 W  S  P  g How do we express  S,  P, &  g in units of pressure?  S, the solute pressure or solute potential.  S = -RTC S Where R is the gas constant, T is Kelvin temp., and C S is the solute concentration. R = MPa liters o K -1 mol -1 C s = mol liter -1 Bottom line: adding solutes to water decreases the solute potential.

 S = -RTC S What is the solute (osmotic) potential of sea water? assume 25 o C or 298 o K C S = 1.15 mole liter -1 of Na + + Cl - + other ions  S = ( MPa liter o K -1 mol -1 )(298 o K)(1.15 mol liter -1 )  S = MPa

 W  S  P  g The pressure potential  P is just what we would measure with a pressure gauge.

 W  S  P  g 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 10 5 Pa or 0.98 MPa So, to hold water at that height, there must be a counteracting negative pressure of at least MPa in the xylem

What do various values of  W mean for plant function?

How do changes in the components of  w affect others and the total value of  w ?

Turgor of living cells changes depending on solute concentration and total water potential. Plants can regulate turgor by “osmotic adjustment”, i.e. changing the solute concentration of cells.

Reducing cell volume concentrates solutes and reduces  S.

Water potential gradient tells us which direction water will move, but how do we understand how rapidly water or other molecules move along their concentration gradients?

Back to diffusion - net movement of molecules from regions of higher concentration to lower concentration. Diffusive flux = diffusion coefficient x concentration gradient J = -D s  C s /  x Fick’s first law J is flux rate, moles per m 2  C s /  x is the concentration gradient, moles m -3 /m D s is the diffusion coefficient, m 2 s -1

Values of D depend on the type of molecule and the medium Larger, heavier molecules have lower D. D values are higher in air than water D CO2 in air = 1.51 x m 2 s -1 D O2 in air = 1.95 x m 2 s -1 D H2O in air = 2.42 x m 2 s lower in water!

How effective is diffusion for transport across membranes? from roots to leaves? Diffusion time = L 2 /D s Double the distance means 4X the time. Compare 50µm membrane to 1 m long corn leaf D glu in water is m 2 s -1 (50 x m) 2 /10 -9 m 2 s -1 = 2.5 seconds!

(1 m) 2 /10 -9 m 2 s -1 = 10 9 seconds About 32 years! So how does water move long distances through plants? Bulk flow

Let’s build an equation that describes the various influences on the rate of liquid moving through a straw. “Volume flow rate” m 3 s -1 =

Hagen - Poiseuille Equation m 3 s -1 =  r 4  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