Chemical Kinetics- - Examples For Rate Determining Step

Chemical Kinetics

Examples for rate determining step

The rate determining step is the slowest step in a chemical reaction.
It determines the overall rate of the reaction.
The overall reaction rate cannot exceed the rate of the rate determining step. Example 1:
Consider the reaction A + B -> C
The rate determining step involves the collision of A and B to form an activated complex. Example 2:
In the reaction 2A + B -> C + D, the rate determining step involves the collision of two A molecules. Example 3:
For the reaction A + 2B -> C, the rate determining step involves the collision of one A molecule and two B molecules. Example 4:
In the reaction A + B -> C + D + E, the rate determining step involves the collision of one A molecule and one B molecule. Example 5:
For the reaction A + B + C -> D + E, the rate determining step involves the collision of one A molecule, one B molecule, and one C molecule.

Activation Energy

Explanation and Calculation

Activation energy (Ea) is the energy required for a reaction to occur.
It is the minimum energy barrier that reactant molecules must overcome to convert into products.
The rate of reaction is directly proportional to the activation energy. Calculating Activation Energy:
The Arrhenius equation relates the rate constant (k), activation energy (Ea), temperature (T), and the pre-exponential factor (A).
The equation is given as: k = A * e^((-Ea) / (RT)), where R is the gas constant. Example:
Given a reaction with a rate constant of 2.5 x 10^(-3) s^(-1) at 273 K and 1.5 x 10^(-2) s^(-1) at 303 K.
Using both values to calculate the activation energy, rearrange the Arrhenius equation and solve for Ea.

Rate Laws

Determining Rate Expressions

Rate laws describe the relationship between the rate of a reaction and the concentrations of reactants.
The rate law equation is written as: rate = k[A]^m[B]^n, where k is the rate constant and m and n are the reaction orders. Zero Order Reactions:
In a zero order reaction, the reaction rate is independent of the concentration of the reactants.
The rate law equation is written as: rate = k. First Order Reactions:
In a first order reaction, the reaction rate is directly proportional to the concentration of one reactant.
The rate law equation is written as: rate = k[A]. Second Order Reactions:
In a second order reaction, the reaction rate is directly proportional to the square of the concentration of one reactant or the product of the concentration of two reactants.
The rate law equation is written as: rate = k[A]^2 or rate = k[A][B].

Reaction Mechanisms

Elementary Steps and Overall Reaction

A reaction mechanism is a series of elementary steps that together make up the overall reaction.
Each elementary step involves the collision of molecules to form transient species called intermediates.
The overall reaction represents the sum of the elementary steps. Example: Reaction: A + B -> C Mechanism:

A + B -> Intermediate 1

Intermediate 1 -> C Overall Reaction:

The overall reaction is the sum of the elementary steps.
In this case, the overall reaction is A + B -> C.

Reaction Rate and Temperature

Relationship and Effect

The rate of a chemical reaction is influenced by temperature.
An increase in temperature generally increases the reaction rate.
This is due to an increase in the kinetic energy of the reactant molecules. Effect of Temperature on Rate:
Increasing the temperature leads to more frequent and forceful collisions between reactant molecules.
This increases the chance of effective collisions, leading to a higher reaction rate. Activation Energy and Temperature:
Activation energy (Ea) determines the temperature dependence of the reaction rate.
A higher activation energy requires a greater increase in temperature to significantly speed up the reaction rate.
A lower activation energy means the reaction rate is more sensitive to temperature changes.

Catalysts and Reaction Rate

Mechanism and Effect

A catalyst is a substance that increases the rate of a chemical reaction without being consumed during the reaction.
Catalysts work by providing an alternative reaction pathway with a lower activation energy.
This lowers the energy barrier for the reaction to occur, resulting in a faster reaction rate. Mechanism of Catalysis:
Catalysts provide an alternate pathway for the reaction, creating a new reaction intermediate.
This new intermediate has a lower energy barrier compared to the uncatalyzed reaction.
By providing this lower energy pathway, the catalyst increases the reaction rate. Effect of Catalysts:
Catalysts can significantly increase reaction rates, leading to faster reactions.
They can also work selectively, promoting specific reactions while leaving others unaffected.
Catalysts are not consumed in the reaction and can be reused.

Factors Affecting Reaction Rate

Concentration, Surface Area, and Pressure

Concentration:

Increasing the concentration of reactants increases the rate of a reaction.
This is because it provides more reactant molecules, leading to more collisions and a higher chance of effective collisions.

Surface Area:

Increasing the surface area of solid reactants increases the rate of a reaction.
This is because more surface area allows for more collisions with other reactant molecules.

Pressure:

For gas-phase reactions, increasing the pressure increases the rate of reaction.
Higher pressure increases the number of gas molecules per unit volume, resulting in more frequent collisions and a higher chance of effective collisions.

Reaction Rate and Concentration

Kinetics and Stoichiometry

The rate of a reaction is directly proportional to the concentration of reactants.
This relationship is determined by the stoichiometric coefficients in the balanced chemical equation. Rate and Stoichiometry:
In a balanced chemical equation, the stoichiometric coefficients represent the ratios of reactants and products.
The rate of the reaction is directly related to the concentrations of the reactants involved in the rate-determining step. Example:
For the reaction A + 3B -> 2C, the rate expression is rate = k[A][B]^3.
The stoichiometric coefficients of 1 for A and 3 for B correspond to their respective powers in the rate expression.

Rate Laws and Reaction Orders

Experimental Determination

The rate law equation describes the relationship between the concentration of reactants and the rate of a reaction.
The reaction order represents the power or exponent of the concentration term in the rate law equation. Determining Reaction Order:
The reaction order for each reactant can be determined experimentally.
This is done by varying the concentration of one reactant while keeping the others constant and measuring the corresponding change in rate. Method of Initial Rates:
The initial rates of the reaction are measured for different reactant concentrations.
The reaction order can be determined by comparing the change in rate with the corresponding change in concentration.

Integrated Rate Laws

Relation between Concentration and Time

Integrated rate laws show the relationship between the concentration of reactants and products over a certain period of time.
They are derived from the rate laws and help determine the reaction order and rate constant. Zero Order Reactions:
In a zero order reaction, the concentration of the reactant decreases linearly with time.
The integrated rate law equation is written as: [A] = [A]0 - kt. First Order Reactions:
In a first order reaction, the concentration of the reactant decreases exponentially with time.
The integrated rate law equation is written as: ln[A] = -kt + ln[A]0. Second Order Reactions:
In a second order reaction, the concentration of the reactant decreases with time, following an inverse relationship.
The integrated rate law equation is written as: 1/[A] = kt + 1/[A]0.

Half-Life of Reactions

Time for Half of Reactant to React

Half-life is the time required for half of the reactant to undergo reaction.
It is a useful parameter to understand the rate of a reaction and compare different reactions. Zero Order Reactions:
In a zero order reaction, the half-life is inversely proportional to the initial concentration.
The equation for the half-life is t1/2 = [A]0 / 2k. First Order Reactions:
In a first order reaction, the half-life is a constant and does not depend on the initial concentration.
The equation for the half-life is t1/2 = 0.693 / k. Second Order Reactions:
In a second order reaction, the half-life is inversely proportional to the initial concentration squared.
The equation for the half-life is t1/2 = 1 / (k[A]0).

Chemical Kinetics

Examples for rate determining step

The rate determining step is the slowest step in a chemical reaction.
It determines the overall rate of the reaction.
The overall reaction rate cannot exceed the rate of the rate determining step. Example 1:
Consider the reaction A + B -> C
The rate determining step involves the collision of A and B to form an activated complex. Example 2:
In the reaction 2A + B -> C + D, the rate determining step involves the collision of two A molecules. Example 3:
For the reaction A + 2B -> C, the rate determining step involves the collision of one A molecule and two B molecules. Example 4:
In the reaction A + B -> C + D + E, the rate determining step involves the collision of one A molecule and one B molecule. Example 5:
For the reaction A + B + C -> D + E, the rate determining step involves the collision of one A molecule, one B molecule, and one C molecule.

Activation Energy

Explanation and Calculation

Activation energy (Ea) is the energy required for a reaction to occur.
It is the minimum energy barrier that reactant molecules must overcome to convert into products.
The rate of reaction is directly proportional to the activation energy. Calculating Activation Energy:
The Arrhenius equation relates the rate constant (k), activation energy (Ea), temperature (T), and the pre-exponential factor (A).
The equation is given as: k = A * e^((-Ea) / (RT)), where R is the gas constant. Example:
Given a reaction with a rate constant of 2.5 x 10^(-3) s^(-1) at 273 K and 1.5 x 10^(-2) s^(-1) at 303 K.
Using both values to calculate the activation energy, rearrange the Arrhenius equation and solve for Ea.

Rate Laws

Determining Rate Expressions

Rate laws describe the relationship between the rate of a reaction and the concentrations of reactants.
The rate law equation is written as: rate = k[A]^m[B]^n, where k is the rate constant and m and n are the reaction orders. Zero Order Reactions:
In a zero order reaction, the reaction rate is independent of the concentration of the reactants.
The rate law equation is written as: rate = k. First Order Reactions:
In a first order reaction, the reaction rate is directly proportional to the concentration of one reactant.
The rate law equation is written as: rate = k[A]. Second Order Reactions:
In a second order reaction, the reaction rate is directly proportional to the square of the concentration of one reactant or the product of the concentration of two reactants.
The rate law equation is written as: rate = k[A]^2 or rate = k[A][B].

Reaction Mechanisms

Elementary Steps and Overall Reaction

A reaction mechanism is a series of elementary steps that together make up the overall reaction.
Each elementary step involves the collision of molecules to form transient species called intermediates.
The overall reaction represents the sum of the elementary steps. Example: Reaction: A + B -> C Mechanism:

A + B -> Intermediate 1

Intermediate 1 -> C Overall Reaction:

The overall reaction is the sum of the elementary steps.
In this case, the overall reaction is A + B -> C.

Reaction Rate and Temperature

Relationship and Effect

The rate of a chemical reaction is influenced by temperature.
An increase in temperature generally increases the reaction rate.
This is due to an increase in the kinetic energy of the reactant molecules. Effect of Temperature on Rate:
Increasing the temperature leads to more frequent and forceful collisions between reactant molecules.
This increases the chance of effective collisions, leading to a higher reaction rate. Activation Energy and Temperature:
Activation energy (Ea) determines the temperature dependence of the reaction rate.
A higher activation energy requires a greater increase in temperature to significantly speed up the reaction rate.
A lower activation energy means the reaction rate is more sensitive to temperature changes.

Catalysts and Reaction Rate

Mechanism and Effect

A catalyst is a substance that increases the rate of a chemical reaction without being consumed during the reaction.
Catalysts work by providing an alternative reaction pathway with a lower activation energy.
This lowers the energy barrier for the reaction to occur, resulting in a faster reaction rate. Mechanism of Catalysis:
Catalysts provide an alternate pathway for the reaction, creating a new reaction intermediate.
This new intermediate has a lower energy barrier compared to the uncatalyzed reaction.
By providing this lower energy pathway, the catalyst increases the reaction rate. Effect of Catalysts:
Catalysts can significantly increase reaction rates, leading to faster reactions.
They can also work selectively, promoting specific reactions while leaving others unaffected.
Catalysts are not consumed in the reaction and can be reused.

Factors Affecting Reaction Rate

Concentration, Surface Area, and Pressure

Concentration:

Increasing the concentration of reactants increases the rate of a reaction.
This is because it provides more reactant molecules, leading to more collisions and a higher chance of effective collisions.

Surface Area:

Increasing the surface area of solid reactants increases the rate of a reaction.
This is because more surface area allows for more collisions with other reactant molecules.

Pressure:

For gas-phase reactions, increasing the pressure increases the rate of reaction.
Higher pressure increases the number of gas molecules per unit volume, resulting in more frequent collisions and a higher chance of effective collisions.

Reaction Rate and Concentration

Kinetics and Stoichiometry

The rate of a reaction is directly proportional to the concentration of reactants.
This relationship is determined by the stoichiometric coefficients in the balanced chemical equation. Rate and Stoichiometry:
In a balanced chemical equation, the stoichiometric coefficients represent the ratios of reactants and products.
The rate of the reaction is directly related to the concentrations of the reactants involved in the rate-determining step. Example:
For the reaction A + 3B -> 2C, the rate expression is rate = k[A][B]^3.
The stoichiometric coefficients of 1 for A and 3 for B correspond to their respective powers in the rate expression.

Chemical Kinetics

Examples for rate determining step

The rate determining step is the slowest step in a chemical reaction.
It determines the overall rate of the reaction.
The overall reaction rate cannot exceed the rate of the rate determining step. Example 1:
Consider the reaction A + B -> C.
The rate determining step involves the collision of A and B to form an activated complex. Example 2:
In the reaction 2A + B -> C + D, the rate determining step involves the collision of two A molecules. Example 3:
For the reaction A + 2B -> C, the rate determining step involves the collision of one A molecule and two B molecules. Example 4:
In the reaction A + B -> C + D + E, the rate determining step involves the collision of one A molecule and one B molecule. Example 5:
For the reaction A + B + C -> D + E, the rate determining step involves the collision of one A molecule, one B molecule, and one C molecule.

Activation Energy

Explanation and Calculation

Activation energy (Ea) is the energy required for a reaction to occur.
It is the minimum energy barrier that reactant molecules must overcome to convert into products.
The rate of reaction is directly proportional to the activation energy. Calculating Activation Energy:
The Arrhenius equation relates the rate constant (k), activation