First order kinetics

Definitions and concepts in kinetics

Kinetics is the branch of physical chemistry that informs us on rates of processes as well as experimental methods to measure rates and reaction progress. In this section we introduce the basic concept of a rate law and associated rate constant. In this course we will focus exclusively on first and second order rate constants. However, we should be aware that kinetics accounts for processes that fall outside this scope. We discuss how to determine the reaction order experimentally based on the isolation method. Experimental measurements using spectroscopy, conductivity, pressure and so on are needed to quantitatively describe the rates and derive the rate laws.

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The utility of the half-life

Many first order processes involving a single species can be conveniently described in terms of the half-life formalism. Radioactive decay is one important example, but there are many others. In this section the significance of exponential kinetics is discussed in terms of the natural life time t = 1/k, where k is the rate constant and the half life t1/2 = ln(2)/k.

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The Approach to Equilibrium

When a system is perturbed away from equilibrium it will approach equilibrium again with an observed rate constant that is the sum of the forward and reverse rate constants for the process. This result is proven in the video below and justified using the Principle of Microscopic Reversibility. This principle states that the pathway for the forward and reverse reaction must be the same. Therefore, there is an intrinsic connection between the forward and reverse rate constants. This leads to the equatoin K = kf/kr, which connects the equilibrium constant for the forward and reverse rate constants.

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Parallel and sequential processes

First order rate schemes can involve two main types of kinetic rate schemes. These are known as parallel and sequential. The parallel rate scheme considers two or more reaction paths that deplete population from a state. The compettion between the various paths can be expressed in terms of a quentum yield (fraction) for each path. The sequential rate scheme is another important case, in which the population from an initial state A passes through an intermediate B on the way to the final state C (A -> B -> C). There are two important limiting cases. When the first rate cosntant is large relative to the second there is a significant build up of the intermediate state B. It can be observed experimentally in such cases. On the other hand, when the second rate constant is larger than the first the intermediate cannot be directly observed and must be inferred from other data. In such cases, one may simplitify the rate equations as discussed in the next section on the steady state approximation.

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The Steady State Approximation

In sequential kinetics systems where the rate constant of the second process is at least as large as the first (k2 > k1) one can eliminate the intermediate state from the kinetic equations using the steady state approximation. This short video justifies the assumptions of the steady state approximation using a graphical illustration of how the intermediate state becomes increasingly less concentated and how its rate of change approaches zero in such cases. Always remember that the goal of the steady state approximation is to eliminate an intermediate state from the kinetic equations in order to acheive a simplification. This will help you to define the approximation and to use it properly.

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Practice Problems in the Fundamentals of Kinetics

Practice Problems in Applications of the Half Life