Ψ = Ψp + Ψs

Calculating osmosis

What is it?

A measure of the tendency of water to LEAVE a cell, system or solution when pressured by either concentration OR literal pressure.

It helps explain, for example, why water leaves the soil and enters root cells of plants.

A review of Osmosis

The Amoeba sisters share all.

Remember: osmosis is the diffusion of water.

Water will move across a membrane to reach equilibrium (homeostasis) if solutes cannot or do not diffuse.

remember…osmosis occurs when the 2 solutions

differ in osmotic pressure

same osmolarity**

isoosmotic

NO net movement of water

differ in osmolarity**

greater

solute

concentration

more

dilute

net flow of water

hyperosmotic hypoosmotic

**moles solute/L solution

Dialysis Tubing Experiment

Water Balance

Osmoregulation~ control of water balance

Hypertonic~ higher concentration of solutes

Hypotonic~ lower concentration of solutes

Isotonic~ equal concentrations of solutes

Cells with Walls:

Turgid (very firm)

Flaccid (limp)

Plasmolysis~ plasma membrane pulls away from cell wall

Osmosis = the movement of water molecules from a region of higher water potential to a region of lower water potential through a partially permeable membrane. Osmosis is considered in terms of water potential and solute potential.

The greek symbol for Water Potential, Ψ, is the letter ‘psi’

(pronounced ‘psee’).

Several forces act on water to alter its ability or potential to

do work. The forces measured for water potential are

pressure and concentration.

Added together they make up the Water Potential.

Water Potential = Pressure + Concentration

Water Potential or Ψ

Water Potential Defined as: the measure of the kinetic (free)

energy of water molecules.

Water molecules are constantly moving in a random fashion.

The concepts of free energy and water potential are derived from the second law of thermodynamics.

In thermodynamics, free energy is defined as the potential for performing work. Example: The water at the top of the fall has a higher potential for performing work than the water at the base of the fall. The water is moving from an area of higher free energy to an area of lower free energy. The free energy from water is the power source for waterwheels and hydroelectric facilities.

If this makes no sense whatsoever the key information to learn is: the equations

the water potential of pure water is zero

water moves from areas of higher water potential to areas of lower water potential (i.e. towards the more negative region)

Ψ = Ψs + Ψp

Water potential is determined by the combined effect

of solute concentration and physical pressure .

Water potential is calculated using the formula:

Water moves from regions of high water potential to regions of low water potential.

Water Potential in Cells

higher water potential

lower water potential

higher solute concentration

lower solute concentration

Calculating Water Potential Pressure potential (ΨP ): In a plant cell, pressure is

exerted by water pressing on the rigid cell wall.

Solute potential (ΨS ): The effect of solute concentration.

Ψ = Ψp + Ψs

Ψ is measured in megapascals (MPa) 1 MPa = 10 atm of pressure Ψ for pure water is 0

Some Basic Principles

Water moves spontaneously from places of higher water potential to places of lower water potential

Between points of equal water potential, there is no net water movement

Water potential values are ususally negative

Ψw is increased by an increase in pressure potential (ΨP)

Ψw is decreased by addition of solutes which lowers the solute potential (ΨS )

Water Potential, Ψ Ψ is measured in units of pressure

Pure water at standard temperature and pressure has a Ψ of zero

The addition of solutes to water lowers its Ψ (makes it more negative), just as an increase in pressure makes it more positive

Water will move from higher Ψ to lower Ψ

Ψp -- pressure potential

Ψp is the physical pressure on the system

Ψp can be negative – transpiration in the xylem tissue of a

plant (water tension)

Ψp can be positive – water in living plant cells is under

positive pressure (turgid)

measure of the kinetic energy of water molecules. Water molecules are constantly moving in a random fashion. Some of them collide with cell membrane/cell wall, creating pressure. The higher their kinetic energy, the more they move, the higher the pressure.

Pressure Potential in plant cells.

• Turgor pressure – forced

caused by cell membrane

pushing against cell wall.

• Wall pressure – an equal and

opposite force exerted by cell

wall. Counteracts the

movement of water due to

osmosis.

• Other pressures – tension,

cohesion, atmospheric, root,

etc.

Ψs - solute (osmotic) potential

• Remember: pure water has a solute potential (Ψs) of zero.

• Solute potential can never be positive.

• Adding more solute is a negative experience! the solute potential becomes negative.

calculate solute potential using the following formula:

solute potential (ΨS ) = –iCRT

• i = The ionization constant • for NaCl this would be 2;

• for sucrose or glucose, this number is 1

• C = Molar concentration – Iso-osmolar molarity: would allow you to place a potato in the solution and get

no movement of water. – Point at which the line crosses 0 on the graph.

• R = Pressure constant = 0.0831 liter bar/mole K

• T = Temperature in Kelvin = 273 + °C of solution

Which way will water flow?

Adding solute lowers the water potential. When a solution is enclosed by a

rigid cell wall, the movement of water into the cell will exert pressure on the

cell wall. This increase in pressure within the cell will raise the water

potential.

In summary •Higher water potential (+Value):

- lower solute concentration

- more water

- (hypotonic)

•Zero (0) Value:

- Pure water

•Lower water potential (-Value):

- higher solute concentration

- less water

- (hypertonic)

****Water will move across a membrane in

the direction of the lower water

potential****

Water moves from higher Ψ to lower Ψ

The addition of solutes lowers Ψ

Increasing pressure raises Ψ

In essence, Ψ measures the ability of soil water

to move (into or out of the plant)

Low osmotic concentration = high Ψ

High osmotic concentration = low Ψ

sample problems:

Practice Problem

• The molar concentration of a sugar solution in

an open beaker has been determined to be

0.3M. Calculate the solute potential at 27

degrees. Round your answer to the nearest

hundredth.

s = - iCRT

-(1)(0.3mol)(0.0821 L · bar )(300K)

L mol · K

s = - 7.39

• The pressure potential of a solution open to the

air is zero. Since you know the solute potential

of the solution, you can now calculate the

water potential.

• What is the water potential for this example?

Round your answer to the nearest hundredth.

w = - 7.39 0.30 M

sugar

A solution in a beaker has sucrose dissolved in

water with a solute potential of -0.7MPa. A flaccid

cell is placed in the above beaker with a solute

potential of -0.3 bars.

a) What is the pressure potential of the flaccid cell

before it was placed in the beaker?

b) What is the water potential of the cell before it

was placed in the beaker?

p = 0

w = p + s

w = 0 + -0.3 = -0.3 bars

c) What is the water potential in the beaker

containing the sucrose?

d) Which direction will the water move?

e) Initially, is the cell hypotonic or hypertonic with

respect to the solution in the beaker?

f) If it is hypo/hyper (choose one) tonic – this

means that its water potential is higher/lower

than the outside.

-0.7MPa

Out of the cell.

A solution in a beaker has sucrose dissolved in

water with a solute potential of -0.5 bars. A cell is

placed in the above beaker with a solute potential

of -0.9 bars.

a) What is the water potential of the cell before it was

placed in the beaker?

c) What is the water potential in the beaker containing the

sucrose?

s = - 0.5

s = - 0.9

w= - 0.9

w = - 0.5

d) Which direction will water move?

e) What is the pressure potential of the plant cell

when it is in equilibrium with the sucrose

solution outside? Also, what is its final water

potential when it is in equilibrium?

f) Is the cell now turgid/flaccid/plasmolysed?

s = - 0.5

s = - 0.9

-0.5 = p + -0.9

Ψp = +0.4 MPa w = -0.5 w = p + s

shipwrecked sailor

• % Change in Mass: Final – initial x 100

initial

• Look at your data on the graph.

• approximate the % solute (NaCl)

concentration of the potato cores.

How???

In theory, it is the potato cores with no net

weight gain that gives us our estimate of

the water potential of the potato cells. As

much water is moving into the potato

cores, as is moving out.

w(cells) w(soln)

Water is in

equilibrium

***Where your line crosses the “0” mark

Analyze the results of your sweet potato experiment:

Based on your data, which cores were in the

• Isotonic solution?

• Hypotonic?

• Hypertonic?

Describe the data (evidence) that supports this.

Solute Potential = -iCRT i = ionization constant (glucose = 1) C = molar concentration R = pressure constant (0.0831 liters bars / mol) T = temperature in Kelvin (Celsius + 273)

Plugging in the information we know, the formula becomes -iCRT = (1)(C)(0.0831)(22 + 273) = (C)(0.0831)(295) = (C)(0.0831)(295) = 24.5145(C)

Blue. 24.5145(C) = 24.5145 (1.0 M) = 24.5145 Green 24.5145(C) = 24.5145 (0.2 M) = 4.9029 Red 24.5145(C) = 24.5145 (0.6 M) = 14.7087 Purple 24.5145(C) = 24.5145 (0.4 M) = 9.8058 Yellow 24.5145(C) = 24.5145 (0 M) = 0 Clear 24.5145(C) = 24.5145 (0.8 M) = 19.6116

How can you use your knowledge of water potential to

calculate the concentration of sugars in sweet potato cells?

or how water is transported in plants

Scientists use water potential measurements to determine drought tolerance in plants, the irrigation needs of different crops and how the water status of a plant affects the quality and yield of plants.

Plant Transport How does water get from the

roots of a tree to its top?

Plants lack the muscle tissue and circulatory system found in animals, but still have to pump fluid throughout the plant’s body

Water movement (transport) occurs at three levels:

Cellular Lateral transport (short-distance) Whole plant (long-distance)

Plant Transport Heartwood is the xylem that

has died; much darker

Sapwood is the younger, outermost wood that has not yet become heartwood; conducts water from the roots to the leaves, and to store

Plant Transport Water first enters the roots and

then moves to the xylem, the innermost vascular tissue

Plants need water

As a starting product for photosynthesis

As a solvent to dissolve chemicals

For support

To ‘pay’ for water lost by transpiration

Plant Transport: Cellular level Diffusion – Plays a major role in bulk water transport,

but over short distances

Although water diffuses through cell membranes, ions and organic compounds rely on membrane-bound (protein) transporters and active transport.

Hypertonic solution =

flaccid

Hypotonic solution = turgid

Unlike animal cells, plants have cell walls and

this affects osmosis.

If a plant cell is placed into water (a hypotonic condition for the cell - the concentration of solutes inside the cell is greater than that of the external solution) water will move into the cell by osmosis

The cell expands and presses against the cell wall, a condition known as turgid (swollen), due to the cell’s increased turgor pressure

+Ψp

Typical Water Potential Values

• Outside air (50% humidity): -100 MPa

• Outside air (90% humidity): -13 MPa

• Leaf Tissue: -1.5 MPa

• Stem: -0.7 MPa

• Root: -0.4 MPa

• Soil water: -0.1 MPa

• Hydrated soil (Saturated) +2 - +5 MPa

** When the soil is extremely dry what happens to the

water potential and water movement into the plant?

**Does the value become more negative or more positive?

Water transport – whole plant

Water potential of the soil is negative, but not as negative as the cell, due to the high content of solutes

Root hairs are almost always turgid, because their water potential is greater than that of the surrounding soil

Collectively, have enormous surface area

Water moves from high to low water potential – into the roots

Water then moves along

gradients of successively

more negative water

potentials in the stems,

leaves and air

Evaporation of water in a leaf

creates a negative pressure

(negative water potential) in

the xylem, which literally pulls

water up the stem from the

roots.

Xylem Xylem sap brings minerals to leaves and water to

replace what is lost by transpiration

Moves at rates of 15 meters/hour; travels vertically up distances of 100 meters in the tallest trees

At night, when transpiration is low or absent, root pressure caused by the accumulation of ions in the roots, causes more water to enter the root hair cells by osmosis

Under certain conditions, root pressure is so

strong that water will ooze out of a cut plant

stem for hours or even days

When root pressure is very high, it can force water

up to the leaves, where it may be lost (guttation)

Guttation produces what is more commonly called

dew on leaves