Chemical kinetics

In physical chemistry, chemical kinetics or reaction kinetics study reaction rates in a chemical reaction. Analysing the influence of different reaction conditions on the reaction rate gives information about the reaction mechanism of a chemical reaction.

Kinetics deal with

experimental determination of reaction rates and reaction rate constants
The factors that influence a reaction rate.
homogeneous or heterogeneous environment.

Reaction Rates and Rate Laws

The reaction rate is the change in concentration of a reactant or product over a unit of time (usually expressed in molarity per second $M / s$ ). Generally speaking, the reaction rate decreases as the reaction progresses because the concentration of reactants is decreasing as they are consumed.

For the reaction

$aA + bB \rightarrow \; cC + dD$

the definition of the reaction rate $v$ is such that it is independent of the product or reactant that is followed in time

$v=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=\frac{1}{c}\frac{d[C]}{dt}=\frac{1}{d}\frac{d[D]}{dt}$

where $[A]$ and $[B]$ represent the concentration of the reactants. This equation is only valid when there is no significant build-up of intermediates and the volume is constant during the reaction.

A rate law is an equation that relates concentrations of reactants to the reaction rate. For the above reaction, the rate law is

$v = k [A] m [B] n$

where $k$ is the rate constant, and the exponents are reaction orders. The reaction is of order $m$ in $A$ and of order $n$ in $B$ . The overall reaction order is $m + n$ . Usually, reaction orders are 0, 1, or 2, but they can be fractions or even negative numbers.

A first-order reaction depends on the concentration of only one reactant. Other reactants can be present, but each will be zero order. The rate law for a first order reaction is

$v = -\frac{d[A]}{dt} = k[A]$ .

When integrating this differential equation, the resulting equation is

$ln[A] t = - k t + ln[A] 0$

where $[A] t$ represents the concentration at a particular time and $[A] 0$ represents the initial concentration. The half-life of a reaction describes the time needed for half of the reactant to be depleted. (do not confuse this with the half-life involved in nuclear decay.) It can be determined using the equation $t_\begin{matrix} \frac{1}{2} \end{matrix} = \begin{matrix} \frac{ln2}{k} \end{matrix}$ .

A second-order reaction depends on the concentrations of one second order reactant, or 2 first order reactants.

$R = k [A] 2$ or $R = k [A][B]$ .

When relating these rate laws with time, the results are

$\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$ or $\frac{1} {B_0 - A_0} \ln \frac{A_0 B_t}{B_0 A_t} = kt$ .

The half life equation for a second order reaction is $t_\begin{matrix} \frac{1}{2} \end{matrix} = \frac{1}{k[A]_0}$

Reaction Mechanisms

The series of individual steps by which a reaction occurs is called the reaction mechanism. Each step is called an elementary step, and each has it’s own rate law and molecularity , or number of molecules involved in the step. A unimolecular step involves one reactant, a bimolecular involves two, and so on. All of the elementary steps must add up to the original reaction. When determining the overall rate law for a reaction, the slow step is the step that determines the reaction rate. Consider the following example:

CO + NO₂ → CO₂ + NO

Rate laws cannot be determined just by looking at a chemical equation. (They are determined through experimentation, often involving the use of spectroscopy.) In this case, it has been experimentally determined that this reaction takes place according to the rate law $R = k [N O 2] 2$ . Therefore, a possible mechanism by which this reaction takes place is

2 NO₂ → NO₃ + NO (slow)
NO₃ + CO → NO₂ + CO₂ (fast)

Because the first step is the slow step, it is the rate determining step. Because it involves the collsion of 2 NO₂ molecules, it is a bimolecular reaction with a rate law of $R = k [N O 2] 2$ . If one were to cancel out all the molecules that appear on both sides of the reaction, you would be left with the original reaction.

References

Preparing for the Chemistry AP Exam. Upper Saddle River, New Jersey: Pearson Education, 2004. 131-134. ISBN 0536731578

--Michael 00:24, Mar 20, 2005 (UTC)

Categories: Physical chemistry