Chemical Kinetics - Dependence of reaction rate on concentration

• Introduction to chemical kinetics
  • Definition of reaction rate
  • Factors affecting reaction rate
• Collision theory
  • Explanation of collision theory
  • Activation energy and its significance
• Dependence of reaction rate on concentration
  • Rate law expression
  • Order of reaction
  • Rate constant
• Differential rate equation
  • Derivation of differential rate equation
  • Example of a first-order reaction
• Integrated rate equation
  • Derivation of integrated rate equation
  • Half-life of a reaction
  • Example of a second-order reaction
• Determining order of reaction
  • Initial rate method
  • Method of isolation
  • Graphical method
• Temperature dependence of reaction rate
  • Effect of temperature on reaction rate
  • Arrhenius equation
• Catalysis
  • Definition of catalysis
  • Types of catalysis
  • Enzymatic catalysis example
• Factors affecting reaction rate
  • Nature of reactants
  • Concentration of reactants
  • Surface area
  • Presence of a catalyst
  • Temperature
• Conclusion and summary

11. Rate law expression

• The rate law expression represents the mathematical relationship between the rate of a chemical reaction and the concentration of the reactants.
• It is generally expressed in the form: rate = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are the concentrations of reactants A and B, and m and n are the reaction orders with respect to A and B, respectively.
• The reaction orders determine the effect of concentration on the reaction rate.
• The rate constant is specific to a particular reaction and represents the proportionality constant in the rate equation.

12. Order of reaction

• The order of a reaction defines how the rate of a reaction is affected by the concentration of each reactant.
• It can be zero, first, second, or any other non-negative integer.
• The order of a reaction is determined experimentally and may not match the stoichiometric coefficients in the balanced chemical equation.
• The overall order of a reaction is the sum of the individual reaction orders.

13. Rate constant

• The rate constant (k) is a proportionality constant that relates the rate of a reaction to the concentration of reactants.
• It is specific to a particular reaction and is determined experimentally.
• The rate constant depends on factors such as temperature, presence of a catalyst, and reactant concentrations.
• Units of the rate constant depend on the overall reaction order.

14. Differential rate equation

• The differential rate equation expresses the rate of a reaction as a function of time and reactant concentrations.
• It is derived from the rate law expression by considering infinitesimally small changes in reactant concentrations.
• For a reaction with two reactants A and B, the differential rate equation can be written as: d[A]/dt = -k[A]^m[B]^n, where d[A]/dt represents the rate of change of A with time.

15. Example of a first-order reaction

• Consider the reaction A → products, which follows a first-order rate law: rate = k[A].
• The differential rate equation for this reaction is: d[A]/dt = -k[A].
• The integrated rate equation for a first-order reaction is: ln[A]t - ln[A]0 = -kt, where [A]t is the concentration of A at time t, [A]0 is the initial concentration, and k is the rate constant.

16. Integrated rate equation

• The integrated rate equation relates the concentration of a reactant to time during the course of a reaction.
• It is obtained by integrating the differential rate equation.
• Depending on the reaction order, different forms of integrated rate equations exist.
• The integrated rate equation can be used to determine the concentration of reactants at different time points and to calculate reaction half-life.

17. Half-life of a reaction

• The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value.
• It can be determined using the integrated rate equation.
• For a first-order reaction (rate = k[A]), the half-life (t₁/₂) is given by: t₁/₂ = (0.693)/k, where 0.693 is the natural logarithm of 2.

18. Example of a second-order reaction

• Consider the reaction 2A → products, which follows a second-order rate law: rate = k[A]^2.
• The differential rate equation for this reaction is: d[A]/dt = -2k[A]^2.
• The integrated rate equation for a second-order reaction is: 1/[A]t - 1/[A]0 = kt, where [A]t is the concentration of A at time t, [A]0 is the initial concentration, and k is the rate constant.

19. Determining order of reaction - Initial rate method

• The initial rate method involves measuring the initial rate of the reaction at different reactant concentrations.
• By comparing the initial rates, the reaction order can be determined.
• For example, if doubling the concentration of one reactant doubles the initial rate, it is a first-order reaction.

20. Determining order of reaction - Method of isolation

• The method of isolation involves studying the reaction with one reactant in large excess.
• By keeping the concentration of one reactant constant, the effect of the other reactant’s concentration on the reaction rate can be determined.
• For example, if the rate remains unchanged while one reactant concentration is varied, it is likely a zero-order reaction.

21. Determining order of reaction - Graphical method

• The graphical method involves plotting the concentration of reactant(s) against time and analyzing the resulting curve.
• Different reaction orders exhibit distinct patterns on the graph.
• For example, a first-order reaction shows an exponential decay curve, while a second-order reaction shows a linear, decreasing curve.

22. Temperature dependence of reaction rate

• The rate of a chemical reaction generally increases with an increase in temperature.
• This is because higher temperatures provide greater kinetic energy to the reactant molecules, increasing the frequency and energy of collisions.
• The relationship between temperature and rate of reaction is described by the Arrhenius equation: k = A * exp(-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 in Kelvin.

23. Effect of temperature on reaction rate

• An increase in temperature usually leads to an increase in the reaction rate.
• Conversely, decreasing the temperature slows down the reaction.
• This temperature dependence is quantitatively described by the Arrhenius equation.
• It is important to note that the reaction rate doubles or triples with every 10-degree Celsius rise in temperature, known as the reaction’s temperature coefficient (Q10).

24. Catalysis

• Catalysis is the process of increasing the rate of a chemical reaction by using a catalyst.
• A catalyst is a substance that remains unchanged in a chemical reaction and lowers the activation energy required for the reaction to occur.
• Catalysts provide an alternative reaction pathway with lower energy barriers, leading to faster reaction rates.
• Examples of catalysis include the use of enzymes in biological systems and transition metal catalysts in industrial processes.

25. Definition of catalysis

• Catalysis is the acceleration of a chemical reaction by a catalyst.
• A catalyst increases the reaction rate by lowering the activation energy without being consumed in the reaction.
• It provides an alternative mechanism or pathway for the reaction to occur more rapidly.
• Catalysts can be either homogeneous (in the same phase as the reactants) or heterogeneous (in a different phase).

26. Types of catalysis

• Homogeneous catalysis: The catalyst and reactants are in the same phase (e.g., a soluble transition metal complex).
• Heterogeneous catalysis: The catalyst and reactants are in different phases (e.g., a solid catalyst and a gas or liquid reactant).
• Enzymatic catalysis: Catalysis by enzymes, which are biological catalysts.
• Autocatalysis: A reaction in which one of the reaction products acts as a catalyst for the same reaction.

27. Enzymatic catalysis example

• Enzymes are biological catalysts that facilitate biochemical reactions in living organisms.
• Enzymatic reactions occur under mild conditions of temperature and pressure, making them energy-efficient.
• An example of enzymatic catalysis is the reaction catalyzed by the enzyme amylase, which converts starch into glucose.
• The presence of amylase significantly speeds up the reaction, allowing for efficient digestion of carbohydrates.

28. Factors affecting reaction rate - Nature of reactants

• The nature of reactants influences the rate of a chemical reaction.
• Reactants with stronger bonds or higher stability generally have slower reaction rates.
• Reactive or unstable molecules tend to undergo reactions more rapidly due to their higher energy or reactivity.
• For example, combustion reactions involving highly reactive substances like hydrogen or chlorine typically have fast reaction rates.

29. Factors affecting reaction rate - Concentration of reactants

• The concentration of reactants affects the reaction rate.
• Increasing the concentration of reactants generally leads to an increase in the reaction rate.
• This is because a higher concentration of reactant molecules increases the frequency of collisions, increasing the chances of successful collisions and product formation.
• The relationship between concentration and rate is determined by the reaction’s order.

30. Factors affecting reaction rate - Surface area

• The surface area of solid reactants can significantly affect the rate of a reaction.
• Increasing the surface area of a solid reactant increases the rate of reaction.
• This is because a higher surface area provides more exposed reactant sites, increasing the frequency of collisions and the likelihood of successful collisions.
• Crushing or grinding solid reactants increases their surface area, thereby accelerating the reaction rate.