40 LIBERATION OF ENERGY 



permeable membranes— that is, membranes whieh would allow 

 free passage to one gas but not to another. What will happen 

 in such a case ? Suppose B can pass freely through the septum 

 while A cannot. Both gases are at 1 atmos. pressure. Then 

 B will diffuse through the membrane, and fill up the next space 

 as if A were not there, i.e. there will finally be | atmos. of B on 

 both sides. The total pressure on A wdll be 1| atmos. The 

 excess of pressure is due to the gas A, which cannot pass through 

 the septum. So that by taking the difference of pressure on the 

 two sides of a semi-permeable membrane, we obtain the partial 

 pressure of the gas to which the membrane is impermeable. (See 

 Respiration, Chap. XXIV.) 



An attempt may now be made to apply these laws (which are 

 only absolutely true for perfect gases) to dilute solutions. 



PV= RT 



All these symbols seem applicable to a substance in solution 

 except P. What is the pressure of a solute ? This may be 

 determined in a way similar to the determination of gaseous 

 pressure. If an osmometer be fitted up (Fig. 5) (Part II. p. 511) 

 with a solution of sugar inside and water outside, in a short time 

 the fluid inside will increase in volume and will rise in the osmo- 

 meter tube developing a hydrostatic pressure. To what is this 

 pressure due ? Obviously water (and pressure) will be transferred 

 from a point where its pressure is high to a point where its pres- 

 sure is low. In some way or other the presence of sugar (or other 

 solute) has lowered the pressure of the water. Can this be 

 explained by reference to the kinetic energy ? Reasoning back- 

 wards, it may be argued that the sugar acts as a drag upon the 

 water molecules — that is, the bombardment of the membrane 

 becomes unbalanced. The pure solvent is able to exert a greater 

 pressure than the solution. Experiment has shown that for simple 

 dilute solutions the magnitude of the osmotic pressure depends on 

 the molecular weight of the substance dissolved, the amoimt of 

 substance in the solute per unit volimie and on the temperature of 

 the solution. That is, osmotic pressure is controlled by just those 

 factors which control gaseous pressure. It might be stated that 

 in a simple solution the osmotic pressure of a substance ivould be 

 numericcdly equal to the gaseous pressure which the substance would 

 exert were it a gas occupying the same volume as the solution. 



Now we have seen that the variables connected with gaseous 

 pressure are T and V. As, according to Avogadro's hypothesis, 

 equal volumes of gases under equal T and P contain the same 

 number of molecules, we may state that, if T is kept constant, 



