Chemical Kinetics - Rate law for zero-order reaction

  • Definition of a zero-order reaction
  • Rate law expression for a zero-order reaction
  • Example of a zero-order reaction
  • Determining the rate constant for a zero-order reaction
  • Summary of key points

Definition of a zero-order reaction

  • A zero-order reaction is one in which the rate of reaction is independent of the concentration of reactants.
  • This means that the rate of the reaction remains constant over time.

Rate law expression for a zero-order reaction

The rate law expression for a zero-order reaction is: Rate = k

  • Where:
    • Rate is the rate of reaction
    • k is the rate constant

Example of a zero-order reaction

An example of a zero-order reaction is the decomposition of N2O5: ``

2 N2O5 -> 4 NO2 + O2 ``

  • In this reaction, the rate of decomposition of N2O5 is completely independent of its concentration.

Determining the rate constant for a zero-order reaction

To determine the rate constant for a zero-order reaction, we can use the following equation: Rate = k[A]^0[B]^0 = k

  • Since the exponents for both A and B are 0, their concentrations do not affect the rate of reaction.
  • Therefore, the rate constant is equal to the rate of reaction.

Summary of key points

  • A zero-order reaction has a rate that is independent of the concentration of reactants.
  • The rate law expression for a zero-order reaction is Rate = k.
  • An example of a zero-order reaction is the decomposition of N2O5.
  • The rate constant for a zero-order reaction is equal to the rate of reaction.
  1. Factors Affecting Reaction Rates
  • Temperature: Increasing temperature generally increases the rate of reaction due to the higher kinetic energy of particles.
  • Concentration: Higher concentration of reactants leads to more collisions and faster reaction rates.
  • Catalysts: Catalysts increase the rate of reaction by providing an alternative reaction pathway with lower activation energy.
  • Surface Area: Increasing the surface area of solid reactants exposes more particles to collisions, increasing the reaction rate.
  • Nature of Reactants: Some reactions occur faster due to the reactivity or stability of the reactants.
  1. Rate Law for First-Order Reaction
  • Definition of a first-order reaction: A first-order reaction is one in which the rate of reaction is directly proportional to the concentration of a single reactant.
  • Rate law expression for a first-order reaction: Rate = k[A], where A is the concentration of the reactant and k is the rate constant.
  • Determining the rate constant for a first-order reaction: By plotting ln[A] vs. time, the slope of the resulting graph can be used to calculate k.
  • Example of a first-order reaction: The decomposition of H2O2, given by the equation 2 H2O2 ➜ 2 H2O + O2, is an example of a first-order reaction.
  1. Rate Law for Second-Order Reaction
  • Definition of a second-order reaction: A second-order reaction is one in which the rate of reaction is directly proportional to the square of the concentration of a single reactant or to the product of the concentrations of two reactants.
  • Rate law expression for a second-order reaction: Rate = k[A]^2 or Rate = k[A][B], where A and B are the concentrations of the reactants and k is the rate constant.
  • Determining the rate constant for a second-order reaction: By plotting 1/[A] vs. time or [A]/[B] vs. time, the slope of the resulting graph can be used to calculate k.
  • Example of a second-order reaction: The reaction 2 NO + O2 ➜ 2 NO2 is an example of a second-order reaction.
  1. Reaction Mechanisms
  • Definition of reaction mechanisms: A reaction mechanism is a step-by-step sequence of elementary reactions that shows how a reaction occurs.
  • Elementary reactions: Elementary reactions are individual steps in a reaction mechanism.
  • Rate-determining step: The rate-determining step is the slowest step in a reaction mechanism, which determines the overall rate of the reaction.
  • Proposed reaction mechanisms: Scientists propose reaction mechanisms based on experimental evidence, kinetics studies, and theoretical considerations.
  1. Collision Theory
  • Definition of collision theory: Collision theory explains how reactions occur through particle collisions.
  • Effective collision: An effective collision occurs when colliding particles have sufficient energy with proper orientation to break existing bonds and form new ones.
  • Activation energy: Activation energy is the minimum energy required for a reaction to occur.
  • Factors influencing collision frequency: Concentration, temperature, pressure, and surface area affect the collision frequency and therefore the reaction rate.
  1. Arrhenius Equation
  • Definition of Arrhenius equation: The Arrhenius equation relates the rate constant (k) of a reaction to the activation energy (Ea), temperature (T), and the frequency factor (A).
  • Arrhenius equation: k = A * e^(-Ea/RT), where A is the frequency factor, R is the gas constant, and T is the temperature in Kelvin.
  • Implications of the Arrhenius equation: As temperature increases, the rate constant and the rate of reaction increase exponentially.
  • Use of the Arrhenius equation: The Arrhenius equation is used to determine the rate constant and activation energy of a reaction.
  1. Reaction Order Determination
  • Determining reaction order experimentally: The method of initial rates and graphical analysis are commonly used to determine the reaction order.
  • Method of initial rates: By conducting experiments with different initial concentrations and observing the change in reaction rate, the reaction order can be determined.
  • Graphical analysis: Plotting concentration vs. time and analyzing the resulting graph can help determine the reaction order.
  • Integrated rate law: The integrated rate law expression depends on the reaction order and can be derived from the corresponding differential rate law expression.
  1. Half-Life of a Reaction
  • Definition of half-life: The half-life of a reaction is the time it takes for the concentration of a reactant to decrease by half.
  • Relationship between reaction order and half-life: The half-life of a reaction depends on its order. For zero-order reactions, the half-life is constant. For first-order reactions, it remains constant, regardless of the initial concentration. For second-order reactions, the half-life varies with initial concentration.
  • Calculation of half-life: Different equations and methods can be used to calculate the half-life of a reaction, depending on its order.
  1. Rate Expression from Mechanism
  • Rate-determining step: The rate-determining step provides the overall rate law for a reaction since it is the slowest step.
  • Determining rate expression from mechanism: By examining the stoichiometry and rate-determining step of a reaction mechanism, the rate expression can be derived.
  • Identifying intermediates and catalysts: Intermediates appear in the mechanism but do not appear in the overall rate expression. Catalysts appear in the mechanism and are involved in the reaction but do not affect the overall rate expression.
  • Rate laws for elementary reactions: The rate law for an elementary reaction is the stoichiometric coefficient for the elementary step.
  1. Factors Affecting Reaction Rates - Concentration
  • Collision frequency and rate of reaction: Increasing the concentration of reactants increases the collision frequency and therefore the rate of reaction.
  • Effect of concentration on reaction rate: As the concentration of reactants increases, the number of collisions between particles increases, leading to a higher likelihood of effective collisions.
  • Rate law and concentration: The rate law expression includes the concentrations of reactants raised to various powers, indicating how changes in concentration affect the rate of reaction.
  • Determining the reaction order: By experimentally changing the concentration of a single reactant and observing the effect on the reaction rate, the reaction order can be determined.

Chemical Equilibrium

  • Definition of chemical equilibrium
  • The concept of forward and reverse reactions
  • The equilibrium constant (K)
  • The expression for the equilibrium constant
  • Examples of equilibrium reactions

Definition of chemical equilibrium

  • Chemical equilibrium is a state in which the rate of the forward reaction is equal to the rate of the reverse reaction.
  • In this state, the concentrations of reactants and products remain constant over time.

The concept of forward and reverse reactions

  • In a chemical reaction, reactants are converted into products through the forward reaction.
  • At the same time, products can also convert back to reactants through the reverse reaction.
  • Both of these reactions occur simultaneously in a dynamic equilibrium.

The equilibrium constant (K)

  • The equilibrium constant (K) is a mathematical expression that describes the ratio of product concentrations to reactant concentrations at equilibrium.
  • It provides information about the extent of a reaction at equilibrium.
  • The value of K remains constant at a given temperature.

The expression for the equilibrium constant

The general expression for the equilibrium constant (K) is: K = [C]^c[D]^d / [A]^a[B]^b

  • Where:
    • [A], [B], [C], [D] are the concentrations of reactants and products at equilibrium.
    • a, b, c, d are the stoichiometric coefficients of the balanced chemical equation.

Examples of equilibrium reactions

  • The Haber-Bosch process: N2(g) + 3H2(g) ⇌ 2NH3(g)
  • The formation of water from hydrogen and oxygen: 2H2(g) + O2(g) ⇌ 2H2O(g)
  • The ionization of acetic acid: CH3COOH(aq) ⇌ CH3COO-(aq) + H+(aq)
  • These examples demonstrate the equilibrium state where forward and reverse reactions occur simultaneously, leading to constant concentrations of reactants and products.

Le Chatelier’s Principle

  • Definition of Le Chatelier’s Principle
  • The effect of concentration changes on equilibrium
  • The effect of pressure changes on equilibrium (for gaseous reactions)
  • The effect of temperature changes on equilibrium
  • Examples illustrating Le Chatelier’s Principle

Definition of Le Chatelier’s Principle

  • Le Chatelier’s Principle states that when a system at equilibrium is subjected to an external stress, the system will adjust itself to counteract the stress and reestablish equilibrium.
  • The stress can be changes in concentration, pressure, or temperature.

The effect of concentration changes on equilibrium

  • Increasing the concentration of a reactant or product will shift the equilibrium towards the side with fewer moles of gas molecules (for gaseous reactions) or towards the side with fewer molecules or ions.
  • Decreasing the concentration of a reactant or product will shift the equilibrium towards the side with more moles of gas molecules (for gaseous reactions) or towards the side with more molecules or ions.

The effect of pressure changes on equilibrium (for gaseous reactions)

  • Increasing the pressure (by decreasing volume) will shift the equilibrium towards the side with fewer moles of gas molecules.
  • Decreasing the pressure (by increasing volume) will shift the equilibrium towards the side with more moles of gas molecules.

The effect of temperature changes on equilibrium

  • Increasing temperature endothermic reaction shifts the equilibrium towards the side of the reaction that absorbs heat.
  • Increasing temperature exothermic reaction shifts the equilibrium towards the side of the reaction that releases heat.
  • Decreasing temperature shifts the equilibrium in the opposite direction.

Examples illustrating Le Chatelier’s Principle

  • Fading of a flower’s color due to the addition of acid
  • The effect of temperature on the Haber-Bosch process
  • The effect of pressure on the solubility of gases in liquids
  • These examples demonstrate how systems at equilibrium respond to various external stresses according to Le Chatelier’s Principle.