

[TOP]


7. Empirical Reaction Kinetics (i)
(11) The determination of the rate law from: (a) the isolation method (b) method of initial rates (c) the integration method (d) fractional lifetime method (12) Comparison of these methods [ TOP ]
(1) Identification of the rate law and the calculation of k from
experiments.
(11) The determination of the rate law from: (a) the isolation method
The easiest method to determine a rate law is by the isolation method where the concentrations of all the reactants except one is in large excess. Thus for example, if for the reaction: which has a rate law of the form: we let B and C to be in large excess with concentrations [B_{o}] and [C_{o}], then it may be assumed that their concentration is constant throughout the reaction. Thus we may write: where:This means that if we take logs of both sides we get: which is the equation of a straight line: for plotting ln(v) against ln[A] with gradient a and yintercept of ln(k`). [ TOP ]
In the method of initial rates, the rate is measured at the beginning of the reaction for several different initial concentration of the reactants. Thus for example, for the reaction: which has a rate law of the form: or in the limit of t = 0, we get: where [A_{0}], [B_{0}] and [C_{0}] are the initial concentrations of A, B, C respectively. [ TOP ]
(i) a first order rate law: i.e.: which integrates to: This result is usually expressed in terms of the extent of reaction: i.e.: or in exponential form, i.e.: Note: Fig. 1 shows how the exponential decay of the reactant in a firstorder reaction. The larger the rate constant, the more rapid the decay: here k(large)= 3.k(small).(ii) a second order rate law: In this case we have: which integrates to: i.e.:
for the chemical reaction: In this case we write: i.e.: i.e.: i.e.: where: i.e. by integration:(iv) an n^{th} order rate law: In this case we have: which integrates to: i.e.: [ TOP ]
The half life ( t_{1/2}) of a reaction is the time taken for the initial concentrations [A_{0}], [B_{0}], … of the reactants to decrease by half. [ TOP ]
Of the four methods discussed above, the integration method is the one most widely employed for evaluating empirical rate laws for which an order of reaction can be defined. However, it has a number of disadvantages:
Given this information, one must appreciate that to obtain a full understanding of the rate behaviour initially and throughout a reaction, it is essential to use both initial rate and integration methods to characterise fully the kinetic behaviour of any reaction Systematic studies varying the concentration of each reactant, product and any possible inhibitor or catalyst have to be made, and the resulting kinetic behaviour analysed This is especially true when the rate law does not have a form which allows the assignment of an order of reaction. See Also: Table 1: Click
here  opens in a blank page.


CH237  Chemical Thermodynamics
and Kinetics
Dr.
Joseph N. Grima, Department
of Chemistry

7. Empirical Reaction Kinetics (i) (11) The determination of the rate law from: (a) the isolation method (b) method of initial rates (c) the integration method (d) fractional lifetime method (12) Comparison of these methods [ TOP ]
(1) Identification of the rate law and the calculation of k from
experiments.
(11) The determination of the rate law from: (a) the isolation method
The easiest method to determine a rate law is by the isolation method where the concentrations of all the reactants except one is in large excess. Thus for example, if for the reaction: which has a rate law of the form: we let B and C to be in large excess with concentrations [B_{o}] and [C_{o}], then it may be assumed that their concentration is constant throughout the reaction. Thus we may write: where:This means that if we take logs of both sides we get: which is the equation of a straight line: for plotting ln(v) against ln[A] with gradient a and yintercept of ln(k`). [ TOP ]
In the method of initial rates, the rate is measured at the beginning of the reaction for several different initial concentration of the reactants. Thus for example, for the reaction: which has a rate law of the form: or in the limit of t = 0, we get: where [A_{0}], [B_{0}] and [C_{0}] are the initial concentrations of A, B, C respectively. [ TOP ]
(i) a first order rate law: i.e.: which integrates to: This result is usually expressed in terms of the extent of reaction: i.e.: or in exponential form, i.e.: Note: Fig. 1 shows how the exponential decay of the reactant in a firstorder reaction. The larger the rate constant, the more rapid the decay: here k(large)= 3.k(small).(ii) a second order rate law: In this case we have: which integrates to: i.e.:
for the chemical reaction: In this case we write: i.e.: i.e.: i.e.: where: i.e. by integration:(iv) an n^{th} order rate law: In this case we have: which integrates to: i.e.: [ TOP ]
The half life ( t_{1/2}) of a reaction is the time taken for the initial concentrations [A_{0}], [B_{0}], … of the reactants to decrease by half. [ TOP ]
Of the four methods discussed above, the integration method is the one most widely employed for evaluating empirical rate laws for which an order of reaction can be defined. However, it has a number of disadvantages:
Given this information, one must appreciate that to obtain a full understanding of the rate behaviour initially and throughout a reaction, it is essential to use both initial rate and integration methods to characterise fully the kinetic behaviour of any reaction Systematic studies varying the concentration of each reactant, product and any possible inhibitor or catalyst have to be made, and the resulting kinetic behaviour analysed This is especially true when the rate law does not have a form which allows the assignment of an order of reaction. See Also: Table 1: Click here  opens in a blank page. 
Email me at jgri1@um.edu.mt 