Water Potential in AP Biology

Running ψs = −iCRT on a beaker of sucrose

Say you drop potato cores into an open beaker of 0.2 M sucrose at 22°C. To predict whether the cores gain or lose water, you first need the solution's water potential, and that starts with solute potential: ψs = −iCRT.

Plug in the pieces. The ionization constant i is 1 for sucrose because it doesn't split into ions. C is the molar concentration, 0.2 mol/L. R is the pressure constant, 0.0831 L·bars/mol·K. T is temperature in Kelvin, so 22 + 273 = 295 K. That gives ψs = −(1)(0.2)(0.0831)(295) = −4.9 bars.

The beaker is open to the air, so pressure potential is 0 and ψ = −4.9 bars. If the potato cells sit at −3.5 bars, water moves out of the cells (higher, less negative) into the solution (lower, more negative), and the cores lose mass.

Now swap in 0.1 M NaCl. Because NaCl splits into Na⁺ and Cl⁻, i = 2, and the answer comes out to the same −4.9 bars. Half the molarity gives the same solute potential, which is exactly why forgetting i wrecks the calculation.

How pressure potential lets a plant cell stop gaining water

Solute potential is only half the equation. In a plant cell, water flows into the central vacuole, the vacuole swells, and the cell membrane presses against the cell wall. The wall pushes back, creating turgor pressure, which is a positive ψp.

That positive pressure raises the cell's total water potential. Net water entry stops once ψ inside equals ψ outside, even though the cell still has a higher solute concentration than pure water. This is how a plant cell in a hypotonic solution ends up firm instead of bursting.

Some freshwater protists, such as Paramecium, lack a cell wall that could provide the same resistance to swelling. Water keeps entering from the hypotonic pond, so Paramecium uses a contractile vacuole to collect and expel the excess water. The two make a good contrast for water balance: one cell copes by building pressure, the other by actively pumping water back out.

Active transport sets up the gradient that water follows

A potato core losing water in sucrose spends no ATP doing it. Osmosis itself is passive: water moves down its water potential gradient, often through aquaporins. That puts water potential in Unit 2: Cells, alongside tonicity, osmoregulation, and the mechanisms cells use to move substances across membranes, including which movements cost energy.

The gradient doesn't always appear on its own, though. Cells use ATP-powered pumps such as the Na⁺/K⁺ ATPase to build and maintain ion concentration differences across the membrane. Changing solute concentrations changes ψs, so active transport of ions can set up the water potential difference that water then follows passively. Plant root cells, for example, actively take up mineral ions, which lowers their water potential and draws water in.

This also ties back to osmoregulation and tonicity. When pressure potentials on both sides are equal, "water moves from hypotonic to hypertonic," "water moves from low to high solute concentration," and "water moves from high to low water potential" all predict the same direction. When pressure differs, as in a turgid plant cell, the first two rules can mislead you, so compare total water potentials instead.

Potato cores, U-tubes, and the free-response tasks that use them

A typical item lists ψs and ψp for a cell and its surroundings and asks which way water moves. Another hands you a concentration and temperature and asks for ψs from −iCRT. Both show up in multiple choice, and a calculator is allowed on both sections.

On Question 2 (Interpreting and Evaluating Experimental Results with Graphing), the classic setup is the potato-core data: percent change in mass at several sucrose concentrations. A strong answer graphs concentration on the x-axis and percent mass change on the y-axis, then finds where the line crosses zero. That concentration marks approximately no net water movement, meaning the solution's water potential roughly matches the cells' total water potential. Because the open beaker has a ψp of 0, you can plug that concentration into ψs = −iCRT, and the solution's ψs gives an estimate of the cells' water potential. A matching null hypothesis is that sucrose concentration has no effect on the change in mass.

Question 5 (Analyze Model or Visual Representation of a Biological Concept or Process) can show a U-tube split by a selectively permeable membrane. To predict which side rises, compare water potentials and justify with the direction rule. On Question 4 (Conceptual Analysis), a disruption like blocked aquaporins slows the rate of water movement but doesn't change its direction, because direction depends only on the water potential difference.

Sign and unit errors that flip the direction of water

Most wrong answers on water potential come from a few slips.

• Reading "higher" as the bigger number. Water potential of −2 bars is higher than −6 bars, so water moves from −2 toward −6.
• Dropping the negative sign in −iCRT. Solute potential is always zero or negative, and more solute makes it more negative.
• Using degrees Celsius for T instead of Kelvin.
• Setting i = 1 for a salt. NaCl dissociates into two ions, so i = 2.
• Predicting water movement from ψs alone when ψp isn't zero. A turgid plant cell can have a very negative ψs and still have a total ψ equal to its surroundings.