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AP Water Potential Math
Water potential is the measure of water’s potential energy or it’s ability to do work. Water potential quantifies
the tendency of water to move from one area to another due to osmosis, gravity, mechanical pressure, or matrix
effects such as capillary action (which is caused by surface tension).
Water potential integrates a variety of different potential drivers of water movement, which may operate in the
same or different directions. Within complex biological systems, it is common for many potential factors to be
important. For example, the addition of solutes to water lowers the water's potential (makes it more negative),
just as the increase in pressure increases its potential (makes it more positive). If there is no restriction on flow,
water will move from an area of higher water potential to an area that has a lower water potential.
Ψ = Ψ𝑠 + Ψ𝑝
Pressure potential is based on mechanical pressure, and is an important component of the total water potential
within plant cells. Pressure potential increases as water enters a cell. As water passes through the cell wall and
cell membrane, it increases the total amount of water present inside the cell, which exerts an outward pressure
that is opposed by the structural rigidity of the cell wall. By creating this pressure, the plant can maintain turgor,
which allows the plant to keep its rigidity. Without turgor, plants lose structure and wilt. The pressure potential in
a living plant cell is usually positive. In plasmolysed cells, pressure potential is almost zero. Negative pressure
potentials occur when water is pulled through an open system such as a plant xylem vessel. Withstanding
negative pressure potentials (frequently called tension) is an important adaptation of xylem.
Ψ𝑠 = −𝑖𝐶𝑅𝑇
Osmotic potential has important implications for many living organisms. If a living cell is surrounded by a more
concentrated solution, the cell will tend to lose water to the more negative water potential of the surrounding
environment. A soil solution also experiences osmotic potential. The osmotic potential is made possible due to the
presence of both inorganic and organic solutes in the soil solution. As water molecules increasingly clump around
solute ions or molecules, the freedom of movement, and thus the potential energy, of the water is lowered. As
the concentration of solutes is increased, the osmotic potential of the soil solution is reduced. Since water has a
tendency to move toward lower energy levels, water will want to travel toward the zone of higher solute
concentrations. Osmotic potential has an extreme influence on the rate of water uptake by plants.
a) addition of solutes on right side reduces water potential. S = -0.23. Water flows from hypotonic to
hypertonic or from high  on left to low  on right.
b) adding +0.23 pressure with plunger creates no net flow of water.
c) applying +0.30 pressure increases water potential solution now has  of +0.07. Water moves right to left
d) negative pressure or tension using plunger decreases water potential on the left. Water moves from right
to left
Helpful Hints
 Remember water always moves from [high] to [low].
 Water moves from hypotonic to hypertonic.
 [Solute] is related to osmotic pressure. Pressure is related to pressure potential.
 Pressure raises water potential.
 When working problems, use zero for pressure potential in animal cells & open beakers.
 1 bar of pressure = 1 atmosphere
Directions: Answer the following questions using the equations on the front page. Keep in mind that  is
measured in megapascals (MPa) and 1 Mpa = 10 atmospheres of pressure.
1. If a plant cell’s P = 2 bars and its S = -3.5 bars, what is the resulting ?
a. The plant cell from question 1 is placed in a beaker of sugar water with S = -4.0 bars. In which
direction will the net flow of water be?
b. The original cell from question 1 is placed in a beaker of sugar water with S = -0.15MPa
(megapascals). We know that 1 MPa = 10 bars. In which direction will the net flow of water be?
2. The value for  in root tissue was found to be -3.3 bars. If you place the root tissue in a 0.1 M solution of
sucrose at 20°C in an open beaker, what is the  of the solution, and in which direction would the net flow of
water be?
a. NaCl dissociates into 2 particles in water: Na+ and Cl-. If the solution in question 2 contained 0.1 M
NaCl instead of 0.1 M sucrose, what is the  of the solution, and in which direction would the net
flow of water be?
3. A plant cell with a s of -7.5 bars keeps a constant volume when immersed in an open-beaker solution that
has a s of -4 bars. What is the cell’s P?
4. At 20°C, a plant cell containing 0.6 M glucose is in equilibrium with its surrounding solution containing 0.5 M
glucose in an open container. What is the cell’s P?