208 THE HYDROLYZING ENZYMES 



The velocity of hydrolysis is proportional, at every instant, to the 

 concentration of that portion of the sugar which is actually undergoing 

 hydrolysis, i. e., the sugar-acid compound, and so we have: 



Velocity of hydrolysis = constant X concentration of sugar-acid compound. 



Combining the two equations we find that : 



Velocity of hydrolysis = k X concentration of acid X concentration of sugar. 



For any given concentration of acid, therefore, since the acid is not 

 consumed at all during the reaction, we have : 



Velocity of hydrolysis = k(a x) 



where (a x) is the concentration of unhydrolyzed sugar at any instant. 



The case would be very different, however, if more than a trace of 

 the catalyst were combined with the sugar. Suppose, for example, that 

 in the early stages of the reaction, all of the catalyst were combined 

 with the sugar; then, so long as there were enough sugar present to 

 combine with all of the catalyst the amount of the catalyst-sugar 

 compound would always be the same, namely the chemical equivalent 

 of the amount of the catalyst in the mixture. But since this is the 

 only portion of the sugar which hydrolyzes at any measurable rate, the 

 velocity of hydrolysis would in that event be constant. 



This will, of course, only hold good so long as the sugar which is 

 still unconverted is sufficient to combine with all of the catalyzer. 

 As the reaction proceeds, however, a point will be reached at which 

 the amount of sugar is insufficient to bind all of the catalyzer. After 

 this point in the reaction is reached, the amount of the catalyst bound 

 by the sugar, and therefore the velocity of hydrolysis of the sugar, will 

 become progressively less as the conversion proceeds. In fact it will 

 obviously be equal to the quantity of sugar which is still unconverted, 

 and again we shall have the relationship: 



Velocity of hydrolysis = k X concentration of unhydrolyzed sugar 

 for any given proportion of acid present in the mixture. 



These complications, as has been implied above, are not observed 

 during the hydrolysis of cane-sugar by acids because the proportion of 

 acid which is at any instant bound by the sugar is so small that it has 

 not as yet been quantitatively estimated. But when Invertase is the 

 catalyst instead 'of acid, we meet with precisely the conditions which 

 we have outlined. When the proportion of sugar to invertase is high, 

 all of the invertase is bound by the sugar, and the portion of the sugar 

 which is thus combined is the only portion which undergoes hydrolysis 

 at a perceptible rate. Under such conditions, for a given concentration 

 of invertase, the rate of hydrolysis of the sugar is constant, while for 

 varying amounts of invertase, the velocity of hydrolysis is proportional 

 to the concentration of invertase employed. Algebraically: 



Velocity = kF 



