Every osmosis question reduces to one equation and two terms. Solute potential pulls water potential down, pressure potential pushes it up, and water always moves from the higher number to the lower one. That is the whole topic.
The part students trip over is not the maths, it is the sign. Solute potential is always negative, pressure potential is always positive or zero, and forgetting either convention flips the direction of the answer.
Water potential is the one number that decides which way water moves, and it is just two terms added together. Solute potential pulls it down, pressure potential pushes it up, and the sum is what a cell wall actually feels. The osmosis question at the bottom is the one that turns up in every exam.
Use i = 1 for something that does not split up in water, like glucose. Use i = 2 for salts that dissociate into two ions, like NaCl. Leave pressure at 0 for a cell in equilibrium with pure water, and enter a positive number for turgor.
The equation
Ψw = Ψs + Ψp
Water potential is the sum of two independent terms, and that is the whole idea. Dissolved solute lowers it. Pressure raises it. Neither one can cancel the other out in a way you should ignore, because a cell reaching equilibrium is where the two balance.
Solute potential comes from the van ’t Hoff relation:
Ψs = −iCRT
where C is the molarity in mol/L, T is temperature in Kelvin, and R is 0.0082 L·MPa·mol⁻¹·K⁻¹. Using R = 0.0082 rather than 0.0821 is what makes the answer come out in MPa instead of atmospheres.
Two traps in that line:
- Temperature is in Kelvin. Entering 25 °C where 298.15 is needed gives an answer that is wrong by a factor of about 12. This calculator takes Celsius and converts for you.
- i is not always 1. It is the number of particles a solute breaks into. Glucose does not dissociate, so i = 1. Sodium chloride becomes Na⁺ and Cl⁻, so i = 2. That is why 0.5 M NaCl and 0.5 M glucose do not behave the same.
Worked example
A cell has 0.5 mol/L of solute with i = 2, at 25 °C, with no pressure on it:
Ψs = −(2)(0.5)(0.0082)(298.15) = −2.44 MPa
With Ψp = 0, water potential is also −2.44 MPa. Now put that cell in pure water. Pure water is 0 MPa, which is higher, so water moves into the cell. The cell swells, which builds pressure potential, and equilibrium arrives when turgor has risen to 2.44 MPa. That is the plant version of a blood cell bursting in dilute solution.
Why pressure potential is positive
Ψp is the physical pressure pushing on the cell from outside, and in a healthy plant cell it comes from turgor — water in, cell wall pushing back. That is why a plant stands up without wood, and why a wilting plant is limp: it has lost turgor, so Ψp has dropped even though Ψs has not changed at all.
The same pressure in a plant cell is around 0.4 to 0.8 MPa. Animal cells have no wall, so they cannot build up any and their Ψp is effectively zero. That single difference is why a plant cell can sit in the same solution that makes an animal cell lyse.
Reading the sign
| Ψw value | What it means |
|---|---|
| Negative | There is solute doing the pulling. This cell will take water in from anything more positive. |
| Exactly zero | Pure water at atmospheric pressure. It will not move either way. |
| Positive | Pressure is doing the work, not a lack of solute. This is turgor. |
So a cell with Ψw of −2.4 MPa in a soil solution at −0.1 MPa loses water and wilts. Move it to −3.0 MPa soil and it takes water back in. Pure water at 0 is more extreme than either, which is why overwatering and a waterlogged root both kill plants — the cell fills until the wall cannot hold.
Frequently asked questions
What is the formula for water potential?
Ψw = Ψs + Ψp. Solute potential is −iCRT, and pressure potential is whatever is pushing on the cell from outside.
What is the van t Hoff constant i?
The number of particles a solute dissociates into in water. i = 1 for glucose and sucrose, i = 2 for salts like NaCl, and near 3 for something like CaCl₂.
Why is solute potential always negative?
Because solute can only ever lower water potential. The sign convention is arbitrary, but it is universal, and a positive Ψs would break every comparison you make with it.
Is pressure potential positive or negative?
Positive, or zero. It is the turgor pushing out from inside a walled cell, and it counteracts the negative solute term.
Which way does water move?
From higher water potential to lower. A cell at −2.4 MPa sitting in a −0.1 MPa solution loses water, because −0.1 is the higher of the two numbers.
What happens to a plant cell in pure water?
Water moves in, turgor builds until Ψp balances −Ψs, and the cell becomes firm. Too much of it, and the wall cannot hold — which is why an overwatered plant still dies even though the cells are full.
Do animal cells have a pressure potential?
Effectively no. Without a cell wall, an animal cell cannot build up turgor, so its Ψp stays at zero and it will lyse in anything much more dilute than its own cytoplasm.
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