs + Ψp is what you need.

Calculating solute potential: Ψs = −iCRT

Van 't Hoff's equation, rearranged for biologists, gives the solute potential of a dilute solution:

Ψs = −iCRT

• i is the ionisation constant: how many particles each unit of solute breaks into when it dissolves. Sucrose and glucose don't split, so i = 1. NaCl splits into Na⁺ and Cl⁻, so i = 2 (ideally; in real solutions it's slightly less). CaCl₂ gives i = 3.
• C is the molar concentration, in mol/L.
• R is the pressure constant, 0.0831 L·bar·mol⁻¹·K⁻¹.
• T is the temperature in kelvin: °C + 273.
• The minus sign is there because solutes lower water potential.

Notice what matters: the number of dissolved particles, not their size or type. A 0.1 M NaCl solution has about the same effect as 0.2 M sucrose, because both contain about 0.2 mol of particles per litre.

Tonicity: what happens to cells

Tonicity compares a solution with a cell, using solutes that can't cross the membrane. A hypotonic solution has less solute than the cell, so water moves in. A hypertonic solution has more solute, so water moves out. An isotonic solution matches the cell, so there's no net movement. These words only make sense as comparisons: a solution is hypotonic to something.

• An animal cell in a hypotonic solution swells and may burst (lysis), because nothing pushes back. In a hypertonic solution it shrivels; red blood cells visibly crinkle, which is called crenation. That's why most intravenous drips are isotonic.
• A plant cell in a hypotonic solution takes in water and presses against its cell wall. The wall pushes back, raising Ψp, until the cell's total Ψ matches the outside and water stops moving in. The cell is turgid, which keeps non-woody plants upright.
• A plant cell in a hypertonic solution loses water, turgor falls and the plant wilts. With enough water loss, the membrane pulls away from the wall. This is plasmolysis.
• Freshwater protists such as Paramecium live in a permanently hypotonic world. They use contractile vacuoles to collect incoming water and pump it out, using energy, so they don't burst.

Finding a cell's water potential in the lab

A classic experiment uses potato cores. You weigh cores, soak them in sucrose solutions of different concentrations, and weigh them again. Cores gain mass in solutions that are hypotonic to them and lose mass in hypertonic ones. The concentration where they neither gain nor lose is the isotonic point: there the potato's water potential equals the solution's.

1. 1Calculate the percentage change in mass for each core: (final − initial) ÷ initial × 100. Using percentages lets you compare cores that started at different masses.
2. 2Plot percentage change (y-axis) against sucrose concentration (x-axis).
3. 3Find where the line crosses zero change. If no point lies exactly on zero, interpolate between the two measurements on either side.
4. 4Use Ψs = −iCRT for that sucrose concentration. The solution is in an open beaker (Ψp = 0), so its Ψ = Ψs. At the isotonic point, that's also the water potential of the potato cells.

Key terms

Osmosis

Net movement of water across a selectively permeable membrane, toward lower water potential.

Water potential (Ψ)

A measure of water's tendency to move, in MPa or bars; pure water at atmospheric pressure has Ψ = 0.

Solute potential (Ψs)

The part of water potential due to dissolved solutes; always zero or negative.

Pressure potential (Ψp)

The part of water potential due to physical pressure; zero in an open container, positive in a turgid cell.

Ionisation constant (i)

The number of particles one unit of solute gives when it dissolves (1 for sucrose, about 2 for NaCl).

Hypotonic / hypertonic / isotonic

Having less / more / the same concentration of non-crossing solutes as the cell being compared.

Turgor pressure

The pressure of a plant cell's contents pushing against its wall.

Plasmolysis

The pulling away of a plant cell's membrane from its wall as it loses water.

Check yourself

Try answering in your head before you open each answer.

• 1.A membrane that lets only water through separates 0.10 M NaCl (side A) from 0.15 M sucrose (side B), both at 25 °C in open containers. Which way does water move? Show the Ψs values.Show answerHide

  Side A: Ψs = −(2)(0.10)(0.0831)(298) ≈ −4.95 bar. Side B: Ψs = −(1)(0.15)(0.0831)(298) ≈ −3.71 bar. Water moves from B (higher Ψ) to A (lower Ψ). Even though there's less NaCl by molarity, it splits into two particles, so it has more dissolved particles in total.

• 2.Potato cores change mass by +4% in 0.2 M sucrose, +1% in 0.3 M and −3% in 0.4 M, at 22 °C. Estimate the isotonic point and the water potential of the potato cells.Show answerHide

  The change crosses zero between 0.3 M (+1%) and 0.4 M (−3%), a drop of 4 percentage points over 0.1 M. Zero is ¼ of the way along, so the isotonic point is about 0.325 M. Ψ = Ψs = −(1)(0.325)(0.0831)(295) ≈ −8.0 bar (−0.80 MPa), which is the potato cells' water potential.

• 3.A plant cell with Ψs = −6.0 bar is placed in pure water and left until net water movement stops. What are its Ψ and Ψp at that point? Why would a red blood cell in pure water behave differently?Show answerHide

  Pure water has Ψ = 0, so water enters until the cell's Ψ is also 0. That means Ψp = +6.0 bar, supplied by the wall pushing back. A red blood cell has no wall, so its Ψp can't build up; water keeps entering until it bursts.