Chemical kinetics is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It provides evidence for the mechanism of chemical reactions.
Contents
- Rate of reaction
- Rate law equation, Rate constant and it’s units
- Order and Molecularity of a Reaction
- Rate expression for first order reaction
- Half life period (t1/2)
- Pseudo first order reaction (Pseudo unimolecular reaction)
- Activation Energy (Ea) and Activated complex
- Factors affecting the rate of reaction
- Collision theory of reaction rate
- Numerical Problems
Rate of reaction
Unit of rate of reaction:
Average rate and instantaneous rate of a reaction
Average rate of reaction: Rate of reaction measured over an interval of time is called average rate of reaction.
i.e. the average rate of reaction is the change in concentration of a reactant or product in a given interval of time.
Instantaneous rate of a reaction:
The rate of reaction at any particular moment of time during the course of chemical reaction is called the instantaneous rate of reaction.
i.e. the instantaneous rate of reaction is the change in concentration of a reactant or product at particular instant of time.
Note:
If we want instantaneous rate at any particular time, then ∆t should be infinitesimally small tending to zero.
Rate law equation, Rate constant and it’s units
Rate of reaction depends upon the concentration of reactants.
Let us consider the general reaction,
The rate of reaction may not depend upon all the ‘a’ concentration terms of A and all the ‘b’ concentration terms of B. suppose by experiment, it is found that the rate of reaction depends upon ‘x’ concentration terms of A and ‘y’ concentration terms of B. Then,
If [A] = [B] = 1. The, Rate = k
So, rate constant (k) can be defined as the rate of reaction when the initial concentration of reactant is unit.
Units of Rate constant:
Order and Molecularity of a Reaction
Order of reaction:
The order of reaction is defined as the sum of powers of all concentration terms in the rate law equation.
Order of reaction may also be defined as “the total number of concentration variables which affect the rate of reaction.
1. Zero order reaction:
The reaction whose rate does not depend upon the concentration of the any reactant is known as zero order reaction.
2.First order reaction :
The reaction whose rate depends upon the concentration of only one reactant variable is known as first order reaction.
3. Second order reaction:
The reaction whose rate depends upon two concentration variables is known as second order reaction.
4. Third order reaction:
The reaction whose rate depends upon three concentration variables is known as third order reaction.
Molecularity of Reaction :
The total number of chemical species involved in the rate determining step of the reaction is called molecularity of the reaction. For example,
If the molecularity of reaction is 1, the reaction is unimolecular. If the molecularity is 2, the reaction is bimolecular and so on.
Differences between molecularity and order of reaction:
Rate expression for first order reaction
Half life period (t1/2)
Time required to decompose exactly half of the initial concentration of reactant is known as half life period. It is denoted by t1/2.
Half life period of first order reaction is:
Pseudo first order reaction (Pseudo unimolecular reaction)
The reaction of higher order which follows the kinetics of first order under special conditions is called pseudo first order reaction or pseudo unimolecular reaction.
In other words, the reaction in which molecularity is more than one and is found to be first order is known as pseudo unimolecular reaction.
For example, acidic hydrolysis of ester is a pseudo first order reaction.
Activation Energy (Ea) and Activated complex
The minimum amount of energy required by the reactant to change into product is called activation energy.
OR, The minimum amount of energy which must be supplied to the reactants to enable them to cross over the energy barrier is called activation energy.
If the activation energy is higher in a reaction then slower will be the rate of reaction.
The highest energy state in a chemical reaction in which old bonds are broken and new bonds are formed is called transition state.
The chemical complex formed at highest energy state (i.e. transition state) in a chemical reaction and is highly unstable in nature is called activated complex.
Factors affecting the rate of reaction
The following factors influence the rate of a reaction:
1. Concentration of reactants: The rate of reaction increases with the increase in concentration of reactant except zero order reactions. The chance of collision between reactant molecules to give products increases with the increase in number of reactant particles.
2. Temperature : The increase in temperature generally increase the rate of reaction because increasing temperature increases kinetic energy of reactant molecule and more fraction of molecules become able to cross activation energy barrier to give product.
Experimentally, it has been found that the rate of reaction increases by 2 or 3 times with every rise in temperature by 100C.
3.Surface area of reactant: The rate of reaction increases with increase in total surface area since the reactive site increases. For example, reaction between a marble piece (CaCO3) and dil. HCl is very slow but CaCO3 powder with dil. HCl is very fast.
4. Catalyst : The rate of a reaction can be increased by adding catalyst. A catalyst is a substance which provides a new path for the reaction with lower activation energy and speeds up the reaction.
Collision theory of reaction rate
To occur a reaction there must be collision between the reacting molecules. But all the molecules which collide do not necessary to give products.
Only a certain fraction of total number collisions are capable to give products, such collisions are called effective collisions. Conditions for effective collisions are:
i. The reacting species should have sufficient energy to break the chemical bonds in the reacting molecules.
The minimum amount of energy which the colliding molecules must possess is known as threshold energy. This means only those collisions will give products which possesses energy greater than threshold energy.
ii. The colliding species should have proper orientation so that old bonds existing between reacting species may break and new bonds are formed.
For example: During the reaction between CO and NO2 the products are formed only only when the colliding molecules have proper orientation at the time of collision.
Thus, the collision in which the colliding molecules do not posses the minimum energy for effective collisions (threshold energy) or proper orientation do not form products.
Numerical Problems
Use rate law equation
1. In a reaction H2 (g) + I2 (g) → 2HI (g), the rate of disappearance of I2 is found to be 1×10-6 molL-1sec-1. What will be the corresponding rate of appearance of HI?
2. The reaction X+Y → Product is a second order reaction. Write three different rate law expressions which may be true to the above reaction.
3. For a given reaction, A + B → Product, the rate law is found to be, Rate = K[A]1 [B]2. What happens to the rate of the reaction when
a. Concentration of both A and B are doubled.
b. Concentration of A is doubled and that of B remains constant.
c. Concentration of A is halved and that of B is doubled.
4. The following experimental data are obtained in the college laboratory for the reaction, 2A + B2 → 2AB
|
Expt. No. |
[A] mol L-1 | [B2] mol L-1 |
Rate mol L-1 Sec-1 |
|
1. |
0.5 |
0.5 |
1.6×10-4 |
|
2. |
0.5 |
1 |
3.2×10-4 |
|
3. |
1 |
1 |
3.2×10-4 |
a. What is the order for A and B2 and overall order?
b. Calculate the rate constant.
c. Find the rate law.
d. Calculate the rate of formation of AB if the concentration of A and B2 are 2.0 and 4.0 mol L-1 respectively.
e. Why are chemists interested in obtaining an order of reaction and rate equation?
5. The experimental data for the reaction 2A + B → C is
|
Expt. No. |
[A] mol L-1 | [B2] mol L-1 |
Rate mol L-1 Sec-1 |
|
1. |
0.1 |
0.1 |
7×10-3 |
|
2. |
0.3 |
0.2 |
8.4×10-2 |
|
3. |
0.3 |
0.4 |
3.36×10-1 |
|
4. |
0.4 |
0.1 |
2.8×10-2 |
Determine:-
a. Overall order of reaction.
b. Rate law equation
c. Calculate the rate of formation of C when concentration of [A] and [B] are 0.6 mol L-1 and 0.3 mol L-1 respectively.
6. The reaction between A and B is first order with respect to A and zero order with respect to B. Complete the following table.
|
Expt. No. |
[A] mol L-1 | [B2] mol L-1 |
Rate mol L-1 Sec-1 |
|
1. |
0.1 |
0.1 |
2.0×10-2 |
|
2. |
– |
0.2 |
4.0×10-2 |
|
3. |
0.4 |
0.4 |
– |
|
4. |
– |
0.2 |
2.0×10-2 |
Numerical using first order rate expression
7. A first order reaction has a rate constant of 1.15×10-3 S-1. Calculate the time required for 5 gm of this reactant to reduce to 3 gm.
8. The half life period of first order reaction is 3 hours. Find the time required to complete 87.5% of the reaction.
9. When 50% of reactant in the first order reaction disappears in 20 minutes, find the time taken only when 12.5% of the reactant will have remained.
10. Show that the time required for a first order reaction for 99.9% completion is almost 10 times than required for 50% completion.
11. For a first order reaction, the rate constant is 2.2×10-5 sec-1. Calculate the fraction of the reactant consumed in 1 hour and 30 minutes.
Numerical using Arrhenius Equation
12. Calculate the energy of activation of a reaction if its rate constant doubles when the temperature is raised from 170C to 270C.
13. The rate constant of a first order reaction becomes 5 times when the temperature is raised from 350 K to 400 K. Calculate the activation energy for the reaction.
