Chapter V — 51 — Mechanism of Osmosis 



Figure 15 reveals the following relationships existing among diffusion 



pressure deficit, turgor pressure, and osmotic pressure of an osmotic system : 



OP = DPD + TP (2) 



When TP = O, OP = DPD (state A) (i) 



And when DPD = O, OP = TP (state B) (4) 



At any point intermediate between the two limits indicated by equa- 

 tions (3) and (4) (state A and state B), the osmotic pressure is equalled 

 only by a summation of two lesser pressures — namely, the DPD and the 

 TP of the system at that particular state, as is indicated by equation (2). 



That any of the states of Figure 15 may be set up as equilibrium states 

 is illustrated by the following example. Referring to Figure 14 and as- 

 suming that solution S has an osmotic pressure of 10 atmospheres, state B 

 may be accomplished by applying a positive pressure of 10 atmospheres, 

 by means of piston P2 leaving P^ at atmospheric pressure as indicated 

 under 1 ) on page 49. State A may be accomplished by lowering the pres- 

 sure on W by means of Pi to the extent of 10 atmospheres leaving S at 

 atmospheric pressure (see 2, page 50). To visualize the intermediate 

 states, if Figure 14 is turned so that M is horizontal with S on top and 

 W below, (neglecting pressure due to gravitational force) by using a 

 total weight of 10 atmospheres, if it be divided into two of 5 atmospheres 

 each and one applied to P2 and the other hung on P^ then as equilibrium 

 is attained the situation illustrated by the state DPD ■=. TP or the midpoint 

 of Figure 15 is depicted. By dividing the total 10 atmosphere weight in 

 other ways, any of the innumerable possible states of Figure 15 may be 

 depicted. 



Other methods more comparable to those used in plant physiology may 

 be employed to bring about such equilibria. For instance, instead of hang- 

 ing weights on Pi it is possible to substitute solutions of equivalent DPD 

 values in place of W; gases containing water vapor of equivalent DPD 

 values could be used ; colloids of like water deficiencies would serve. 



In this analysis it should be emphasized that the concentration or osmotic 

 pressure of the solution is the constant characteristic that is unique ; it de- 

 termines the distance between the parallel lines A DP of solvent and A DP 

 of solute and so fixes the value of OP (or DPD -f TP). The total pres- 

 sure upon either or both phases at equilibrium as determined by the exter- 

 nal pressure may vary either above or below the values of one atmosphere 

 as indicated by the dotted extensions shown in Figure 15. In consider- 

 ing plant cell water relations, the concentration or the pressure of the ex- 

 ternal phase (comparable to W) may be of great importance as will become 

 evident in subsequent chapters. 



That the osmotic system of the plant may be described in terms of 

 standard physical units is evident from the following analysis. If A f is 

 defined as the partial specific free energy of the solvent in a solution, A fn 

 as the partial specific free energy of the solvent due to turgor pressure, and 

 A fo the partial specific free energy of the solvent due to osmotic pressure 

 (presence of solute), then 



A f = A fn + A fo (5) 



Transposing in (2) we have 



—DPD = —OP -f TP (<5) 



Af = V (—DPD) (7) 



Afo = V (-0P) (5) 



••■ A fjj = A f — A f^ = V (—DPD -I- OP) = V (TP) (9) 



Where V = specific volume. 



