CHAPTER 3: Reaction kinetics

INTRODUCTION

Kinetics, the study of the rates of chemical reactions, has a profound impact on our daily lives. Even though some reactions are thermodynamically favorable, such as the conversion of diamonds into graphite, they do not occur at a measurable rate at room temperature. Kinetics answers questions about rate, how fast reactions go, and mechanisms, the paths molecules take in going from reactants to products.

To describe the rate of a reaction, we will derive the rate law for a chemical reaction and discuss the factors affecting rate. Additionally, we will describe the experimental techniques, such as the method of initial rates and fitting data to plots based on the integrated rate law, used to determine the rate law for an unknown reaction.

so, in this blog we are going to explain more deeper about this topic.

REACTION RATE

• the decrease in reactant concentration , [A],per unit time, 
• the increase in product concentration, [B], per unit time.

In many reactions, the rate of reaction changes as the reaction progresses. Initially the rate of reaction is relatively large, while at very long times the rate of reaction decreases to zero (at which point the reaction is complete). In order to characterize the kinetic behavior of a reaction, it is desirable to determine how the rate of reaction varies as the reaction progresses.

A rate law is a mathematical equation that describes the progress of the reaction. In general, rate laws must be determined experimentally. Unless a reaction is an elementary reaction, it is not possible to predict the rate law from the overall chemical equation. There are two forms of a rate law for chemical kinetics: the differential rate law and the integrated rate law.

The differential rate law relates the rate of reaction to the concentrations of the various species in the system.

Differential rate laws can take on many different forms, especially for complicated chemical reactions. However, most chemical reactions obey one of three differential rate laws. Each rate law contains a constant, k, called the rate constant. The units for the rate constant depend upon the rate law, because the rate always has units of mole L^-1 sec^-1 and the concentration always has units of mole L^-1.

Zero-Order Reaction

For a zero-order reaction, the rate of reaction is a constant. When the limiting reactant is completely consumed, the reaction abrupts stops.

Differential Rate Law:       r = k

The rate constant, k, has units of mole L^-1 sec^-1.

First-Order Reaction

For a first-order reaction, the rate of reaction is directly proportional to the concentration of one of the reactants.

Differential Rate Law:       r = k [A]

The rate constant, k, has units of sec^-1.

Second-Order Reaction

For a second-order reaction, the rate of reaction is directly proportional to the square of the concentration of one of the reactants.

Differential Rate Law:       r = k [A]²

The rate constant, k, has units of L mole^-1 sec^-1.

HALF LIFE

half life of first order reaction 

 For a first order reaction,the half life is a constant and is dependent of the initial concentration

 

half life of zero order reaction

For a zero order reaction,the half life would be half of its initial concentration.

half life of second order reaction

for a second order reaction,the half life is inversely proportional to the initial concentration.

 

COLLISON THEORY AND TRANSITION STATE

The collision theory is based on three ideas :

• molecule must collide to react
• molecules must posses a certain minimum kinetic energy,called the activation energy,to initiate the chemical reaction.Otherwise they are unable to react.
• molecules must collide in the right orientation.

activation energy

-the minimum amount of energy required to initiate a chemical reaction.

 

TRANSITION STATE THEORY

The transition state theory describes what happens to the reactant molecules prior to their change into products.

FACTORS AFFECTING REACTION RATE

1. Surface Area

• As the surface area of the reactants increases, the reaction rate increases.
• WHY?
  • Increasing the surface area of the reactants results in a higher number of reaction sites.
    • Reaction sites - specific sites on molecules at which reactions occur.
  • Increasing the number of reaction sites increases the number of total collisions.
  • The greater the frequency of total collisions, the greater the frequency of effective collisions.
  • If the frequency of effective collisions increases, so does the reaction rate.

2. Temperature

• As the temperature of a system increases, the reaction rate increases.
• WHY?
  • Temperature (T) - A measure of the average kinetic energy (KE_avg) of the particles of a substance.
  • Increasing T increases KE_avg.
  • At higher T, the fraction of molecules with energies greater than the activation energy (E_a) increases.
    • Activation Energy (E_a) - the energy level that must be overcome for a reaction to occur.

3. Catalysts The presence of a catalyst increases the reaction rate. Catalyst - A substance that increases the rate of a reaction but is not consumed in the reaction.  It does so by lowering the activation energy of a reaction. Possible ways of lowering the Ea of a reaction: Increases the frequency of collisions between the reactant molecules. Changes the relative orientation of the reactant molecules. Donates electron density to the reactant molecules. Reduces the intramolecular bonding within the reactant molecules. Provides an alternate pathway or mechanism for the reaction. For equilibrium reactions, both the forward and reverse reaction rates are affected by the catalyst. i.e. the Ea for both directions is decreased. Therefore, the equilibrium constant is not changed by the presence of a catalyst. The relative concentrations of the reactants and products is not changed. Examples of common catalysts: Platinum Nickel Manganese Dioxide (MnO2) 4. Concentration As the concentration of the reactants increases, the reaction rate increases. WHY? According to the collision theory, the rate of a reaction is directly proportional to the number of effective collisions per second between the reactant molecules. Effective Collisions - the fraction of total collisions that actually result in the formation of the product(s). If the concentration of the reactants increases (i.e. particles per given volume) the greater the number of total collisions. The greater the frequency of total collisions, the greater the frequency of effective collisions. If the frequency of effective collisions increases, so does the reaction rate.

5. pressure

Increasing the pressure on a reaction involving reacting gases increases the rate of reaction. Changing the pressure on a reaction which involves only solids or liquids has no effect on the rate.

Effect of temperature on reaction rate: Boltzmann Distribution

Effect of catalyts on activation energy

 

Adding a catalyst has exactly this effect on activation energy. A catalyst provides an alternative route for the reaction. That alternative route has a lower activation energy.
The Arrhenius equation

DETERMINATION OF THE RATE CONSTANT AT A SPECIFIED TEMPERATURE