Chemical Kinetics

                                                           1) Fundamentals of Chemical Kinetics

Chemical kinetics is the quantitative study of chemical systems that are

changing with time. (Thermodynamics, another of the major branches of

physical chemistry, applies to systems at equilibrium—those that do not

change with time.)

In this course, we will restrict our attention to systems that are homogeneous

and well mixed (a major restriction), and that are at constant volume

(a minor restriction that simplifies the notation, but can be easily lifted.)

With these two restrictions it is useful to describe the chemical system in

terms of concentrations of the species present:

[A] =

nA

V

(1)

where [A] indicates the concentration of species A, V is the volume, and nA

indicates the amount of A present in that volume. In discussions of reactions

in solution, the usual units for [A] are moldm−3 or mol/L, called molar

and written M. (The name “molar” and the symbol M are now regarded

as obsolete by NIST and by IUPAC, and the explicit notations mol dm−3

or mol/L are preferred; however, most chemists appear to be ignoring their

lead.)

For gas phase reactions, the customary units are molecules cm−3, often

written simply cm−3.

The chemical state of a homogeneous system can be described by specifying

the concentrations of all the species present and the pressure and

temperature.

1. Fundamentals of Chemical Kinetics

where γ is the stochiometric coefficient for species Γ in the balanced equation.

The + sign is used if Γ is a product, the − sign if it is a reactant. Thus

rA = −

1

a

d[A]

dt

. (4)

The rate always has units of concentration/time. For solution reactions

the usual units are M s−1, while for gas phase reactions the most common

unit is cm−3 s−1.

These specific rates are not necessarily the same for different species. If

there are no reaction intermediates of significant concentrations, then

rA = rB = rY = rZ = v, (5)

the rate of the reaction. For very many systems, intermediates are important,

all the specific rates are different, and it is then necessary to specify

which specific rate is being discussed.

1.3 Rate laws

For most reactions, the rate(s) depend on the concentrations of one or more

reactants or products. Then we write

rΓ = f ([A], [B], [Y], [I], [C], T, p, . . .) (6)

where the list shows explicitly that r might depend on the concentrations

of species other than those in the balanced equation, as well as on temperature,

pressure, and so on. Often the dependence on variables other than

concentrations is suppressed (a set of conditions is implied or specified), so

that we write

rΓ = f ([A], [B], [Y], [I], [C], . . .). (7)

This kind of expression, giving the rate of the reaction as a function of the

concentrations of various chemical species, is called a rate law. Notice that

the rate law is a differential equation: it gives the derivative (with respect

to time) of one of the concentrations in terms of all the concentrations. The

solution to such a differential equation is a function that gives the concentration

of species Γ as a function of time.

1.3.1 Examples

The gas phase reaction that is the foundation of the very powerful infrared

HBr laser is

H2 + Br2 −−→ 2HBr.

1)Integration of simple rate laws

Generally the rate law for a reaction is determined by measurements of the

concentrations of one or more species as a function of time. I will approach

the problem backwards, first showing what concentration-vs-time behavior

might be expected for several simple rate laws, then talking about how

to design experiments to measure rates and how to extract rate laws from

kinetic data.

2.1 First order reactions

While true first order reactions are comparatively rare, first-order rate behavior

is extremely important because many more complicated reactions

can be “tricked” into behaving like first-order ones and first-order behavior

is easier to handle experimentally than any other type.

If the general reaction

aA + bB + . . . −−→ yY + zZ + . . . (15)

is first order with respect to A, and its rate depends on no other concentrations

(it is zero order with respect to all other species), then the rate law

is

−

1

a

d[A]

dt

= k[A]. (16)

Notice that k must have units of s−1; that will always be true of first-order

rate coefficients. k is a positive number that does not depend on any concentrations,

though it does depend (usually strongly) on temperature.

2.1.1 Integration of the rate law

The rate law is a differential equation; in this case it is a separable equation,

and can be solved simply by isolating the terms corresponding to the different

variables [A] and t on different sides of the equation and integrating

Experimental Techniques

7.1 Elementary considerations

Several questions must be answered before an experimental approach can

be selected.

• Over what time does the reaction occur?

• Are the reactants stable or unstable?

• What range of temperature is interesting?

All these questions are relevant to the choice of experimental technique

independent of the particular detection method employed.

7.2 Stable reactants, slow to medium time scales

7.2.1 Batch mixing

This is kinetics on classical stir-in-a-pot reactions. It works for τ 10 s. You

can analyze the concentrations by removing samples at intervals and titrating,

using GC, whatever. A method for stopping reaction in your sample

(freezing, neutralization, etc) is handy. Or, you can monitor the reaction in

situ - optical absorption, polarimetry, ion-selective electrodes, conductivity,

etc. all work.

7.2.2 Flow Experiments

For faster reactions, say τ 0.1 s, you can let the reactants come together

continuously in some sort of mixing chamber, then allow them to react

while flowing along a tube. At each point along the tube, the concentrations

are steady, so signals can be averaged to get good signal to noise; experiments

at different distances along the flow tube yield concentrations at

different times since the reaction began. One disadvantage is that it usually

requires lots of reactants.

Discharge flow experiments for gas phase reactions with unstable reactants

use a steady electric discharge to produce one or both reactants before

they enter the main reaction tube. This is a very popular method for studying

reactions of radical and ionic species. Spectroscopic detection along the

length of the tube, or mass spectrometry at the end of the flow tube, using a

moveable injector to vary the flow distance, are the most popular detection