Che-Unit 2 Chemical Kinetics
Che-Unit 2 Chemical Kinetics
Che-Unit 2 Chemical Kinetics
Chemical kinetics is the branch of physical chemistry which deals with the study of the rates
of chemical reactions and the factors which affect the reaction rates. Such studies also enable
us to understand the mechanism by which the reaction occurs.
Reaction Rates
Rate of a chemical reaction = change in concentration (mol/L) of a reactant or product with
time (s, min, hr);
Change in Concentration
Rate of Reaction = Change in Time
For gaseous reactants & products, conc. is usually expressed as partial pressures, so unit of
rate is atm s-1.
The rate is a measure of the change in concentration of reactant or product with time.
The change in concentration of any of the reactants or the products over a specified interval
of time is called the average rate of reaction (r).
Change in Concentration
Rate (r) = Time interval
It is determined by finding the slope of the tangent to the concentration Vs time curve at that
time.
C2 − C1
Slope = t2 − t1
The initial rate is the instantaneous rate at the very beginning of a reaction.
A → Products
First-order reaction can be defined as a chemical reaction in which the reaction rate is
linearly dependent on the concentration of only one reactant. Thus, the order of these
reactions is equal to 1.
Rate = k [A]
2.303 a
k1 = log 𝑎−𝑥
t
The unit of the rate constant in a second order reaction is litre. mol-1. time-1.
The concentration of water does not get altered much during the process (because it is in
excess), we can take it as constant.
Rate = k [CH3COOC2H5]
Some molecules having sufficient energy (activation energy) did not collide to form the
product. Only a few of them made effective collisions (formation of products). The scientists
found that the kinetic energy of the molecules is not the only parameter that directs the
reaction.
They concluded that only those molecules that have the threshold energy (activation energy)
and proper orientation during the collision will form products.
They introduced a probability factor P to account for the effective collisions. So now the rate
of a reaction is given by:
The activation energy and proper orientation of the reacting molecules together determine the
condition for a collision that will result in the formation of products (an effective collision).
So in collision theory, both activation energy and effective collision direct the rate of a
reaction.
Arrhenius Theory:
Temperature has a very significant effect on the rate of chemical reaction. In general the rate
of chemical reactions increases with the rise in temperature.
The temperature dependence of the rate of a chemical reaction can be accurately explained
by Arrhenius.
Ea
The plot of ln k vs 1/T gives a straight line according to the equation with slope = – and
R
Thus activation energy of a reaction can be determined from the above equation by knowing
the values of constants k1 and k2 at temperaturesT1and T2.
In 1935, Henry Eyring develop a new theory called the Transition State Theory (TST).
According to TST, between reactants and the products, there is a state known as the
transition state.
In the transition state, the reactants are combined in a species called the activated complex.
The activated complex is clearly different than the reactants or the products.
Three major factors that determine whether a reaction will occur:
The concentration of the activated complex
The rate at which the activated complex breaks apart
The way in which the activated complex breaks apart: whether it breaks apart to reform
the reactants or whether it breaks apart to form a new complex, the products.
Consider a bimolecular reaction. In the transition state model, the activated complex AB is
formed:
A certain amount of energy is required for the reaction to occur. The transition state, AB‡, is
formed at maximum energy. This high-energy complex represents an unstable intermediate.
Once the energy barrier is overcome, the reaction is able to proceed and product formation
occurs.
…………….i
The rate can be rewritten:
……………….ii
From these two equations:
…………iii
where, v is the frequency of vibration, k is the rate constant and K‡ is the thermodynamic
equilibrium constant.
………………iv
Substituting equation (iv) into equation (iii),
…………….v
The equilibrium constant K‡ can be expressed in terms of (∆Go)‡, called the standard Gibbs
free energy of activation.
For the activated complex, we can write,
(∆Go)‡ = -RT ln K‡ and (∆Go)‡ = (∆Ho)‡ - T(∆So)‡
K‡ = e-(∆Go)‡/RT
K‡ = e-[(∆Ho)‡ - T(∆So)‡]/RT
K‡ = e(∆So)‡/R. e - (∆Ho)‡/RT
kBT
From equation (v), we get: k = e - (∆Go)‡/RT
ℎ
kBT
k= e (∆So)‡/R. e - (∆Ho)‡/RT
ℎ
Now, if ZA and ZB are the charge numbers of the participating ions and x as the distance of
separation, the force of electrostatic interaction (FAB) between them can be given from the
Coulomb’s law as:
The symbol e represents the elementary charge and has a value equal to 1.6 × 10 −19C. The
value of parameter varies from ∞ to r with the mutual approach of two ions. The amount of
work done in moving the two ions closer by an extant dx will be
The work given the above equation is actually the potential energy of the system which
would have a negative sign for oppositely charged ions and positive sign if the ions have
same charges.
Furthermore, this work is the free energy change due to electrostatic interactions, therefore,
multiplying it by Avogadro number (N) would give the value of the corresponding molar free
∗
energy change (ΔG𝐸𝑙 ), i.e.,
∗
Correcting the above equation for non-electrostatic contribution (ΔG𝑁𝐸𝑙 ), the total molar free
energy change for the whole process can be given by the following relation.
where k0 represents the magnitude of the rate constant for the ionic reaction carried out in a
solvent of infinite dielectric constant so that the electrostatic interactions become zero.
In the initial state, the ions are considered as separate; while in the final state, they assumed
to form a single-sphere activated complex with ʻr*ʼ as the overall radius.
The rate law for this case was derived by Born by considering the energy required to charge
an ion in solution.
𝑑𝑤 = 𝑑𝐹 × 𝑑𝑥
The work given the above equation is actually the contribution of the electrostatic
interactions to the Gibbs free energy of the ion.
From the above correlation, the electrostatic contribution to the Gibbs free energy of distinct
ions and activated complex can be written as
Dr M Suneetha, Asst. Prof., Dept. of Chemistry, RGUKT-Nuzvid 14
Hence, the change in electrostatic contribution can be obtained simply by subtracting the
sum of individual contributions from the overall contribution i.e.,
∗
Correcting the above equation for non-electrostatic contribution (ΔG𝑁𝐸𝑙 ), the total molar
free energy change for the whole process can be given by the following relation.
where k0 represents the magnitude of the rate constant for the ionic reaction carried out in a
solvent of infinite dielectric constant so that the electrostatic interactions become zero.
The first successful explanation for unimolecular reactions was provided by Lindemann in
1921 and therefore known as Lindemann theory.
This is the simplest theory of unimolecular reaction rates and was successfully explained
first order kinetics of many unimolecular reactions.
Lindemann assumed that there is time lag between activation and reaction during which the
activated molecules may either react to give products or deactivated to ordinary molecules.
Lindemann assumed a situation where “A reactant molecule A becomes energetically
excited by collision with another molecule of reactant A”.
…………(i)
Steady state approximation/Principle: This principle states that when a short lived reaction
intermediate such as 𝐴∗ exists in a system, the rate of formation of the intermediate can be
considered to be equal to its rate of disappearance. Applying this to [𝐴∗] gives,
This is the rate law expression for unimolecular reaction based on Lindemann theory. The
rate law as given by above equation is not first order.
Case I: 𝑘−1[𝐴] ≫>>𝑘2
When the pressure of the gas is very high then there will be more number of collisions
between the molecules. So the energized molecule will be de-energized more by collisions
rather than decomposing into products.
Case II: 𝑘−1[𝐴] ≪<<𝑘2
When the pressure of gas is so low, then the molecule will be very far apart and hence
instead of getting de-energized by collision with another molecule, the energized molecule
A* will decomposed into products.
So, “at low pressures the rate is of second order whereas at high pressure conditions, the rate
becomes of first order”.
The ionic strength of the solution is a measure of the concentration of ions in that solution.
Ionic strength of a solution can significantly affect the rates of reactions.
The influence of ionic strength (I) on the rate of ionic reactions is:
where zA and zB are the charges on the reactants A and B and the charge on the activated
complex is equal to zA+zB.
The rate of the reaction is proportional to the concentration of the activated complex, hence
R = k [X]
The equilibrium between the activated complex and the reactants is written as
….(i)
where γA, γB and γ# are the activity coefficients for the reactant A, B and the activated
complex X, respectively.
Now, rearranging equation (i), we get
Since the left-hand side simply equals to a second-order rate constant, the above equation
takes the form
……….(ii)
According to Debye-Huckel theory, the activity coefficient of an ion is related to the ionic
strength by the equation,
……….(iii)
where B is the Debye-Huckel constant.
From (ii) and (iii) equations, we get
which is clearly the equation of straight line (y = mx + c) with a positive slope (2𝐵𝑧𝐴𝑧𝐵) and
positive intercept (log 𝑘0).
For aqueous solutions at 25°C, this equation becomes,
……(iv)
where k0 is the rate constant at zero ionic strength and can be obtained by the extrapolation of
log k vs square root of the ionic strength.
According to the equation (iv), A plot of log (k/k0) versus I1/2 gives a straight line with slope
1.02 zAzB.
The plot for different ionic reactions in aqueous solution at 25°C is as shown in Figure.
H2 + Br2⟶ 2HBr
The chain mechanism for the hydrogen-bromine reaction can be proposed as:
In order to obtain the overall rate expression, the steady-state approximation must be applied
to the two intermediates H and Br.
𝑑[𝐻]
The steady state equation for hydrogen radical is = 0 (or)
𝑑𝑡
Now substitute the value of [Br] from equation (iv), in the equation (iii), we have,
……….(v)
Substitute the value of equation (ii) in equation (i), we have,
Taking k3[Br2] as common in the denominator and then canceling out the same form
numerator, we get,
Hence, the order of the hydrogen-bromine reaction in the initial stage will be 1.5 only.
An explosion occurs when a reaction rate accelerates out of control. Some reactions proceeds
explosively.
The explosions are of two types:
(i)Thermal explosion, (ii) Explosion depends on chain reaction
Thermal explosion: If the energy of an exothermic reaction cannot escape, the temperature of
the system rises and the reaction goes faster and it leads to explosion.
In some chain reactions, each chain carrier produces more than one free radical in
propagation steps resulting in a rapid increase in the concentration of active species. This in
turn further increase the production of free radicals. The reaction thus occurs rapidly and an
explosion takes place.
Ex: 2H2 (g) + O2 (g) → 2H2O (g)
Though this may appear to be a very simple reaction, and is still not fully understood.
Involving carriers such as H, O and OH radicals.
Each of reactions 2 and 3 produce two radical chain carriers from one chain carrier.
When such chain branching occurs, the number of free radicals in the system can increase
extremely rapidly, and an explosion may result.
The free radicals may also be destroyed mainly by colliding with walls of the container.