**Chemical Kinetics class 12 notes Chemistry chapter 4**

**Rate, Order, and Molecularity of a Chemical Reaction: **

**Rate of a Chemical Reaction: **

It can be defined as the change in concentration of reactants or products in unit time. The rate of a reaction can be expressed in terms of rate of disappearance of any one of the reactant or rate of appearance of any one of the products, e.g., for a reaction

A +2B —–> C

**Rate of disappearance of A** = Decrease in concentration of A/ Time taken = – A[A]/∆t

rate = – ½ ∆ [B]/∆t = ∆[C]/∆t

**Instantaneous Rate of Reactions: **

It is defined as the rate of change in concentration of any one of the reactants or products at a particular instant of time.

Instantaneous rate, dx/dt = – d[A]/dt = – ½ d [B]/dt = d [C]/dt

**Average Rate of Reaction: **

It is the appearance of product or disappearance of reactants over a long time interval.

**Average rate r _{av}** = – ∆A/∆t = – ½ ∆[B]/∆t = ∆[C]/∆t

It is determined from the slope of the graph as given below

Unit of a rate of reaction is mot L^{-1} s^{-1} or atm s^{-1} .

**Factors Influencing Rate of a Reaction: **

The rate of a reaction depends upon experimental conditions such as the concentration of the reactants, temperature and catalyst. It also depends upon the nature of reactants.

**Dependence of Rate on Concentration: **

The concentration of reactants and products is one of the factors on which the rate of reaction at a given temperature depends. The rate law or rate equation or rate expression is the representation of reaction rate in terms of concentration of the reactants.

**Rate Expression and Rate Constant: **

aA + bB —–> cC + dD

where a, b, c and d represents the stoichiometric coefficients of the reactants and the products.

The rate expression is

Rate α [A]^{x }[B]^{y}

where x and y may or may not be equal to a and b respectively of the reactants.

Above equation can be rewritten as

Rate =k [A]^{x} [B]^{y }

where, k is a proportionality constant called rate constant.

Thus, **rate law** is defined as the expression in which rate of reaction is expressed in terms of molar concentration of reactants with each term raised to some power. The power to which each term is raised may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation.

**Note:** As the concentration of reactants decrease, reaction rate decreases with the passage of time. Conversely, When reactant concentration increase, rates increase.

**Order of Reaction: **

The order of a chemical reaction is defined as the sum of the powers of the concentration of the reactants in the rate law expression.

In the rate equation,

Rate =k [A]^{x} [B]^{y }

Order of reaction = (x + y)

Order of a reaction is experimentally determined quantity. It may be zero, whole number, fractional and even negative. It is very rare that the reaction gets completed in one step. The reactions taking place in one step are called the elementary reactions. A reaction is said to be a complex reactions when a sequence of elementary reactions gives us the products. Complex reactions proceed in two or more steps and each step of a complex reaction is known as an elementary step. The rate of a complex reaction is given by the slowest step among these steps (rate determining step).

**Units of Rate Constant: **

In the table, mol L^{-1} and s are the SI unit of concentration and time respectively. In case of gaseous reactions, concentration is expressed in terms of pressure, i.e., atmosphere.

Rate constant increases with increase in temperature. Presence of a catalyst also influences the rate of the reaction. Nature and concentration of reactants are other two factors which affect the rate of a chemical reaction.

**Example:** Find the order of the reaction from each of the following rate constants.

(i) k = 2.3 x 10^{-5} L mol^{-1} s^{-1}

(ii) k = 3 x 10^{-4} s^{-1}

**Sol.** (i) k = 2.3 x 10^{-5} L moI^{-1} s^{-1} Here, the unit of rate constant is L mo1^{-1} s ^{-1}. So, the reaction is of second order.

(ii) k = 3 x 10^{-4} s^{-1} Here, the unit of rate constant is s^{-1}. So, the reaction is of first order.

**Molecularity of a Reaction: **

Molecularity is defined as the number of reacting species (it may be an atoms, ions or molecules) which takes part in an elementary reaction and collide simultaneously in order to bring about a chemical reaction. It is a theoretical concept. Its value can never be zero or fractional. It is a whole number. For a complex reaction, generally, molecularity of the slowest step is same as the order of the overall reaction.

**Comparison of Order and Molecularity of a Reaction: **

(i) Order of a reaction is an experimental quantity. It can be even a fraction and zero but molecularity cannot be a non-integer or zero.

(ii) Order is relevant to both elementary and complex reactions whereas molecularity is relevant only for elementary reactions. Molecularity has no meaning in case of a complex reaction.

(iii) Order is given by the slowest step of the reaction in case of complex reaction and molecularity of the slowest step is same as the order of the overall reaction.

**Integrated Rate Equation and Pseudo First Order Reaction: **

**Integrated Rate Equations: **

It gives a relation between directly measured experimental data, i.e., the concentration at different times and rate constant. The integrated rate equations are different for the reactions of different orders.

**Zero Order Reactions: **

When the rate of the reaction is proportional to zero power of the concentration of reactant R, i.e., Rate =k [R]° =k, then the reaction is said to be Zero order reaction.

For the reaction, R —–> P, k [R]_{0} —[R]/t

where [R]_{0} is initial concentration of reactant and [R] is the concentration of the reactant time t.

If we plot [R] with time t, we get a straight line with slope = -k and intercept equal to [R]_{o }as shown in the figure.

Some examples of zero order reaction are decomposition of gaseous ammonia on a hot platinum surface and the thermal decomposition of HI on the gold surface.

**First Order Reactions: **

When the rate of the reaction is proportional to the first power of the concentration of the reactant R i.e., then the reaction is said to be First order reaction.

** k = 2.303/t log [R] _{0}/[R]**

where [R]_{0} is the initial concentration and [R] is the concentration of the reactant at time t.

All natural and artificial radioactive decay of unstable nuclei takes place by first order kinetics.

If we plot a graph between log [R]_{o}/[R] with time t, we get a straight line with slope = k/2.303 as shown in the figure.

**For a typical first order gas phase reaction, **

A (g) —-> B (g) + C (g)

k =2.303/t log P_{i}/P_{A }or k = 2.303/t log P_{i}/(2P_{i} -P_{t})

where P_{i} is the initial pressure of A at time t = 0 and P_{t }is the total pressure at time t.

Decomposition of N_{2}O_{5} and N_{2}O are some examples of first order reaction.

**Half-Life (t _{1/2}) ofa Reaction: **

It is the time in which the concentration of a reactant is reduced to one half of its initial concentration.

**For a zero order reaction,** t_{1/2 }= [R]_{o}/2k

**For first order reaction,** t_{1/2} = 0.693/k

For zero order reaction t_{1/2} α [R]_{o} and for first order reaction, t_{1/2 }is independent of [R]_{o}.

**In general,** N = [N]_{o} (1/2)^{n}

where N_{o} = initial amount of reactant and N = amount of reactant left after time t

n= Total time t/Half-life t_{1/2 }

The relation between half-life period of a reactant and its initial concentration for a reaction of n^{th }order is

t_{1/2 }= 1/ k [R]_{0} ^{n-1}

**Pseudo First Order Reaction: **

Pseudo first order reactions are not actually of first order but show first order kinetics under certain conditions. For example, inversion of sugar and acidic hydrolysis of an ester. These reactions are bimolecular but have order one. In other words, we can say that when a reaction is first order w.r.t. each of the two reactants, it becomes pseudo first order when one of the reactants is taken in excess. e.g., CH_{3}COOC_{2}H_{5} + H_{2}0(excess) –H^{+}—- > CH_{3}C00H+ C_{2}H_{5}OH

**Temperature Dependence of the Rate of a Reaction and Collision Theory of Chemical Reactions: **

Most of the chemical reactions are accelerated by an increase in temperature. It has been found that for a chemical reaction with the rise in temperature by 10°, the rate constant is nearly doubled. The effect of temperature is usually expressed in terms of temperature coefficient.

**Temperature Coefficient: **

It is defined as the ratio of rate constant at temperature 308 (298+10) K to the rate constant at temperature 298 K.

**Temperature coefficient** = Rate constant at 308 K/Rate constant at 298 K

The Arrhenius equation explains accurately the temperature dependence of the rate of a chemical reaction.

**Arrhenius Equation: **

It is the mathematical relationship between rate constant and temperature,

k = A .e^{-Ea/RT}

where, A = Arrhenius factor or frequency factor, also called pre-exponential factor,

Ea = activation energy in joules/mole,

R= gas constant and T= temperature

**Activation Energy:**

The energy required to form the intermediate called activated complex (C), is known as activation energy (Ea). It is the extra energy contained by the reactant molecules that results in an effective collision between them to form the products.

To convert reactants into products they have to cross an energy barrier (corresponding to threshold energy) as shown in the figure, which has been obtained by plotting potential energy versus reaction coordinate. Reaction coordinate represents the profile of energy change/ when reactants change into products. Here, we have taken the example of the formation of HIfrom H_{2} and I_{2} molecules.

**Threshold Energy: **

Threshold energy is the minimum energy which the colliding molecules must have for effective collisions, those i.e., collisions which lead to the formation of product molecules.

**Maxwell Boltzmann Energy Distribution Curve: **

According to Ludwig Boltzmann and James Clark Maxwell, the distribution of kinetic energy may be expressed by plotting the fraction of molecules (N_{E} /N_{T}) with a given kinetic energy (E) vs kinetic energy, where N_{E } and N_{T} is the number of molecules with energy E and the total number of molecules respectively.

The peak of the curve corresponds to the most probable kinetic energy.

Distribution Curve showing Energies among Gaseous Molecules

Taking natural logarithm on both sides, Arrhenius equation becomes

In k = – E_{a}/2.303 RT + ln A

A plot of Ink with 1/T gives a straight line with slope = – E_{a }/2.303 R as shown in the figure.

If k_{1} and k_{2} are rate constants at temperatures T_{1} and T_{2} respectively then

log k_{1} = logA – E_{a}/2.303 RT_{1 } (i)

log k_{2} = log A – E_{a}/2.303 RT_{2 } (ii)

Subtracting Eq. (i) from Eq. (ii), we get

log k_{2}/k_{1 }= E_{a}/2.303 R [T_{2}-T_{1}/T1 .T2]

**Effect of Catalyst: **

The rate of a chemical reaction alters by the presence of a catalyst. It alters the rate by providing an alternative path of lower activation energy to the reactants. A catalyst does not change the enthalpy of reaction (∆_{r}, H) and the equilibrium constant of a reaction. It helps only in attaining the equilibrium faster.

**Collision Theory of Chemical Reactions: **

According to the collision theory, rate of reaction depends on the collision frequency and effective collisions. Collision frequency (Z) is the number of collisions per second per unit volume of the reaction mixture.

Rate = Z_{AB} e^{-Ea/RT}

where, Z_{AB} = the collision frequency of reactants A and B and

e^{-Ea/RT} =the fraction of molecules with energies equal to or greater than the activation energy E_{a}.

**Effective Collisions: **

It is defined as the collisions in which molecules collide with sufficient kinetic energy ( i.e., the threshold energy) and proper orientation to assist the breaking of bonds between the reacting species and formation of new bonds resulting in the formation of the desired products.

Collision of correctly oriented particles will be effective, if the kinetic energy of collision ≥ activation energy (E_{a}).