Part 1

Chemical Kinetics

Clive McKee and Michael Mortimer

INTRODUCTION

Movement is a fundamental feature of the world we live in; it is also inextricably linked with time. The measurement of time relies on change — monitoring the swing of a pendulum, perhaps — but conversely, any discussion of the motion of the pendulum must involve the concept of time. Taken together, time and change lead to the idea of rate, the quantity which tells us how much change occurs in a given time. Thus, for example, for our pendulum we might describe rate in terms of the number of swings per minute. Or, to take a familiar example from everyday life, we refer to a rate of change in position as speed and measure it as the distance travelled in a given time (Figure 1.1).

The study of movement in general is the subject of kinetics and chemical kinetics, in particular, is concerned with the measurement and interpretation of the rates of chemical reactions. It is an area quite distinct from that of chemical thermodynamics which is concerned only with the initial states of the reactants (before a reaction begins) and the final state of the system when an equilibrium is reached (so that there is no longer any net change). What happens between these initial and final states of reaction and exactly how, and how quickly, the transition from one to the other occurs is the province of chemical kinetics. At the molecular level chemical kinetics seeks to describe the behaviour of molecules as they collide, are transformed into new species, and move apart again. But there is also a very practical side to the subject which is quickly appreciated when we realize that our very existence depends on a balance between the rates of a multitude of chemical processes: those controlling our bodies, those determining the growth of the animals and plants that we eat, and those influencing the nature of our environment. We must also not forget those changes that form the basis of much of modern technology, for which the car provides a wealth of examples (see Box 1.1). Whatever the process, however, information on how quickly it occurs and how it is affected by external factors is of key importance. Without such knowledge, for example, we would be less well-equipped to generate products in the chemical industry at an economically acceptable rate, or design appropriate drugs, or understand the processes that occur within our atmosphere.

Historically, the first quantitative study of a chemical reaction is considered to have been carried out by Ludwig Wilhelmy in 1850. He followed the breakdown of sucrose (cane sugar) in acid solution to give glucose and fructose and noted that the rate of reaction at any time following the start of reaction was directly proportional to the amount of sucrose remaining unreacted at that time. For this observation Wilhelmy richly deserves to be called 'the founder of chemical kinetics'. Just over a decade later Marcellin Berthelot and Péan de St Gilles made a similar but more significant observation, In a study of the reaction between ethanoic acid (CH3COOH) and ethanol (C2H5OH) to give ethyl ethanoate (CH3COOC2H5) they found the measured rate of reaction at any instant to be approximately proportional to the concentrations of the two reactants at that instant multiplied together. At the time, the importance of this result was not appreciated but, as we shall see, relationships of this kind are now known to describe the rates of a wide range of different chemical processes. Indeed, such relationships lie at the heart of empirical chemical kinetics, that is an approach to chemical kinetics in which the aim is to describe the progress of a chemical reaction with time in the simplest possible mathematical way.

By the 1880s, the study of reaction rates had developed sufficiently to be recognized as a discipline in its own right. The 21 December 1882, issue of the journal Nature noted,

'What may perhaps be called the kinetic theory of chemical actions, the theory namely, that the direction and amount of any chemical change is conditioned not only by the affinities, but also by the masses of reacting substances, by the temperature, pressure, and other physical circumstances — is being gradually accepted, and illustrated by experimental results.'

Over a century later, chemical kinetics remains a field of very considerable activity and development; indeed nine Nobel prizes in Chemistry have been awarded in this subject area. The most recent (1999) was to A. H. Zewail whose work revealed for the first time what actually happens at the moment in which chemical bonds in a reactant molecule break and new ones form to create products. This gives rise to a new area: femtochemistry). The prefix femto (abbreviation 'f') represents the factor 10-15 and indicates the timescale, which is measured in femtoseconds, of the new experiments. As some measure of how short a femtosecond is, while you read these words light is taking about 2 million femtoseconds (2 x 106 fs) to travel from the page to your eye and a further 1000 fs to pass through the lens to the retina.

QUESTION 1.

In an empirical approach to chemical kinetics, what would be the simplest mathematical way of representing the information...