Chemical Kinetics - Units Of Rate Constants

Chemical Kinetics - Units of rate constants

Rate of a chemical reaction is determined by the rate constant.
Rate constant is the proportionality constant that relates the rate of a reaction to the concentration of reactants.
The unit of rate constant depends on the overall order of the reaction. Zero Order Reaction:
Rate = k[A]⁰ = k
The unit of the rate constant is the concentration per unit time, i.e., mol L⁻¹ s⁻¹. First Order Reaction:
Rate = k[A]
The unit of the rate constant is the reciprocal of time, i.e., s⁻¹. Second Order Reaction:
Rate = k[A]²
The unit of the rate constant is the reciprocal of concentration and time, i.e., L mol⁻¹ s⁻¹. Examples:

Zero Order: Decomposition of H₂O₂, Rate = k[H₂O₂]⁰

First Order: Radioactive decay, Rate = k[N]

Second Order: Reaction between two different reactants, Rate = k[A][B] Equation for Reaction Rate:

The rate equation represents the relationship between the rate of a reaction and the concentrations of reactants.
It is expressed as Rate = k[A]^m[B]^n, where m and n are the orders of reactants A and B, respectively. Overall Order of Reaction:
The overall order of a reaction is the sum of the orders of all reactants in the rate equation.
It determines the unit of the rate constant. Key Points:
Rate constants have different units based on the order of the reaction.
The rate equation represents the relationship between the rate of a reaction and the concentrations of reactants.
The overall order of a reaction is the sum of the orders of all reactants in the rate equation.

Slide 11: Reaction Rate Determining Step

In a multistep reaction, the rate-determining step (RDS) is the slowest step that controls the overall rate of the reaction.
The rate law of the RDS gives the overall rate law for the reaction.
The RDS is typically the step with the highest activation energy.

Slide 12: Collision Theory

The collision theory states that for a reaction to occur, particles must collide with sufficient energy and proper orientation.
The frequency of collisions is directly proportional to the concentration of reactants.
Increasing the concentration or temperature increases the rate of reaction.

Slide 13: Activation Energy

Activation energy is the minimum energy required for a reaction to occur.
It is the energy barrier that separates the reactants from the products.
The Arrhenius equation relates the rate constant to the activation energy.

Slide 14: Factors Affecting Reaction Rate

Concentration: Increasing the concentration of reactants increases the frequency of collisions and thus the rate of reaction.
Temperature: Higher temperature increases the kinetic energy of particles, leading to more collisions and faster reaction rates.
Surface Area: Increasing the surface area of solid reactants increases the number of exposed particles available for reaction.

Slide 15: Catalysts

Catalysts are substances that increase the rate of a reaction by providing an alternative pathway with lower activation energy.
Catalysts remain unchanged at the end of the reaction and can be reused.
They can increase the rate of both exothermic and endothermic reactions.

Slide 16: Rate-Determining Step of Elementary Reactions

Elementary reactions are simple, single-step reactions that occur in one step.
The slowest elementary step determines the rate of the overall reaction.
The rate law of the overall reaction is determined by the stoichiometry of the rate-determining step.

Slide 17: Rate Constant and Temperature

The rate constant increases with increasing temperature.
The relationship between the rate constant and temperature is described by the Arrhenius equation: 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 absolute temperature.

Slide 18: Reaction Mechanisms

Reaction mechanisms are step-by-step sequences of elementary reactions that collectively describe a complex reaction.
Intermediates are produced and consumed during the reaction but are not present in the overall balanced equation.
The rate law for the overall reaction is determined by the slowest step in the reaction mechanism.

Slide 19: Rate Laws and Stoichiometry

The rate law for a reaction does not necessarily match the stoichiometry of the balanced equation.
The rate law is determined experimentally and can be different from the stoichiometric coefficients.
The rate-determining step and reaction mechanism determine the actual rate expression.

Slide 20: Integrated Rate Laws

Integrated rate laws express the concentration of reactants or products as a function of time.
They are derived from the rate law and are useful for determining the order of a reaction.
The integrated rate laws can be linearized to determine the rate constants and reaction orders.

Slide 21: Reaction Rate and Concentration

The rate of a reaction is directly proportional to the concentration of reactants.
The rate equation is written as: Rate = k [A]^m [B]^n
m and n represent the orders of reactants A and B, respectively.
The concentration of reactants can be determined using chemical analysis techniques.
Changes in concentration over time can be used to calculate the rate of reaction.

Slide 22: Effect of Temperature on Rate

Increasing temperature increases the rate of a reaction.
Higher temperature leads to greater kinetic energy of particles, increasing their collision frequency.
The collision energy also increases, allowing a larger fraction of collisions to have sufficient energy to overcome the activation energy barrier.
The Arrhenius equation relates the rate constant (k) to the temperature (T) and activation energy (Ea).

Slide 23: Effect of Surface Area on Rate

Increasing the surface area of solid reactants increases the rate of reaction.
Larger surface area provides more exposed particles available for reactions.
For example, grinding a solid reactant to a powder increases its surface area, leading to higher reaction rates.

Slide 24: Effect of Catalysts on Rate

Catalysts increase the rate of a reaction without being consumed in the process.
They provide an alternative pathway with lower activation energy.
The presence of a catalyst increases the frequency of effective collisions and enhances reaction rates.
Common catalysts include enzymes, transition metals, and acids or bases.

Slide 25: Reaction Mechanisms and Intermediates

Reaction mechanisms describe the series of elementary steps that make up a complex chemical reaction.
Intermediates are reactive species formed and consumed during the reaction steps.
Intermediates are not present in the overall balanced equation.
Determining the reaction mechanism helps understand the rate-determining step and the behavior of intermediates.

Slide 26: Determining Reaction Order and Rate Constant

Reaction order can be determined experimentally by measuring the rate of reaction at different concentrations.
The order with respect to a specific reactant can be found by comparing the rate when its concentration is changed.
The overall reaction order is the sum of the individual orders for each reactant.
The rate constant (k) can be determined from the rate equation and the concentrations of reactants.

Slide 27: Integrated Rate Laws and Half-Life

Integrated rate laws express the concentration of reactants or products as a function of time.
For example, the integrated rate law for a first-order reaction is ln([A]t/[A]0) = -kt.
Half-life (t1/2) is the time required for the concentration of a reactant to decrease to half its initial value.
It can be calculated using the rate constant and integrated rate laws.

Slide 28: Collision Theory and Effective Collisions

The collision theory states that particles must collide with sufficient energy and proper orientation for a reaction to occur.
Not all collisions are effective, meaning they don’t result in a reaction.
Effective collisions have sufficient energy to overcome the activation energy barrier and proper orientation for bond formation.
Increasing temperature and concentration increases the frequency of effective collisions.

Slide 29: Activation Energy and Arrhenius Equation

Activation energy (Ea) is the minimum energy required for a reaction to occur.
It is the energy barrier that separates the reactants from the products.
The Arrhenius equation relates the rate constant (k) to the temperature (T) and activation energy (Ea): k = A * e^(-Ea/RT)
A is the pre-exponential factor related to collision frequency, R is the gas constant, and T is the absolute temperature.

Slide 30: Catalytic Mechanism and Enzymes

Catalysts increase reaction rates by providing an alternative reaction pathway.
Enzymes are biological catalysts that accelerate chemical reactions in living organisms.
Enzymes lower the activation energy by forming enzyme-substrate complexes and stabilizing transition states.
The catalytic mechanism of enzymes involves specific binding sites, induced fit, and enzymatic action.