Chemical Kinetics - Summarising the 3 rates of reaction

• The rate of a chemical reaction measures how quickly the reactants are transformed into products
• There are three different ways to express the rate of a reaction
• Let’s summarize these three rates of reaction in this lecture

Average Rate of Reaction

• The average rate of reaction is calculated by dividing the change in concentration of a reactant or product by the change in time
• It gives the overall rate of reaction over a specific time interval
• It is represented by the equation: Average Rate = (Change in concentration of reactant or product) / (Change in time)
• For example, if the concentration of reactant A decreases by 0.1 M over 10 seconds, the average rate of reaction would be 0.01 M/s

Instantaneous Rate of Reaction

• The instantaneous rate of reaction is the rate of reaction at a specific point in time
• It is determined by calculating the gradient of the tangent to the concentration-time graph at that point
• It gives the rate of reaction at a particular moment
• The equation for instantaneous rate of reaction can be written as: Instantaneous Rate = -d[A] / dt = d[B] / dt (where [A] is the concentration of reactant A, [B] is the concentration of reactant B, and dt is the change in time)

Initial Rate of Reaction

• The initial rate of reaction is the rate of reaction at the start of the reaction
• It is determined by measuring the change in concentration of a reactant or product over a very short time interval
• It provides information about the rate at which the reaction begins
• The equation for initial rate of reaction can be written as: Initial Rate = -d[A] / dt = d[B] / dt (where [A] is the concentration of reactant A, [B] is the concentration of reactant B, and dt is the time interval)

Example: Determining Rates of Reaction

• Let’s consider the reaction: A + B → C
• We can measure the changes in concentration of A, B, and C over different time intervals to determine the rates of reaction
• By dividing the change in concentration by the corresponding time interval, we can calculate the average, instantaneous, and initial rates of reaction for each reactant or product Example Calculation for Reactant A:
  • Time interval 1: Change in [A] = 0.1 M, Change in time = 10 s
  • Average Rate = (0.1 M) / (10 s) = 0.01 M/s
  • Instantaneous Rate at t = 5 s = -d[A] / dt = 0.05 M/s
  • Initial Rate = Instantaneous Rate = 0.05 M/s (Similar calculations can be done for reactant B and product C)

Factors Affecting Rate of Reaction

• There are several factors that can affect the rate of a chemical reaction:
  1. Concentration of reactants: Increasing reactant concentration generally increases the rate of reaction
  2. Temperature: Higher temperatures usually result in faster reaction rates
  3. Surface area: Increasing the surface area of reactants can accelerate the reaction
  4. Catalysts: Certain substances (catalysts) can speed up the rate of reaction without being consumed in the process
• These factors influence the collision frequency and energy collisions, both of which affect the rate of reaction

Collision Theory

• The collision theory explains how chemical reactions occur
• According to this theory, for a reaction to occur, particles must collide with sufficient energy and proper orientation
• The rate of reaction depends on the frequency of effective collisions
• Effective collisions have sufficient energy and correct orientation to break bonds and form new ones
• Activation energy is the minimum energy required for a reaction to occur
• Only particles with energy greater than or equal to the activation energy can undergo a successful collision

Relationship between Rate and Concentration

• In general, the rate of a reaction is directly proportional to the concentration of the reactants
• The rate equation expresses this relationship mathematically
• For a reaction: A + B → C, the rate equation can be written as: Rate = k[A]^m[B]^n (where k is the rate constant, [A] and [B] are the concentrations of reactants A and B respectively, and m and n are the reaction orders) The coefficients m and n are determined experimentally and can be different from the stoichiometric coefficients

Reaction Orders

• The reaction order determines how the concentration of a reactant affects the rate of reaction
• It is determined experimentally and can be zero, positive, or negative
• Zero Order:
  • The rate of reaction is independent of the concentration of the reactant
  • The rate equation is: Rate = k[A]^0 = k (constant)
  • Example: Decomposition of dinitrogen pentoxide
• First Order:
  • The rate of reaction is directly proportional to the concentration of the reactant
  • The rate equation is: Rate = k[A]^1 = k[A]
  • Example: A → B
• Second Order:
  • The rate of reaction is proportional to the square of the concentration of the reactant
  • The rate equation is: Rate = k[A]^2
  • Example: 2A → B (Similar orders can be observed for reactions involving multiple reactants)

Summary

1. The average rate of reaction measures the overall change in concentration over a specific time interval.

2. The instantaneous rate of reaction is the rate at a specific point in time, determined by the gradient of the concentration-time graph.

3. The initial rate of reaction is the rate at the start of the reaction, measured over a short time interval.

4. Factors affecting the rate of reaction include reactant concentration, temperature, surface area, and catalysts.

5. The collision theory explains how reactions occur, emphasizing the importance of effective collisions.

6. The rate equation relates the rate of reaction to the concentrations of reactants, with reaction orders determining their impact on rate.

11. Relationship between Concentration and Rate

• The rate of a chemical reaction is directly proportional to the concentration of the reactants
• This relationship can be expressed using the rate law equation: Rate = k[A]^m[B]^n
• The rate constant, k, depends on the temperature and the specific reaction
• The exponents, m and n, are the reaction orders and can be determined experimentally

12. Example: Reaction Order Calculation

• Consider the reaction: 2A + B → C
• Experimental data gives the following initial rates at different concentrations:
  • [A]0 = 0.1 M, [B]0 = 0.2 M, Rate1 = 0.05 M/s
  • [A]0 = 0.2 M, [B]0 = 0.2 M, Rate2 = 0.2 M/s
• Let’s calculate the reaction orders (m and n) using these data

13. Calculation of Reaction Orders (Continued)

• Using the rate equation: Rate = k[A]^m[B]^n
• For the first set of data:
  • Rate1 = k(0.1)^m(0.2)^n = 0.05 M/s
• For the second set of data:
  • Rate2 = k(0.2)^m(0.2)^n = 0.2 M/s
• Taking the ratio of the two rate equations:
  • Rate2 / Rate1 = (0.2 M/s) / (0.05 M/s) = 4 = (0.2)^m(0.2)^n / (0.1)^m(0.2)^n
• Simplifying the equation, we find:
  • 4 = 2^m
  • m = 2

14. Calculation of Reaction Orders (Continued)

• Substituting the value of m into the equation:
  • 4 = (0.2)^2(0.2)^n / (0.1)^2(0.2)^n
  • 4 = (0.04) / (0.01)(0.2)^n
  • (0.2)^n = (0.04) / (4)(0.01) = 0.01
  • n = 0

15. Rate Law Equation for the Reaction

• Now that we have determined the reaction orders:
  • m = 2, n = 0
• We can write the rate law equation for the reaction as:
  • Rate = k[A]^2
• The rate of this reaction is directly proportional to the square of the concentration of reactant A

16. Determining the Rate Constant (k)

• In order to fully define the rate law equation, we need to determine the rate constant (k)
• This can be done by using experimental data and substituting into the rate equation
• Let’s take a set of data where [A]0 = 0.1 M and [B]0 = 0.2 M, and the rate is 0.05 M/s
• Plugging these values into the rate equation, we get:
  • 0.05 M/s = k(0.1)^2(0.2)^0 = k(0.01)
• Solving for k, we find:
  • k = 5.0 s^-1

17. Summary: Rate Law Equation for the Reaction

• The rate law equation for the reaction 2A + B → C is:
  • Rate = k[A]^2[B]^0 = k[A]^2
• The reaction is second order with respect to reactant A and zero order with respect to reactant B
• The rate constant, k, can be determined experimentally
• The rate of the reaction is directly proportional to the square of the concentration of reactant A

18. Reaction Mechanism and Elementary Steps

• A reaction mechanism describes the sequence of elementary steps that make up a complex reaction
• Elementary steps are individual molecular events that occur in a reaction
• Each elementary step has its own rate equation and can be classified as either a bimolecular or unimolecular reaction

19. Unimolecular Elementary Steps

• Unimolecular reactions involve the collision of only one molecule
• The rate of an unimolecular reaction is proportional to the concentration of the reactant
• Example: A → B
  • The rate equation for this unimolecular reaction is: Rate = k[A]

20. Bimolecular Elementary Steps

• Bimolecular reactions involve the collision of two molecules
• The rate of a bimolecular reaction is proportional to the product of the concentrations of the two reactants
• Example: A + B → C
  • The rate equation for this bimolecular reaction is: Rate = k[A][B]

21. Integrated Rate Laws: Zero Order Reactions

• Integrated rate laws relate the concentration of a reactant to time
• For zero order reactions, the integrated rate law equation is:
  • [A] = [A]0 - kt
• Example: A → B (zero order)
  • Initial concentration of A: [A]0 = 0.2 M
  • Rate constant: k = 0.1 M/s
  • After 5 seconds: [A] = 0.2 M - (0.1 M/s)(5 s) = 0.2 M - 0.5 M = -0.3 M
  • The concentration of A decreases linearly over time in a zero order reaction

22. Integrated Rate Laws: First Order Reactions

• For first order reactions, the integrated rate law equation is:
  • ln[A] = -kt + ln[A]0
• Example: A → B (first order)
  • Initial concentration of A: [A]0 = 0.2 M
  • Rate constant: k = 0.1 s⁻¹
  • After 5 seconds: ln[A] = -(0.1 s⁻¹)(5 s) + ln(0.2 M) = -0.5 + ln(0.2 M)
  • The natural logarithm of the concentration of A decreases linearly over time in a first order reaction

23. Integrated Rate Laws: Second Order Reactions

• For second order reactions, the integrated rate law equation is:
  • 1/[A] = kt + 1/[A]0
• Example: A → B (second order)
  • Initial concentration of A: [A]0 = 0.2 M
  • Rate constant: k = 0.1 M⁻¹s⁻¹
  • After 5 seconds: 1/[A] = (0.1 M⁻¹s⁻¹)(5 s) + 1/(0.2 M) = 0.5 + 5 M⁻¹
  • The inverse of the concentration of A increases linearly over time in a second order reaction

24. Reaction Mechanisms: Elementary Steps and Molecularity

• A reaction mechanism describes the step-by-step sequence of elementary reactions that make up a complex reaction
• Molecularity refers to the number of molecules or ions involved in an elementary step
• Unimolecular reactions:
  • Only one molecule is involved in the elementary step
  • Example: A → B
• Bimolecular reactions:
  • Two molecules collide during the elementary step
  • Example: A + B → C
• Termolecular reactions:
  • Three molecules collide during the elementary step
  • Relatively rare due to the lower probability of three molecules colliding simultaneously

25. Rate-Determining Step and Overall Reaction Rate

• The rate-determining step (RDS) is the slowest step in a reaction mechanism

• It determines the overall rate of the reaction

• Example: A + B → C (reaction mechanism with multiple steps)

  • Step 1: A + B → D (slow step)
  • Step 2: D + B → C (fast step)

• In this example, the rate of the overall reaction is determined by the rate of the slow step, Step 1

26. Catalysts

• Catalysts are substances that increase the rate of a chemical reaction without being consumed in the process
• They provide an alternate reaction pathway with lower activation energy
• Catalysts speed up both the forward and reverse reactions
• Example: Enzymes
  • Enzymes are biological catalysts that facilitate biochemical reactions in living organisms
  • They lower the activation energy, allowing reactions to occur at cellular temperatures

27. Collision Theory Revisited

• The collision theory provides a basis for understanding the factors that influence reaction rates
• It states that for a reaction to occur, reactant particles must collide with sufficient energy and proper orientation
• Activation energy:
  • The minimum energy required for a successful collision
  • Energy needed to break existing bonds and form new ones
• Effective collisions:
  • Collisions that result in a reaction
  • Have sufficient energy and proper orientation

28. Factors Affecting Reaction Rates

• Reactant concentration:
  • Increasing reactant concentration leads to more frequent collisions and higher reaction rates
• Temperature:
  • Higher temperatures increase the kinetic energy of molecules and the frequency of collisions, leading to faster reaction rates
• Surface area:
  • Increasing the surface area of solid reactants increases the number of exposed particles, leading to more collisions and faster reaction rates

29. Factors Affecting Reaction Rates (Continued)

• Catalysts:
  • Catalysts provide an alternative reaction pathway with lower activation energy, resulting in faster reaction rates
  • They are not consumed in the reaction and can be used repeatedly
• Nature of reactants:
  • Different combinations of reactants have different reaction rates
  • Reactants with higher bond strengths or greater steric hindrance may have slower reaction rates

30. Summary

• Chemical kinetics is the study of reaction rates and mechanisms
• Three rates of reaction: average, instantaneous, and initial rate
• Factors affecting reaction rates: concentration, temperature, surface area, catalysts, and nature of reactants
• Collision theory explains how reactions occur through effective collisions and activation energy
• Reaction orders determine the relationship between concentration and rate
• Reaction mechanisms describe the step-by-step sequence of elementary reactions
• Catalysts increase reaction rates by lowering the activation energy