Lectures for Plant Physiology
Fall 2000

Water Relations of Plant Cells and Tissues

In order to understand plant water relations, we have to understand some basic physical principles of water, and water vapor.

Vapor pressure is the partial pressure of water molecules in the gaseous state. Just as Henry's Law for partial pressures works for other gases, so it applies to water too. Thus, the more water in the air, the greater the vapor pressure that water exerts.

Pure water, if placed in a sealed container, will initially lose some water molecules by evaporation to the airspace above the liquid. Eventually though, the air will become saturated by water, at which point, the rate of evaporation from the surface will just equal the rate of condensation, and the amount of water in the air will remain constant.

When the air is completely saturated above pure water, we say that the air is at 100% relative humidity at that temperature. Relative humidity is defined as:

                %RH = The amount of water in the air*100/amount of water the air could hold at that temp.

The kinetic activity of the water in the liquid determines the number of water molecules that escape from the surface and go into the gaseous form. The higher the kinetic activity, the faster the rate at which water molecules evaporate. When substances are dissolved in the water, such as salt or sugar, they cause water molecules to lose kinetic energy, because they are attracted to charged sites on these ions and molecules, effectively immobilizing them, and keeping them from evaporating. This lowers the overall energy state of the water, and fewer molecules evaporate as a result.

This means that the same vapor pressure can not develop over a solution as compared to pure water. Thus, the vapor pressure over a solution will be lower than that over pure water, and hence the humidity too will be lower. This principle can be used to develop calibrations for humidity sensors, as various saturated salt solutions achieve defined humidities. For example, a saturated solution of LiCl yields a RH of about 15%, while NaCl gives a much higher humidity of 75% (See Table E-46 in the 56th Edition of the CRC Handbook of Physics and Chemistry for other values).

Now, if we were to take two containers of water, and separate them by a semi-permeable membrane (one that allows water to go through its pores, but not solutes like salt or sugar), and add sugar to one side, this would result in a lowering of the kinetic energy of the water-sugar solution. Thus, from a statistical-probability point of view, we would expect the molecules of pure water to encounter the membrane more often than the lower energy water molecules on the solution side, and thus, over time, water will move from the pure water to the solution. Of course some water molecules do go the other way, but the net exchange favors movement into the solution. This is known as osmosis. It is a special case of diffusion.

Thus, the solution will increase in volume, and become more diluted. Over time, this will slow the flux of water into the solution, but not stop it entirely. However, eventually, the weight of the water will exert a backpressure on the solution, which, if given enough time (and large enough container) will increase the pressure on the membrane and force water molecules to go back into the pure water. If the pressure is great enough, it can totally balance the number coming in, and the net flux of water will cease. The amount of pressure needed to totally balance the flows of water is known as the osmotic pressure and symbolized as with units of pressure (e.g., pounds per square inch, atmospheres, bars, Megapascals).

Diffusion - A Digression

Diffusion can be defined as the random movement of molecules from an area of high concentration to one of lower concentration. Note the emphasis on random. If pressure is used to move molecules, then the process is known as bulk flow. Fick's Law can be used to express diffusion: 

                                                                    J = - DaC

where       J is the flux of material crossing a unit area per unit time (i.e., moles m2 s-1)

                 D is the diffusion coefficient, a proportionality constant that is influenced by the medium in which the molecule
                            travels, and the molecule itself

                 a is the area over which the material passes,

                  l is the length over which the molecule diffuses, and

                 C is the difference in concentration between the two ends of the path

C is the true driving force for diffusion. If there is no difference, than this term is zero, and no diffusion takes place. The negative sign in the equation simply means that diffusion goes towards the region with lower concentration. C could apply to any gas, including water, and if water, then the difference is one of vapor pressures.

In summary, as Hopkins points out, diffusion is directly proportional to the diffusion coefficient, area, and C, and inversely proportional to the distance moved.

Diffusion can be applied to any solutes moving from high to low concentration, in almost any medium, including both air and water.

Digression into Pressure Units

Pressure is simply force per unit area, and in physics is expressed as Newtons / m2.

1 atmosphere = 14.7 lbs/in2 or 760 mm Hg or 1.013 x 105 N/m2

This is equivalent to the pressure of 10.35 meters of water.

In plant physiological work, we don't usually use the above units, but go metric, with either bars or megapascals (MPa).

1 bar = 14.5 lbs/in2 or 0.9869 atmospheres or 10.22 m of water.

1 Mpa = 10 bars or turned around, 0.1 Mpa = 1 bar

The more solutes that are dissolved in solution, the greater the osmotic pressure that can build up. V'ant Hoff, a chemist in the 18th century, discovered a mathematical relationship between moles of solute and osomotic pressure, known today as V'ant Hoff's Law:

                                                                 pi      =       nRT/V

where pi is the osmotic pressure (let's use bars for now)

          n is the number of moles of solute

         R is the gas constant (0.08314 liter bar mol-1 K-1)

         T is temperature in Kelvin (K) and

         V is the volume of solvent (i.e., water) (liters)

If you re-arrange the above equation, V = nRT/pi, you'll see it is strictly analogous to Boyle's Law, which you learned in chemistry, but now which applies to a liquid situation.

Suppose we dissolved 1 mole of ideal solute into 1000 g of water. What would be the osmotic pressure?  Assume a temperature of 1oC, or 274.16oK. At this temperature, 1 g of water is essentially 1 cm3, and 1000 cm3 is one liter.  Therefore:

                                      pi    =     (1)(0.08314)(274.16)/1 = 22.79 bars or 2.279 MPa

What if we use salt, NaCl, instead of an ideal solute? Then the osmotic pressure comes out to be 43.2 bars, not 22.79. Why?

Remember, NaCl dissolves into Na+ and Cl-, so one mole of solid salt yields two moles of ions!! Substitute n = 2 into the above equation, and you'll get 45.58 bars. This is slightly different from the actual 43.2, and is due to other physical factors which we'll not go into. Suffice it to say, if you want to know the exact osmotic pressure generated by a particular solute, you have to go to tables prepared by researchers who have documented the values exactly.

If you dissolve one mole of sugar into one liter of water, you also don't get 22.79 bars, but rather, something closer to 25.1 bars. Why again does this not match up with the predicted? Turns out sugar, especially glucose, has charges on it that result in a shell of 6 water molecules around the sugar, and this further lowers the kinetic energy of the water molecules, similar to adding more ideal solute. Thus sugar solutions result in higher than predicted osmotic pressures.

Chemical Potential of Water
In this section we shall derive the concept of water potential, a thermodynamic expression of the relative water status of a plant.  If you remember back to your introductory chemistry courses, you'll recall the concept of chemical potential. We can use that concept, and adapt it specifically to the situation involving water, to derive a measure of plant water status known as water potential.

Why derive this, when perhaps there are other, simpler ways to express plant water status? Let's go over those, and see why they don't work.

Plant Water Content
One way to express the water content of a plant is to simply weigh the plant, or plant organ, then dry it, and reweigh, and express the water status as percent water weight. But the problem with this is that plants vary in the amount of cell wall material, and other structural materials, such that two different plant species might contain the same water, but have different cell weights, which would lead us to think that their water status differed, when in fact, it might not.

Relative Water Content (RWC)
This is simply a refinement of the above method, but which standardizes water content to the maximum amount of water a plant or plant organ might hold. How is it measured? First, you obtain a plant weight, known as fresh weight. Then you hydrate a plant (put it in standing water, or water it thoroughly) to full turgor (this means it has taken up all the water it can) and you reweigh it. Then, you dry the plant completely, and get the dry weight. Then you express the amount of water in the plant as a percentage of the total amount of water the plant could take up:

                                       RWC (%)= (Fresh Wt. - Dry Wt.)*100/(Turgid Wt. - Dry Wt.)

Since the numerator is equivalent to the fresh water weight and the denominator to total water weight, the equation reduces to:

                                       RWC (%) = Fresh Water*100/Total Water

This works quite well within a particular species, but studies have shown it does not carry over among different species or the same species grown under different conditions. The problem again is that even relative water contents don't mean the same thing to different plants, or even to the same plant under different growth conditions. Thus, researchers in the middle part of this century began a search for an alternative water status parameter which could be applied across all plants, and all conditions. At a meeting of plant physiologists in the early 1960's it was suggested that thermodynamic properties should apply for all plants, and the concept of water potential, which is based in thermodynamics, was born.

Water Potential
The chemical potential of water can be defined as the free energy per mole of water. Chemical potential is, simply put, the potential for a substance to react or move, or in other words, to do work. Work results when a force applied on an object causes it to move from one location to another. Thus, if osmosis results in the movement of water from one location to another, then work has been done. This implies that the chemical potential must be different on either side of the membrane, or else there would have been no potential to do work in the first place. This also suggests that water moves from higher potential to lower potential. As an example, consider that if gravity causes water to run downhill, then gravity has lowered the chemical potential of that water. At the top of the hill, there is abundant potential energy, as the water is supported against the pull of gravity. But, if a gate is opened, and the water runs out, then that potential energy is converted to kinetic energy, and as that kinetic energy moves the water downhill the mean free energy of that water decreases until it reaches a lower stable energy level in the ocean or lake.

Chemical potential depends on the mean free energy of water, and the concentration of water molecules (which chemically is referred to as the mole fraction).

You already know that solutes act by (1) decreasing the mean free energy of water, and, (2) by decreasing the mole fraction of water (solutes take up room that otherwise would be occupied by water molecules, thus decreasing the density of water in solution).  Given this, pure water will have a higher chemical potential than will a solution. We can express this mathematically as the reduction in chemical potential between pure water and that of a solution:

                                                               µw = µwo + RTln(C)

where            µw is the chemical potential of a solution
                     µwo is the chemical potential of pure water
                     R is the gas constant
                     T is temperature in K
                     ln is the natural log symbol
                     C is the concentration of water

Normally, as your book explains, potential is expressed as a function of chemical activity (a), but for our purposes, we'll substitute concentration. They are closely related: a is approximately equivalent to C (see your book for more details). Taking the ln of a and multiplying it by RT (the right hand term in the equation above) converts chemical activity to energy per mole.

Simply put, the chemical potential of water is that of pure water plus the contribution (usually negative) of whatever solutes are dissolved in it.

We can add another term for the effect of pressure on chemical potential, VP, where V is the partial molal volume of water, or more simply, the volume occupied by 1 mole of water.  Since 1 liter of water (1000 g = 1000 cm3) is 55.5 moles, then V is 1000/55.5 = 18 ml/mole, or 18 cm3/mole.  P is the pressure. Since plants can develop significant pressures, we usually express P as the difference between atmospheric and that in the plant cells.  Now we can add the influence of pressure on chemical potential to our equation:

                                                                µw = µwo + RTln(C) + VP

If we substitute the value for osmotic pressure from the V'ant Hoff relationship into our chemical potential relationship, we can express the chemical potential as:

                                                               µw = µwo - piVw + VwP

Note here that we have substituted for RTlnC.  If we make the assumption that the activity coefficient for pure water is 1, then we see that the osmotic potential of pure water comes out to zero, since the ln of 1 is always zero.

Thus, the difference in chemical potential between pure water and a solution is due to its osmotic and pressure potentials.

To get to water potential, we will need to use relative values, since expressing the absolute chemical potential of water is difficult. Rearranging the above equation, we get:

                                                              w - µwo )/Vw   =     P - pi

 We use the symbol psi (here written as Y) to symbolize water potential, and therefore:

                                                             Y     =     P -pi

This is not a trivial usage.  It means we can measure the water status (or chemical potential of the water) of a plant by using pressure units, rather than trying to measure the actual energy it would take to move the water (remember, if water moves, energy is being expended).

Normally, we don't use osmotic pressure, but rather, osmotic potential, which is equal to osmotic pressure, but carries a negative sign (to indicate that it lowers the chemical potential of the solution).  Pressure potential is positive, since it tends to increase the potential a solution.

Water potential can be broken down into its components as:

                                                                                        Yw   =    Yo + Yp + Ym + g

where                            Yw is total water potential,
                                                 Yo is the osmotic potential,
                                     Yp is pressure potential,
                                    Ym is matric potential,
                                      g is the potential due to gravitational forces

We have already discussed osmotic and pressure potentials.  Matric potential is the lowering of water potential due to the adhesion of water molecules to other molecules on cell membranes.  For example, membranes often contain many negatively charged sites, and these will attract and "hold" the polar water molecules.  In most situations, the matric potential is small and can be ignored, since only a very small fraction of the total cellular water is affected by matric forces.  And for small plants, the contribution to total water potential from gravitational forces is also small (g works out to be -0.1 bar per meter height). Thus, for most purposes, total water potential can be defined from the contributions of just the osmotic and turgor components.