Chemical Kinetics- - More About Molecularity

Chemical Kinetics - More about Molecularity

So far, we have discussed the basics of chemical kinetics
Let’s dive deeper into the topic and learn about molecularity
Molecularity describes the number of molecules reacting in an elementary step of a reaction
It helps us understand the order of the reaction and the rate law equation

Molecularity 1: Unimolecular Reactions

A unimolecular reaction involves the decomposition of a single molecule
The rate equation for a unimolecular reaction is typically first-order
Example: Decomposition of $ A $ follows the equation: $ A \rightarrow P $ (where $ P $ is the product)

Molecularity 2: Bimolecular Reactions

A bimolecular reaction involves the collision of two molecules
The rate equation for a bimolecular reaction is typically second-order
Example: The reaction between $ A $ and $ B $ follows the equation: $ A + B \rightarrow P $ (where $ P $ is the product)

Molecularity 3: Termolecular Reactions

A termolecular reaction involves the collision of three molecules
Termolecular reactions are relatively rare due to the lower probability of three molecules colliding simultaneously
The rate equation for a termolecular reaction is typically third-order
Example: The reaction between $ A $ , $ B $ , and $ C $ follows the equation: $ A + B + C \rightarrow P $ (where $ P $ is the product)

Elementary Steps and the Overall Reaction

The overall reaction can be made up of multiple elementary steps
Each elementary step has its own rate equation and molecularity
The overall reaction rate is determined by the slowest elementary step, known as the rate-determining step

Rate Law Equation

The rate law equation relates the rate of a reaction to the concentrations of reactants
The rate law equation is determined experimentally
The general form of a rate law equation is: Rate = k[A]^m[B]^n
The exponents (m and n) indicate the order of the reaction with respect to each reactant

Determining the Rate Law

The rate law can be determined by the method of initial rates
In this method, the initial rates of reaction are measured for different initial concentrations of reactants
By comparing the rates, we can determine the order of the reaction with respect to each reactant

Determining the Rate Constant

The rate constant (k) is a proportionality constant in the rate law equation
It depends on temperature and the presence of a catalyst
The rate constant can be determined by plotting experimental data and using integrated rate laws

Integrated Rate Laws

Integrated rate laws relate the concentration of reactants or products to time
The integrated rate law equations differ based on the order of the reaction
These equations can be used to determine the concentration of reactants or products at any given time

Half-Life

The half-life of a reaction is the time required for half of the reactant to be consumed or half of the product to be formed
Half-life is a useful concept for understanding the progress of a reaction
It can be calculated using the rate constant and the initial reactant concentration

Rate-Determining Step

The rate-determining step is the slowest step in a reaction mechanism
It determines the overall rate of the reaction
The rate equation of the overall reaction is based on the rate-determining step
Rate-determining step often involves higher activation energy

Collision Theory

Collision theory explains the factors that influence the rate of a chemical reaction
According to collision theory, reactions occur when particles collide with sufficient energy and proper orientation
Factors affecting reaction rate include: temperature, concentration, surface area, and presence of a catalyst
Increased temperature and concentration increase the rate of collisions, leading to a faster reaction
Catalysts provide an alternate pathway with lower activation energy, increasing the reaction rate

Rate Law Example 1

Consider the reaction: 2A + B →C
The rate law for this reaction is determined experimentally: Rate = k[A]^2[B]
The order of the reaction with respect to A is 2, and with respect to B is 1
The overall order of the reaction is 2 + 1 = 3

Rate Law Example 2

Consider the reaction: A + B → C + D
The rate law for this reaction is determined experimentally: Rate = k[A][B]^2
The order of the reaction with respect to A is 1, and with respect to B is 2
The overall order of the reaction is 1 + 2 = 3

Rate Law Example 3

Consider the reaction: A + 2B → C + D
The rate law for this reaction is determined experimentally: Rate = k[A][B]^2
The order of the reaction with respect to A is 1, and with respect to B is 2
The overall order of the reaction is 1 + 2 = 3

Determining the Rate Constant

The rate constant (k) is specific for each reaction and temperature
It can be determined experimentally by measuring the rate of reaction at different concentrations and temperatures
The units of the rate constant depend on the overall order of the reaction
The rate constant is affected by temperature and activation energy

Integrated Rate Laws for First-Order Reactions

For a first-order reaction, the rate equation is: Rate = k[A]
The integrated rate law for a first-order reaction is: ln[A]t = -kt + ln[A]0
The half-life (t1/2) of a first-order reaction is: t1/2 = 0.693/k

Integrated Rate Laws for Second-Order Reactions

For a second-order reaction, the rate equation is: Rate = k[A]^2
The integrated rate law for a second-order reaction is: 1/[A]t = kt + 1/[A]0
The half-life (t1/2) of a second-order reaction is: t1/2 = 1/(k[A]0)

Integrated Rate Laws for Zero-Order Reactions

For a zero-order reaction, the rate equation is: Rate = k[A]^0 = k
The integrated rate law for a zero-order reaction is: [A]t = -kt + [A]0
The half-life (t1/2) of a zero-order reaction is: t1/2 = [A]0/(2k)

Summary

Molecularity describes the number of molecules involved in an elementary step
Unimolecular reactions have a rate equation of first order
Bimolecular reactions have a rate equation of second order
Termolecular reactions have a rate equation of third order but are relatively rare
Rate laws describe the relationship between reactant concentrations and the rate of reaction

Integrated Rate Laws for Higher-Order Reactions

For reactions with orders higher than first or second, the integrated rate laws become more complicated
The integrated rate law equations involve higher powers of concentrations or multiple terms
These equations can be derived by solving the differential rate equation for the specific order of the reaction

Determining the Order of a Reaction

The order of a reaction can be determined by inspecting the rate equation or experimentally
In the rate equation, the exponents indicate the order with respect to each reactant
Experimentally, the order can be determined by measuring the initial rates at different concentrations and comparing them

Comparison of Reaction Orders

By comparing the rate equations of different reactions, we can determine the relative order of the reactions
We consider the exponents and the overall order of the reactions
Reaction orders determine the mechanism and the rate-determining step of the reaction

Factors Affecting Reaction Rates

Temperature: Increasing temperature generally increases the reaction rate as it provides more kinetic energy for collisions
Concentration: Higher reactant concentrations increase the rate by increasing the frequency of collisions
Surface area: Increased surface area can enhance reaction rates by providing more contact surface for collisions
Catalysts: Catalysts increase the rate of reaction by providing an alternate pathway with lower activation energy

Arrhenius Equation

The Arrhenius equation relates the rate constant (k) to the temperature (T)
It is given by: k = A * e^(-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 how the rate constant depends on temperature

Activation Energy

Activation energy (Ea) is the minimum energy required for a reaction to occur
Reactant molecules must have sufficient energy to overcome the activation energy barrier and convert into products
Higher activation energy usually leads to slower reactions
Catalysts lower the activation energy by providing an alternative reaction pathway

Effect of Temperature on Reaction Rate

Increasing temperature generally increases the reaction rate
The higher temperature provides more kinetic energy to reactant molecules, increasing the frequency of effective collisions
According to the Arrhenius equation, the rate constant (k) exponentially increases with temperature

Effect of Concentration on Reaction Rate

Increasing the concentration of reactants generally increases the reaction rate
Higher concentrations increase the frequency of collisions between reactant molecules, leading to more successful collisions
This is especially true for reactions with lower orders

Effect of Surface Area on Reaction Rate

Increasing the surface area of reactants generally increases the reaction rate
More surface area provides more contact area for reactant molecules, leading to more collisions and a faster reaction rate
This is particularly relevant for reactions involving solids or heterogeneous mixtures

Effect of Catalysts on Reaction Rates

Catalysts increase the reaction rate by providing an alternative reaction pathway with lower activation energy
They do not participate in the reaction, so they are not consumed
Catalysts can be in different forms (solid, liquid, or gas) depending on the reaction
They can significantly increase reaction rates, making reactions feasible at lower temperatures.