First-order Reaction: Hydrolysis of Sucrose to Glucose and Fructose - QS Study
QS Study

First-order Reaction: Hydrolysis of Sucrose to Glucose and Fructose catalyzed by acid

Hydrolysis of cane sugar (sucrose) to glucose and fructose catalyzed by acid follows first order kinetics.

C12H22O11 (sucrose) + H2O + (H+) → C6H12O6 (glucose) + C6H12O6 (fructose) + (H+)

Since sucrose is optically active and dextrorotatory and an equimolar mixture of glucose and fructose is laevorotatory, the optical rotation of plane of plane polarized light will change during the progress of the above reaction. Consequently, the reaction rate can be conveniently followed by measuring the angle of rotation of the plane of polarization of plane polarized light at suitable time intervals.

Let, α0 be the angle of rotation

α1 be the angle of rotation at time t.

αw be the angle of rotation at infinite time (say after 72 hours)

Then, (α0 – αw) is proportional to initial concentration and (α0 – α1) is proportional to the concentration at time t.

Therefore [α0 – αw – (α0 – α1)] = (α1 – αw) is proportional to the concentration remaining unreacted at time t, i.e., (a – x).

These data when substituted in equation 12.22 yield,

k = 2.303/t log [(α0 – αw)/ (α1 – αw)]

Results shown in Table show the constancy of the values of k, so obtained over a wide concentration change. The specific reaction rate is also independent of initial concentration of the sugar. In this case the concentration of water (although it is a reactant) does not enter into the rate expression involving the two reactant species due to its presence in large excess in the reaction mixture. Such a reaction in which one reactant does not enter into the rate equation due to its presence in large excess is sometimes called pseudo-unimolecular reaction. It is to be noted that the acid in the reaction mixture acts as catalyst.

Table: Hydrolysis of at 300 in 2.5 mol L-1 formic acid

Experimental date of this reaction can also be treated in a different manner by using the Guggeheim method of calculation. In this method α0 and αw need not be known.