Transport Across the Cell Membrane

Lessons

Senior 5 · Biology

Transport Across the Cell Membrane

5 lessons

Lesson 2 of 5

Osmosis, water potential and osmotic pressure

25 min

Why does the liquid stop rising?

Set up the osmometer in Figure 1: a bag of Visking tubing full of sucrose solution, tied to a narrow glass tube and hung in distilled water. Within minutes the liquid starts to climb the tube, because water enters the bag by osmosis. But after some hours the level stops rising, even though the solution in the bag is still more concentrated than the water outside. To explain why, biologists stopped talking only about concentrations and began to measure water potential, which includes the effect of pressure. You met the term in Senior 2. In this lesson you calculate with it.

Definition

Osmosis: the net movement of water molecules from a region of higher water potential to a region of lower water potential, through a partially permeable membrane.

Water potential, $\psi$ (psi): a measure of the tendency of water to move out of a system, in kilopascals (kPa). Pure water at atmospheric pressure has $\psi = 0$ ; every solution has a negative $\psi$ .

Solute potential, $\psi_s$ : the part of the water potential due to dissolved solutes. It is always negative; more solute makes it more negative.

Pressure potential, $\psi_p$ : the part due to pressure. In a plant cell the wall pushes back on the swelling protoplast, so $\psi_p$ is usually positive.

Osmotic pressure: the pressure that must be applied to a solution to stop pure water entering it across a partially permeable membrane. It has the same size as the solute potential but the opposite sign: osmotic pressure $= -\psi_s$ .

The water potential equation

The water potential of a cell is the sum of its two components:

\psi = \psi_s + \psi_p

Water always moves from the higher (less negative) water potential to the lower (more negative) one. Now the osmometer makes sense. At first the bag's $\psi$ is well below 0, so water enters. As the column rises, its weight presses on the solution, raising $\psi_p$ . When $\psi_s + \psi_p = 0$ , the bag's water potential equals that of the pure water outside, and net movement stops. The height of the column then measures the osmotic pressure of the solution.

Calculating solute potential

For dilute solutions, the solute potential follows the van 't Hoff equation:

\psi_s = -iCRT

where $C$ is the concentration in $\mathrm{mol\,m^{-3}}$ , $R = 8.31\,\mathrm{J\,mol^{-1}\,K^{-1}}$ , $T$ is the temperature in kelvin, and $i$ is the number of particles each solute unit gives in solution (1 for sucrose, about 2 for NaCl, which forms Na⁺ and Cl⁻). With these units, $\psi_s$ comes out in pascals. Solute potential depends on the number of dissolved particles, not their type or size. Concentrated sucrose solutions deviate from the equation and have a more negative $\psi_s$ than it predicts.

Worked example 1: solute potential of a sucrose solution

Calculate the solute potential of a 0.30 mol dm⁻³ sucrose solution at 25 °C. Then compare it with a 0.30 mol dm⁻³ NaCl solution at the same temperature.

Convert units: $0.30\,\mathrm{mol\,dm^{-3}} = 0.30 \times 1\,000 = 300\,\mathrm{mol\,m^{-3}}$ ; $T = 25 + 273 = 298\,\mathrm{K}$ .
$\psi_s = -iCRT = -1 \times 300 \times 8.31 \times 298 = -742\,914\,\mathrm{Pa} \approx -743\,\mathrm{kPa}$ .
NaCl gives two particles per unit, so $i \approx 2$ : $\psi_s \approx 2 \times (-743) \approx -1\,490\,\mathrm{kPa}$ (3 s.f.).

Interpretation: at the same molar concentration, a salt solution draws water about twice as strongly as a sugar solution. This is why salting fish or meat dries it out so effectively.

Worked example 2: which way does water move?

Figure 2 shows three neighbouring plant cells. Find the water potential of each cell and the direction of water movement.

$\psi_X = -800 + 300 = -500\,\mathrm{kPa}$ ; $\psi_Y = -700 + 400 = -300\,\mathrm{kPa}$ ; $\psi_Z = -1\,000 + 300 = -700\,\mathrm{kPa}$ .
Order from highest to lowest: Y (−300) > X (−500) > Z (−700).
Water moves Y → X, Y → Z and X → Z: always towards the more negative water potential.

Notice that you cannot decide from $\psi_s$ alone: Y has a less negative $\psi_s$ than X, but you must add each $\psi_p$ before comparing.

Worked example 3: a cell reaching equilibrium

A flaccid plant cell ( $\psi_p = 0$ ) has $\psi_s = -1\,000\,\mathrm{kPa}$ . It is placed in a solution of water potential $-400\,\mathrm{kPa}$ . Assuming the cell's $\psi_s$ does not change, find $\psi_p$ at equilibrium.

At the start $\psi_{cell} = -1\,000 + 0 = -1\,000\,\mathrm{kPa}$ , lower than $-400\,\mathrm{kPa}$ , so water enters the cell.
The protoplast swells and presses on the wall, so $\psi_p$ rises until $\psi_{cell} = \psi_{solution}$ .
$-1\,000 + \psi_p = -400$ , so $\psi_p = +600\,\mathrm{kPa}$ .

Important

Older terms you may meet. Some books describe osmosis with pressures instead of potentials:

Older term	Water potential term
Osmotic pressure (OP)	$-\psi_s$
Turgor pressure (TP), or wall pressure	$\psi_p$
Suction pressure, or diffusion pressure deficit (DPD) = OP − TP	$-\psi$

Water moves towards the cell with the higher suction pressure, which is the same as the lower water potential.

Bozeman Science: "Water Potential". Watch for how solute potential and pressure potential add up, and for the worked problems near the end, which use the same equation as this lesson.

Warning

Common mistakes

"−700 kPa is higher than −300 kPa." It is lower. On the water potential scale, closer to zero means higher.
Saying water moves "from a high concentration to a low concentration" in an osmosis answer. Say "from higher to lower water potential", or you will confuse solute and water concentrations.
Forgetting to convert mol dm⁻³ to mol m⁻³ and °C to K in $\psi_s = -iCRT$ .

Tip

Memory hook: "Water runs downhill." Picture water potential as height: 0 is the top of the hill, and water always flows down towards more negative values.

✦

Practice: water potential

Define water potential and state its value for pure water at atmospheric pressure.
Explain why the solute potential of a solution is always negative.
A cell has $\psi_s = -950\,\mathrm{kPa}$ and $\psi_p = +350\,\mathrm{kPa}$ . Calculate its water potential.
Cell P has $\psi = -450\,\mathrm{kPa}$ and cell Q has $\psi = -620\,\mathrm{kPa}$ . In which direction does water move, and why?
Calculate the solute potential of a 0.20 mol dm⁻³ sucrose solution at 25 °C.
Explain why the liquid in an osmometer stops rising even though the solution inside is still concentrated.
A flaccid cell with $\psi_s = -800\,\mathrm{kPa}$ is placed in pure water. What is its $\psi_p$ at equilibrium, if $\psi_s$ does not change?
A 0.10 mol dm⁻³ solution of NaCl and a 0.20 mol dm⁻³ solution of sucrose are separated by a partially permeable membrane at 25 °C. Predict the net movement of water, with a reason.

Show answersHide answers

The tendency of water to move out of a system, in kPa; 0 kPa for pure water.
Solute molecules attract water molecules and reduce the number free to move, so the solution's tendency to lose water is less than that of pure water, which is defined as 0.
$\psi = -950 + 350 = -600\,\mathrm{kPa}$ .
From P to Q, because −450 kPa is higher (less negative) than −620 kPa.
$C = 200\,\mathrm{mol\,m^{-3}}$ , $T = 298\,\mathrm{K}$ : $\psi_s = -200 \times 8.31 \times 298 = -495\,276\,\mathrm{Pa} \approx -495\,\mathrm{kPa}$ .
The rising column exerts pressure on the solution, increasing $\psi_p$ . When $\psi_s + \psi_p$ reaches 0, equal to the pure water outside, net movement stops.
Water enters until $\psi_{cell} = 0$ : $-800 + \psi_p = 0$ , so $\psi_p = +800\,\mathrm{kPa}$ .
No net movement (approximately): NaCl gives about 2 × 0.10 = 0.20 mol dm⁻³ of particles, the same as the sucrose, so both have $\psi_s \approx -495\,\mathrm{kPa}$ .

Key points

$\psi = \psi_s + \psi_p$ ; pure water has $\psi = 0$ ; solutions are negative.
Water moves from higher to lower water potential across a partially permeable membrane.
$\psi_s = -iCRT$ for dilute solutions; osmotic pressure $= -\psi_s$ .
Pressure potential explains why osmosis stops before concentrations are equal.

Sources and credits

Written by Ganzaa.
Video: Water Potential, Bozeman Science, embedded from YouTube.

Figures 1 and 2, the tables, the worked examples and the practice questions are written by Ganzaa.

1Why does the liquid stop rising?

2The water potential equation

3Calculating solute potential

Why does the liquid stop rising?

The water potential equation

Calculating solute potential