156 PRINCIPLES OF GENERAL PHYSIOLOGY 



molecular concentration. For further details, the reader is referred to the paper 

 by Timmermans (1907), and for the application to urine, the paper by Atkins and 

 Wallace (1913). 



OSMOTIC WORK AND VOLUME ENERGY 



In order to increase the osmotic pressure of a solution requires tin- 

 performance of work just as the compression of a gas does. The amount of 

 work depends, of course, on the volume of the solution compressed as well 

 as on the pressure to which it is raised. It is, just as in the case of a gas, 

 as described on page 33 above, equal to 



RT log, & 

 Pi 



for one gram molecule, where p l and j 2 are the lower and higher pressures 

 respectively ; and n times this quantity for n gram-molecules. 



The osmotic pressure of a solution can be raised by removal of part of 

 the solvent in any manner, and it follows, from the second law of energetics, 

 that the work done is identical in all cases (Nernst, 1911, p. 19), provided 

 that the process is isothermal. Suppose that a part of the solvent is removed 

 by evaporation, it can be shown by a simple process, details of which will be 

 found in the book by Nernst (1911, pp. 132-135), that the work done is also 

 expressed by the formula 



where m is the molecular weight of the solvent, the specific gravity of the 

 solution, and P the osmotic pressure of the solution. 



The foundation of the general theory can best be grasped by the following 

 imaginary model, based on the considerations of van't Hoff(1887). In a vessel, W 

 (Fig. 50), containing a solution, S, is a cylinder, C, closed below by a membrane, 

 impermeable to the solute, permeable to the solvent. The cylinder contains 

 a more concentrated solution of the same substance, and is fitted with 

 a movable piston on which weights can be placed so that the osmotic pressure 

 due to the difference in concentration of the two solutions is balanced and 

 the system is in equilibrium. A further weight is then placed on the piston ; 

 the result is that water is driven out through the membrane, so that the osmotic 

 pressure is raised. In doing this, the weight falls through a certain height, thus 

 doing a definite amount of work on the solution. If the added weight is 

 removed again, water will enter, raising the original weight and so doing 

 external work. We see thus that solutions, like gases, possess volume energy, 

 which can be taken in or given out. 



An important physiological application of this fact is that, when a secretion, 

 such as urine, is formed at a higher osmotic pressure than the blood, work must 

 be done, and that the work can be calculated. 



OSMOTIC PRESSURE AND VELOCITY OF REACTIONS 



In the inversion of cane-sugar by acid, when concentrated solutions are taken, 

 the rate is found to be not in accordance with the law of mass action, " that 

 the rate of change is proportional to the active mass of the substance taking 

 part in the reaction." That is, if we understand by "active mass" the actual 

 concentration in gram-molecules per litre. But Arrhenius has shown (1899) that, 

 if we substitute for " active mass," in the above statement, the words " osmotic 

 pressure," the experimental results agree with the law. As Mellor (1904, p. 283) 

 puts it : " The osmotic pressure of cane-sugar in solution, kept at a constant 

 temperature, is proportional to the number of collisions of the sugar molecule 

 with the ' semi-permeable ' wall of the containing vessel. Again, the amount 

 of sugar inverted in unit time will be proportional to the number of collisions 

 of the sugar molecule with the molecules, or rather the ions, of the acid. But 



