Chapter VII — 17 — Osmotic Quantities of Cells 



where 



f = partial molal free energy of water in the given state, in ergs; 



i° r= molal free energy in its standard state, in ergs; 

 V° =: the molal volume of water in its standard state, in liters; 

 po = the pressure on the water in its standard or reference state, in atmospheres; 

 p = the pressure on the medium in the given state, necessary to make f equal to f°, in atmos- 

 pheres. 



The osmotic "solute" specific free energy is therefore equal to the change in free 

 energy brought about by the formation of the solution (addition of solute to solvent). 

 In the state as defined, the free energy change due to solute is equal in magnitude to 

 the DPD of water in the solution at the reference pressure, or to the TP of the system 

 at water equilibrium, both of which are numerically equal to the osmotic pressure as 

 indicated by Figure 15 of Chapter V. As with diffusion pressures, free energies are 

 not determined; only the differences between the given and some arbitrarily chosen 

 standard state are considered. 



Another system is that employed by Brooks and Brooks (1941). The terms and 

 concepts selected to explain movement of water and solutes are fugacity and activity. 

 Fugacity (f) is defined as a corrected vapor pressure, corrected for deviation from 

 ideal gas behavior. Activity (a) is defined as a corrected concentration, and propor- 

 tional to a fugacity ratio, a =: -t^, where f° is the fugacity in an arbitrarily chosen 



standard state. The close connection between these two quantities is apparent, since 

 both are functions of partial molal free energy of a constituent in a solution, and from 

 the fact that both are used as measures of what is qualitatively termed the "escaping 

 tendency." By definition f° may be set equal to one, whereupon the activity numerically 

 equals the fugacity. 



The use of "fugacity gradients," "activity gradients," "escaping tendency gradi- 

 ents," in explanations of water and solute movement in osmotic phenomena, is sound, 

 and the concepts which these terms represent are essential in a clear understanding of 

 the problems. 



In addition to the above terms. Brooks and Brooks use osmotic pressure, but 

 they have given it a meaning different than that used in this volume (cf. Chapter V), 

 tending to identify osmotic pressure gradients with activity gradients (1941, p. 6, 32). 

 In animal cells, where there is little or no effect of turgor on the activity of water in 

 the cell, this may be justified. But the significant turgor in plant cells requires a clear 

 distinction between these two quantities. Osmotic pressure, in our usage, is not a 

 function of pressure, except to the extent that concentrations may be altered. Activity 

 is a definite function of pressure. 



There is much to be said for the adoption by physiologists of the terminology of 

 physical chemistry. It would have a unifying eifect and would provide a series of 

 accurately defined units for expressing quantitative results. On the other hand, since 

 the methods of measurement remain the same and the same numerical values must be 

 relied upon, no new or more accurate information is acquired. Measurement of the 

 forces involved in movement and retention of water by plants does not submit to highly 

 accurate methods and certain qualitative aspects such as the health and vigor of tissues 

 do not come within the scope of physico-chemical determination. There are many 

 plant functions that cannot yet be measured by physical or chemical methods. 



Furthermore, compared with the OP = TP -f- DPD system, the physico-chemical 

 terminology is not more simple. The concept of DPD which is now accepted by many 

 plant physiologists (Meyer, 1945) is represented, at least partially, in the terms net 

 influx specific free energy, activity gradient, fugacity gradient, and escaping tendency 

 gradient. And, finally, in view of the inadequate preparation of undergraduate stu- 

 dents in biology, it may be premature to attempt a thermodynamic treatment of biologi- 

 cal systems, except at the graduate level. 



Membranes and Permeability: — In order that the osmotic pressure 

 of a solution may find expression as turgor, there must be a membrane 

 having differential properties in the osmotic system. Ideally a differentially 

 permeable membrane is one that allows the passage of solvent but not of 

 solute. In the living cell this role is largely played by the protoplasm, which 

 is relatively permeable to water, but much less permeable to solutes. The 

 selective capacity of the cell is believed due, more specifically, to two 



