Chemical Kinetics - Order Of Reaction

Chemical Kinetics - Order of reaction

Chemical kinetics is the branch of chemistry that studies the rate at which reactions occur.
The order of a reaction refers to the relationship between the concentrations of the reactants and the rate of the reaction.
The order of a reaction can be determined experimentally and is represented by the rate equation.
The rate equation is of the form: rate = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are the concentrations of the reactants, and m and n are the orders of reaction with respect to A and B, respectively.
The overall order of reaction is the sum of the individual orders: overall order = m + n.

Determination of Order of Reaction

The order of a reaction can be determined experimentally by the method of initial rates.
In the method of initial rates, the concentrations of the reactants are varied while keeping the concentration of other reactants constant, and the initial rate of the reaction is measured.
By comparing the initial rates at different concentrations, the order of reaction with respect to each reactant can be determined.
For example, if doubling the concentration of reactant A doubles the initial rate, the order of reaction with respect to A is 1.
Similarly, if doubling the concentration of reactant B quadruples the initial rate, the order of reaction with respect to B is 2.
The overall order of reaction is the sum of the orders with respect to each reactant.

Zero Order Reactions

In a zero order reaction, the rate of the reaction is independent of the concentration of the reactant.
The rate equation for a zero order reaction is: rate = k[A]^0 = k.
This means that the rate of the reaction remains constant throughout the reaction.
Examples of zero order reactions include the decomposition of ozone (O3), the decomposition of hydrogen peroxide (H2O2), and the reaction between nitric oxide (NO) and hydrogen (H2).
The half-life of a zero order reaction can be calculated using the equation: t1/2 = [A]0 / 2k, where [A]0 is the initial concentration of the reactant.

First Order Reactions

In a first order reaction, the rate of the reaction is directly proportional to the concentration of the reactant.
The rate equation for a first order reaction is: rate = k[A]^1 = k[A].
This means that as the concentration of the reactant increases, the rate of the reaction also increases.
The half-life of a first order reaction is inversely proportional to the initial concentration of the reactant: t1/2 = 0.693 / k.
Examples of first order reactions include radioactive decay and the hydrolysis of esters.

Second Order Reactions

In a second order reaction, the rate of the reaction is directly proportional to the square of the concentration of the reactant.
The rate equation for a second order reaction is: rate = k[A]^2.
This means that as the concentration of the reactant increases, the rate of the reaction increases exponentially.
The half-life of a second order reaction is inversely proportional to the initial concentration of the reactant: t1/2 = 1 / k[A]0.
Examples of second order reactions include the reaction between two different reactants and the disproportionation of a single reactant.

Determination of Order of Reaction from Graph

The order of a reaction can also be determined from the graph of concentration vs. time.
For a zero order reaction, the concentration decreases linearly with time.
For a first order reaction, the concentration decreases exponentially with time.
For a second order reaction, the concentration decreases faster than exponential with time.
By analyzing the graph of concentration vs. time, the order of reaction can be determined.
The rate constant can be calculated by using the following equation: k = 0.693 / t1/2.

Integrated Rate Laws

Integrated rate laws represent the relationship between the concentration of a reactant and time for a given order of reaction.
For a zero order reaction, the integrated rate law is: [A] = [A]0 - kt.
For a first order reaction, the integrated rate law is: ln[A] = -kt + ln[A]0.
For a second order reaction, the integrated rate law is: 1/[A] = kt + 1/[A]0.
These integrated rate laws can be used to determine the concentration of the reactant at a given time or the time required for a given concentration.
These equations can also be used to determine the rate constant of the reaction.

Arrhenius Equation

The Arrhenius equation relates the rate constant of a reaction to the temperature and activation energy.
The Arrhenius equation is: k = Ae^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature.
This equation shows that the rate constant increases exponentially with increasing temperature.
By plotting ln(k) vs. 1/T, the activation energy can be determined from the slope of the graph.
The Arrhenius equation is used to calculate the rate constant for a reaction at different temperatures.

Collision Theory

The collision theory explains how chemical reactions occur at the molecular level.
According to the collision theory, for a reaction to occur, reactant particles must collide with each other in an effective collision.
An effective collision is one in which the particles have sufficient energy and the correct orientation.
The rate of a reaction is directly proportional to the number of effective collisions per unit time.
Factors that affect the rate of reaction include concentration, temperature, surface area, and presence of a catalyst.

Rate Equation and Rate Constant

The rate equation relates the rate of a reaction to the concentration of the reactants.
Rate equation: rate = k[A]^m[B]^n
[A] and [B] are the concentrations of reactants A and B, respectively.
m and n are the orders of reaction with respect to A and B.
The rate constant (k) is a proportionality constant specific to a particular reaction.

Determination of Rate Equation

The rate equation can be determined experimentally by measuring the initial rates of the reaction.
The initial rates are measured with different concentrations of reactants and the results are compared.
For example, if doubling the concentration of A doubles the initial rate, A is first order.
By repeating this process for all reactants, the rate equation can be determined.

Examples of Rate Equations

Example 1: rate = k[NO2]^2[H2]
Example 2: rate = k[NH3]^3[O2]

Overall Order of Reaction

The overall order of a reaction is the sum of the orders of each reactant.
For example, if the order with respect to A is 2 and with respect to B is 1, the overall order is 3.
The rate equation would be rate = k[A]^2[B]^1.

Reaction Order and Reaction Rate

The order of a reaction with respect to a reactant determines how its concentration affects the rate of the reaction.
Zero-order: Concentration doesn’t affect rate.
First-order: Rate increases linearly with concentration.
Second-order: Rate increases exponentially with concentration.

Half-life of a Reaction

The half-life of a reaction is the time required for the concentration of a reactant to decrease by half.
For zero-order reactions: t1/2 = [A]0 / 2k
For first-order reactions: t1/2 = 0.693 / k
For second-order reactions: t1/2 = 1 / k[A]0

Determining Order from Experimental Data

Plotting concentration vs. time allows us to determine the order of a reaction.
Zero order: Straight line with constant slope.
First order: Exponential decay curve.
Second order: Steeper than exponential decay curve.

Integrated Rate Laws for Zero-Order Reactions

The integrated rate law for a zero-order reaction is: [A] = [A]0 - kt.
It shows how the concentration of reactant A changes over time.
[A]0 is the initial concentration of reactant A, k is the rate constant, and t is time.

Integrated Rate Laws for First-Order Reactions

The integrated rate law for a first-order reaction is: ln[A] = -kt + ln[A]0.
It shows how the natural logarithm of the concentration of reactant A changes over time.
[A]0 is the initial concentration of reactant A, k is the rate constant, and t is time.

Integrated Rate Laws for Second-Order Reactions

The integrated rate law for a second-order reaction is: 1/[A] = kt + 1/[A]0.
It shows how the inverse of the concentration of reactant A changes over time.
[A]0 is the initial concentration of reactant A, k is the rate constant, and t is time.

Slide 21

The rate constant (k) represents the speed of the reaction at a given temperature.
It is specific to a particular reaction and is independent of reactant concentration.
The value of k depends on the temperature and can be determined experimentally.

Slide 22

The rate constant can be calculated using the Arrhenius equation: k = Ae^(-Ea/RT).
A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
The Arrhenius equation shows that as the temperature increases, the rate constant increases exponentially.
By plotting the natural logarithm of the rate constant (ln(k)) against the reciprocal of temperature (1/T), the activation energy can be determined.

Slide 23

Activation energy (Ea) is the minimum energy required for a reaction to occur.
It represents the energy barrier that reactant molecules must overcome to form products.
Reactant molecules need to collide with sufficient energy and the correct orientation to overcome the activation energy barrier.

Slide 24

Catalysts are substances that increase the rate of a reaction by lowering the activation energy.
Catalysts provide an alternative reaction pathway with a lower energy barrier.
They do not participate in the reaction and remain unchanged at the end.
Catalysts increase the rate of both forward and reverse reactions, thereby aiding equilibrium as well.

Slide 25

Homogeneous catalysts are in the same phase as the reactants and can interact directly with them.
Heterogeneous catalysts are in a different phase and typically adsorb reactant molecules onto their surface, facilitating the reaction.
Enzymes are biological catalysts that are highly specific for certain reactions and decrease the activation energy in biological systems.

Slide 26

Factors affecting the rate of a reaction include concentration, temperature, surface area, and the presence of a catalyst.
Increasing the concentration of reactants leads to more frequent collisions and a higher reaction rate (except for zero-order reactions).
Higher temperatures provide reactant molecules with greater kinetic energy, increasing the chances of effective collisions.
By increasing the surface area of solid reactants, more reactant particles are exposed to each other, resulting in a higher reaction rate.

Slide 27

The rate-determining step is the slowest step in a reaction mechanism and determines the overall rate of the reaction.
It involves the highest activation energy and is responsible for the rate expression.
The rate equation is derived from the slowest elementary step in the reaction mechanism.

Slide 28

Reaction mechanisms depict the step-by-step sequence in which reactants are converted to products.
Elementary steps are individual molecular events with distinct reaction equations.
The overall chemical equation is the sum of the elementary steps.
Intermediates are species formed and consumed within the reaction mechanism.

Slide 29

The rate equation and reaction mechanism can be used to predict the effect of changing reaction conditions on the rate of a reaction.
For example, increasing the concentration of a reactant involved in the rate-determining step will increase the reaction rate.
Understanding the reaction mechanism allows for the optimization of reaction conditions to achieve desired reaction rates.

Slide 30

In summary, the order of a reaction determines the relationship between reactant concentration and reaction rate.
The rate equation represents this relationship and can be determined experimentally.
The rate constant is specific to a particular reaction and can be calculated using the Arrhenius equation.
Catalysts, activation energy, and other factors affect the rate of reactions.
Reaction mechanisms provide a detailed understanding of the steps involved in a reaction.