Concise notes for chemical kinetics rate laws

Chemical Kinetics
Reaction rate is the speed of a chemical reaction (Molarity/second)
For a reaction A B,
Rate = - Δ[A]/ Δ t

Factors that affect rate:
(a) Concentration of reactants (higher concentration of reactants produce faster rates)
(b) Temperature (increased temperature increases reaction rate) - higher T = larger k = increased rate
Temperature can affect the speed of a reactant (minor effect, plays a higher role in gases) or the
kinetic energy of reactants (major effect)
(c) Physical state of reactants (Increased surface area increases rate of reaction)
(d) Presence of catalyst - Catalyst = lower Ea = larger k = higher rate
(e) Increased structural complexity results in decreased rate
(f) Smaller Ea = larger f (fraction of collisions with energy greater than Ea : f = e–Ea/RT) = larger k =
higher rate

For a reaction aA + bB cC + dD

−1A −1B +1C +1D
= = = (these are the rates of disappearance of reactants and appearance of
at bt ct d t
products and are stoichiometrically related in the reaction)

However, measured rate for each species is dependent on concentration, physical state and follows its
own reaction kinetic order and is independent of the stoichiometric coefficient in the reaction.
A
RateA =
t
B
RateB =
t
C
RateC =
t
D
RateD =
t

To find the co-efficients a, b, c and d, you have to regard any two species at a time:

−1A −1B
Rate A/ Rate B = 
at bt
−1rateA −1rateB

a b
−1rateA b
X
a −1rateB

, rateB
b= xa
rateA

Similarly,
rateC
c= xa
rateA
rateD
and d = xa
rateA

Differential Rate Law:

For a reaction aA + bB Products

Rate = k[A]m [B]n,
Where k is the rate constant, [A] is the molar concentration of reactant A, [B] is the molar concentration
of reactant B and the exponents m and n are number of molecules of A or B that collide and a and b
coefficients to balance the equation.
The concentrations of each reactant are multiplied to obtain the differential rate.

The mechanisms of most reactions consist of two or more elementary steps and the molecularity of this
step equals the number of reactant particles which equals the reaction order (m or n, the exponents for
the reactants in the rate law)

Elementary step Molecularity Rate law
A product unimolecular Rate = k[A]
2A product bimolecular Rate = k[A]2
A+B product bimolecular Rate = k[A][B]
2A + B product termolecular Rate = k[A]2[B]

Only for the elementary step, we use the reaction coefficient as the reaction order. The rate-
determining step is the slowest step and its rate law is equivalent to the overall rate law.

Differential rate can be measured as initial rate, instantaneous rate (slope of tangent at points on the
graph) or average rate (slope of the line joining two points). However, it does not indicate what is at
other points on the curve.

Integrated Rate Law:

Rate = Δ[A]/Δt = k[A]n, where n is the order of the reaction.

Integrated Rate laws can be used to find the time needed to reach a certain concentration of reactant or
the concentration after time t.

The area under the curve of [A] vs t can be integrated to obtain the integrated rate law, since here we
are dealing with incremental changes in concentration and time. This can be rearranged as a linear
equation with appropriate t (x values) and [A] (y values) and used graphically to determine k or the
reaction order.