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How do we express S, P, & g in units of pressure?

S, the solute pressure or solute potential.

S = -RTCS

Where R is the gas constant, T is Kelvin temp.,and CS is the solute concentration.

R = 0.008314 MPa liters oK-1 mol-1

Cs = mol liter-1

Bottom line: adding solutes to water decreases the solute

potential.

S = -RTCS

What is the solute (osmotic) potential of sea water?assume 25 oC or 298 oK

CS = 1.15 mole liter-1 of Na+ + Cl- + other ions

S = (-0.008314MPa liter oK-1 mol-1)(298oK)(1.15 mol liter-1)

S = -2.84 MPa

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The pressure potential P is just what we wouldmeasure with a pressure gauge.

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How do we calculate the gravitational potential?

g = gh

g = density x g x height

Dimensional analysis= density x g x height= kg m-3 x m s-2 x m= force and 1/area in there?= N m-2

= Pa

Example: what is gravitational potential of water at 100 m in a tree?

g = 1000 kg m-3 x 9.8 m s-2 x 100m

= 9.8 x 105 Pa or 0.98 MPa

So, to hold water at that height, there must be a counteracting negative pressure of at least -0.98 MPa in the xylem

What do various values of W mean for plant function?

How do changes in the components of w affectothers and the total value of w?

Turgor of living cells changes depending on soluteconcentration and total water potential.

Plants can regulate turgor by “osmotic adjustment”,i.e. changing the solute concentration of cells.

Reducing cell volume concentrates solutesand reduces S.

Water potential gradient tells us which directionwater will move, but how do we understand how rapidlywater or other molecules move along their concentrationgradients?

Back to diffusion - net movement of molecules fromregions of higher concentration to lower concentration.

Diffusive flux = diffusion coefficient x concentration gradient

J = -Ds Cs/x Fick’s first law

J is flux rate, moles per m2

Cs/x is the concentration gradient, moles m-3/mDs is the diffusion coefficient, m2 s-1

Values of D depend on the type of moleculeand the medium

Larger, heavier molecules have lower D.

D values are higher in air than water

DCO2 in air = 1.51 x 10-5 m2 s-1

DO2 in air = 1.95 x 10-5 m2 s-1

DH2O in air = 2.42 x 10-5 m2 s-1

10-4 l

ower i

n wate

r!

How effective is diffusion for transport

• across membranes?•from roots to leaves?

Diffusion time = L2/Ds

Double the distance means 4X the time.

Compare 50µm membrane to 1 m long corn leaf

Dglu in water is 10-9 m2 s-1

(50 x 10-6m)2/10-9 m2 s-1 = 2.5 seconds!

(1 m)2/10-9 m2 s-1 = 109 seconds

About 32 years!

So how does water move long distances through plants?

Bulk flow

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Bulk flow

Let’s build an equation that describes the various influences on the rate of liquid moving through a straw.

“Volume flow rate”

m3 s-1 =

Hagen - Poiseuille Equation

m3 s-1 = r4 P

8 x

Water flow in xylem “pipes”

Pressure gradients

Diameter of tracheids or vessel elements

The viscosity of xylem fluid - does it vary?

Conductive Vessel Element in Mountain Mahogany Wood (SEM x750). This image is copyright Dennis Kunkel at www.DennisKunkel.com