108 VELOCITY OF REACTION. chap.
(This is quite evident if the walls consist of semi-permeable membranes which do not allow the sugar to pass through.) On the other hand, there is a proportionality between this number and the number of collisions of the sugar molecules with the active molecules of the inverting acid. As we shall see later, it is the hydrogen ions of the acid which must be considered. Now, since the concentration of the acid is constant during the experiment, the number of collisions between sugar molecules and acid molecules must be proportional to the osmotic pressure of the sugar. It has been assumed that the reaction only takes place when an acid molecule meets a molecule of sugar which can be attacked, and therefore we should take account only of the osmotic pressure of the sugar molecules in this condition. It is clear from what has previously been said (page 86), that if we denote the osmotic pressure of the ordinary sugar molecules by tt,, and that of the molecules which can be attacked by 7r„, then —
KtT,^ =r TT,. or— {K + l)7r« = TTi + TT,.
where iT is a constant, i.e. the osmotic partial pressure 7r« of the molecules which can be attacked stands in a constant ratio to the osmotic pressure iti + tt^ of all the sugar mole- cules. From this it follows that the number of collisions per second between active molecules of acid and attackable molecules of cane sugar is proportional to the osmotic pressure of the sugar. Furthermore, the velocity of the reaction, %,e, the quantity of substance transformed in unit time, must be proportional to the number of such collisions, and consequently to the osmotic pressure of the sugar — a conclusion which is confirmed by experiment.
It would appeal*, therefore, in calculations concerned mth the velocity of i*eaction to be more correct to use osmotic pressures and not concentrations, in the same way as has been pointed out for equilibria. The above example shows that using the former (theoretically more exact) method
�� �
