# Chemical Kinetics

Table of Contents:

- Chemical Kinetics - Introduction
- Basic Idea of Chemical Kinetics
- Composite Reactions or Reaction Mechanisms
- Advanced Idea in Chemical Kinetics Exercises
- Exercises
- Glossary of Terms
- Links

### Chemical Kinetics - Introduction

Chemical kinetics, a topic in several chemistry courses, illustrates
the connection between mathematics and chemistry. Chemical kinetics deals
with chemistry experiments and interprets them in terms of a mathematical
model. The experiments are perfomed on *chemical reactions* as they
proceed with time. The models are *differential equations* for the
rates at which reactants are consumed and products are produced. By combining
models with experiments, chemists are able to understand how chemical reactions
take place at the molecular level.

### Basic Ideas of Chemical Kinetics

Stoichiometry in chemical reactions and
relation to differential rate laws and integrated rate laws.

Definition of the rate of a chemical reaction.

Extent of reaction, extent variable: x.

Define rate law, rate constant
and order of a reaction.

Temperature and reaction rates: Arrhenius Equation
and activation energy.

Differential versus Integrated
rate laws.

Empirical Rate Equations: FIRST ORDER chemical
kinetics equations and solutions.

Empirical Rate Equations: SECOND ORDER chemical
kinetics equations and solutions.

### Composite Reactions or Reaction Mechanisms

Mechanism and rate laws.

How to Construct the differential equations
of chemical kinetics.

Example mechanism: consecutive reactions using DynaSys, A
-->B --> C.

Example mechanism: Michaelis-Menton enzyme catalysis
using mathcad.

### Advanced Ideas in Chemical Kinetics

#### Oscillating Chemical Reactions:

History of oscillating reactions.

Example chemical oscillator: Lotke-Volterra.

Example chemical oscillator: Brusselator.

Example chemical oscillator: Oregonator.

#### Thermogravimetric Analysis

TGA refers to the process of monitoring the mass of a sample while it is heated. The rising temperature causes chemical reactions to occur and may result in loss of mass. Background for TGA and illustrative examples are found by clicking here .

### Exercises

- First Order chemical kinetics equations
- Second Order chemical kinetics equations
- How to Construct the differential equations of chemical kinetics

### Glossary of Terms

- Stoichiometry determines the molar ratios
of reactants and products in an overall chemical reaction. We express the
stoichiometry as a balanced chemical equation. For kinetics it is convient
to write this as products minus reactants: n
_{p}P + n_{q}Q - n_{a}A - n_{b}B (instead of the conventional equation n_{a}A + n_{b}B ---> n_{p}P + n_{q}Q). This indicates that n_{a}and n_{b}moles of reactants A and B, resp., produce n_{p}and n_{q}moles of products P and Q. - The rate of a chemical reaction is defined
in such a way that it is independent of which reactant or product is monitored.
We define the rate, v, of a reaction to be v = (1/n
_{g}) d[G]/dt where n_{g}is the signed (positive for products, negative for reactants) stoichiometric coefficient of species G in the reaction. Namely, v = (-1/n_{a}) d[A]/dt = (1/n_{p}) d[P]/dt, etc. - It is convenient to refer to the extent of
reaction. As the reactants are sonsumed and the products are produced,
their concentrations change. If the initial concentrations of A, B, P and
Q are [A], [B], [P] and [Q], resp., then the extent of reaction is defined:
x = -([A]-[A]
_{0})/n_{a}= -([B] - [B]_{0})/n_{b}= ([P]-[P]_{0})/n_{p}= ([Q]-[Q]_{0})/n_{q}. Alternately, each species concentration is a function of the extent of reaction: [A] = [A]_{0}- n_{a}x, etc. - Many reactions follow elementary differential rate laws such as v = k f([A], [B], ...) where f([A], [B], ...) is a function of the concentrations of reactants and products. That is, the rate varies as the concentrations change. A proportionality constant, k, is called the rate constant of the reaction.
- When the rate law has the special form of a product
(or quotient) of powers, f([A], [B], ...) = [A]
[B]^{a}[P]^{b}[Q]^{p}then^{q}*a*is the order of the reaction with respect to A,*b*is the order w.r.t. B, etc. Note that order may be positive, negative, integer, or non-integer. Further, the sum*a + b + p + q*is the overall order of the reaction rate law. - NOTE: there is no necessary relation between
orders and stoichiometric coefficients. That is,
*a*might differ from n_{a}. - Reaction rate constants are usually temperature dependent; the rate of a reaction usually increases as the temperature rises. The temperature dependence often follows Arrhenius' equation: k(T) = A exp(-Ea/RT) where T is the absolute temperature, R the universal gas constant, Ea is the activation energy (specific to each reaction), and A is the "pre-exponential" or "frequency" or "entropy" factor.
- One objective of chemical kinetics is to solve the differential rate law d[G]/dt = k f([A], [B], ...), and thereby express each species concentration as a function of time: [G](t). Since solution requires integration, we call it the integrated rate law.
- A reaction mechanism is a set of steps at the molecular level. Each step involves combinations or re-arrangements of individual molecular species. The steps in combination describe the path or route that reactant molecules follow to reach the product molecules. The result of all steps is to produce the overall balanced stoichiometric chemical equation for reactants producing products.

### Links

Extensive collection of physical chemistry problem solutions using MathCad can be found at the scicomp site.

### Feedback:

You are invited to send your comments about these chemical kinetics pages to Ron Poshusta <poshustr@mail.wsu.edu>.

### References

*Physical Chemistry*by K.J. Laidler & J.H. Meiser [Houghton Mifflin Co., 1995] Chapters 9 and 10.*Physical Chemistry*by P. Atkins [W.H. Freeman & Co., 1994] Chapters 25 and 26.- More references will be found under subtopics in chemical kinetics.

CODEE, the Consortium for Differential Equations Experiments, has been
revitalized. CODEE was quite active in the 1990s in spreading differential
equations activities, information, and software tools. In particular,
CODEE formed the organization for the ODE Architect software. Recently,
an NSF project headed by Darryl Young of Harvey Mudd College has
reinvigorated CODEE.

New activities! There are two new activities concerning
the Idaho plan for wolf management, and a model for an insurgency.
See the project page for details.