INTRODUCTION:
Chemical reactions are rearrangement of atoms to form different molecules with different number and kind of atoms based on valency rules and obeying law of conservation of mass.
Chemical kinetics is a part of physical chemistry that studies speed of reaction. The rate of reaction can be defined as rate at which the reactants disappear or the rate at which the product is formed. The rate of reaction depends on concentration of reacting species raised to the power called order of reaction.
The rate at which the reactant ‘a’ is disappearing is proportional to its concentration at any instance.
Where ‘x’ is amount of reactant ‘a’ reacted; k = rate constant
Rate Constant (k):
The rate constant will quantify the speed of a chemical reaction. The rate constant for the following reaction is given as.
Hydrolysis of an ester (Methyl acetate) in presence of mineral acid (HCl):
Hydrolysis is a chemical decomposition involving breaking of an bond and the addition of elements of water. The mineral acid will catalyze and accelerates the hydrolysis.
Methyl acetate (Ester) Acetic acid Methyl alcohol
In dilute aqueous solution of ester, the concentration of H2O remains constant and so also the concentration of acid. Hence, according to the first order reaction, the rate of reaction is directly depending upon the concentration of reactants, i.e., ester.
where 
= rate of reaction; k = rate constant
Rearrangement gives
Acetic Acid is produced as a result of hydrolysis of Ester. The Kinetics of reaction can be calculated by withdrawing a fixed volume of reaction mix from time to time interval and titrating against with standard alkali.
Experimental Procedure: Fill the burette with 0.1M NaOH Solution.
1. Take 10 ml of methyl acetate into clean 250ml beaker
2. Now add 100ml of 0.5M HCl to the beaker containing methyl acetate. Shake the solution and immediately note down the time
3. Immediately pipette out 10 ml of this mixture into conical flask containing ice water to stop the reaction
4. Record the time to nearest 10 sec when the pipette has been half discharged into the flask
5. Add 3 drops of Phenolphthalein indicator to this
6. Titrate this mixture with NaOH present in the burette till the colour changes to pink. Note down the volume of NaOH rundown
7. Repeat the same procedure with 10 ml of reaction mixture for every 20 minutes time interval up to obtaining 5 readings
8. Finally we have to heat the remaining reaction mixture up to 20 min and note down the Vmax value
9. Calculate the rate constant by substituting the values of V0, Vmax, Vtat different time intervals
10. Plot a graph by taking (log Vmax - V0 / Vmax - Vt) on Y- axis and time on X- axis. A straight line passing through the origin is obtained whose slopes gives k/2.303 value. From this we have to calculate the rate constant. Refer fig – 1.
11. Calculate the average rate constant by taking the rate constants at different time intervals.
MATHEMATICAL FORMULATION:
Assuming Michaelis-Mentene Kinetics, 
, (Vmax is average rate constant of
reaction Km is Michaelis constant)to be generally applicable to this problem ,
it is categorized in to two parts
i. Expressing Michaelis- Menten Kinetics, derivative equation and it is a function of time , and concentration
ii. For the given Parameters Vmax and Km to generate best fit of the kinetic model to the experimental data.
The Michaelis-Menten equation is numerically
integrated. The simplest approach uses Euler’s Method :
. Further, Modified Euler’s Method is used
for better approximations it is calculated as
]
The Runge-Kutta Algorithm makes for evaluations of dC/dt between each time step, which are combined to create a single step. The four evaluations are weighted and used to create a single step from i to i+1
The equations are:
These equations are incorporated, permitting evaluation of C as a function of time, given a set of values for Vmax, Km and Co.
Parameter Optimization obviously there are choices for Vmax (Average rate constant of reaction), Km (Michaeli’s constant) and Co (initial concentration) to sort through manually when trying to fit a model to real data.
Numerical methods have been written with a given set of Vmax, Km and C0 values calculated (predicted) values are compared with measured values. It is concluded that the increase of time the rate of concentration reaction is increasing and the experimental readings has got good agreements with the numerical methods and it is depicted through the graph.
Parameters :
|
C(0) (µM): |
0.568000 |
|
Vmax: |
0.23 |
|
Km (µM): |
42.02 |
|
DeltaTime: |
20 |