Data: reaction between two species A and B was carried out in the gas phase. the
ID: 707075 • Letter: D
Question
Data: reaction between two species A and B was carried out in the gas phase.
the rate constant for the reaction was found to vary as follows;
T/K
273
323
373
423
473
k/mol/L.s
2.22E-4
4.31E-3
0.0371
0.185
0.789
Through use of a graph determine the activation energy.
b) it ws found that isotopically labelling species A changed the rate of reaction. Demonstrate the origin of this effect using the expression for the bimolecular rate constant, assuming there is no change in either the activation energy or the reactive cross-section.
c) when the reaction was carried ut at 473K at starting concentrations of the reagents of [A] = 0.250mol l-1 and [B] = 0.00123 moll-1, the process was shown to be first order with a half life of 3.45s. Is this consistant with the data in part a of the question?
Part c) is the main part of this question i need assistance with but confirmation for part B would be appreciated.
T/K
273
323
373
423
473
k/mol/L.s
2.22E-4
4.31E-3
0.0371
0.185
0.789
Explanation / Answer
(c) No, it is not consistent. For any reaction rate constant term is independent of reactant concentration (but changes with temperature). On comparing with the rate constant at 473K, we find that the unit of rate constant K/mol/L.s indicate that it is not a first order reaction since a first order reaction rate constant has the unit of s-1. Thus, merely changing the reactant concentration will not change the order of reaction rate. Moreover, for a first order reaction, half-life is defined as 0.693/k (s). But half life of 3.45 sec, gives a k = 0.201 s-1 which is not the rate constant given in the table (0.789).
(b) The phenomenon is known as reaction kinetic isotope effect. When an atom (A) of a reactant undergoing bond breaking (A-X) in the reaction rate determining step is replaced by its isotope (a), the activation energy for the reaction and its reaction rate gets altered. This is because the bond strength of the atom (A-X) and its isotope (a-X) is different. This is known a primary kinetic isotope effect.
While, if an atom not directly involved in bond breaking gets replaced by its isotope, the activation energy barrier for the reaction remains unaltered. But the reaction rate gets altered. This is known as secondary kinetic isotope effect. Compared to a primary kinetic isotope effect, the magnitude of change in reaction rate is much smaller in case of secondary kinetic isotope effect.
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