Chemical Kinetics: Rate Laws and Reaction Orders

• These study notes cover chemical kinetics, rate laws, reaction orders, and reaction mechanisms.

Reaction Orders and Rate Laws

• Understanding the rate law is vital to determine the relationship between reactant concentrations and reaction rates.
• For the reaction 2 HgCl₂(aq) + C₂O₄²⁻(aq) → 2 Cl⁻(aq) + CO₂(g) + Hg₂Cl₂(s):
  • Determining the reaction order with respect to HgCl₂: Comparison of experiments 1 and 3 reveals that when the concentration of HgCl₂ is halved while C₂O₄²⁻ remains constant, the reaction rate is quartered, indicating a second order reaction with respect to HgCl₂. Therefore, m = 2.
  • Finding the reaction order with respect to C₂O₄²⁻: Comparing experiments 1 and 2 shows that doubling the concentration of C₂O₄²⁻ while keeping HgCl₂ constant doubles the reaction rate, suggesting a first order reaction with respect to C₂O₄²⁻. Thus n = 1.
  • The rate law for the reaction is rate = k[HgCl₂]²[C₂O₄²⁻].
  • The overall reaction order is the sum of the individual orders, which equals 3.
  • The rate constant is calculated using experimental data, any experiment can be chosen and gives an answer of: k= 7.62 x 10⁻³ M⁻²s⁻¹.
• For the reaction C₅H₅N(aq) + CH₃I(aq) → C₅H₅NCH₃⁺(aq) + I⁻(aq) at 25°C:
  • The reaction order with respect to C₅H₅N: Comparing experiments 1 and 2, doubling the concentration of C₅H₅N while keeping CH₃I constant doubles the reaction rate, resulting in a first order reaction with respect to C₅H₅N
  • The reaction order regarding CH₃I: By comparing experiments 2 and 3 it is shown that doubling the concentration of CH₃I while holding C₅H₅N constant, the reaction rate also doubles, indicating a first order reaction in regard to CH₃I.
  • The determined rate law is rate = k[C₅H₅N][CH₃I].
  • The rate constant calculated from experimental data gives: k = 75 M⁻¹s⁻¹.
  • Prediction of initial rate with changed concentrations: With [C₅H₅N] = 5.0 x 10⁻⁵ M and [CH₃I] = 2.0 x 10⁻⁵ M, the predicted rate equals 7.5 x 10⁻⁹ M s⁻¹.
• For the reaction BrO₃⁻(aq) + 5Br⁻(aq) + 6H⁺(aq) → 3Br₂(aq) + 3H₂O(l):
  • Determining the reaction order with respect to BrO₃⁻: A comparison of rates and concentrations between experiments 1 and 2, where [BrO₃⁻] doubles while [Br⁻] and [H⁺] are constant, indicates a first order reaction with respect to BrO₃⁻.
  • Reaction order regarding Br⁻: Comparison of experiments 1 and 3, where Br⁻ triples while other concentrations are kept consistent indicates a first order reaction with respect to Br⁻.
  • Reaction order in terms of H⁺: The comparison of experiments shows a second order relationship with H⁺ which means it is proportional to [H⁺]².
  • Rate Law: Rate = k[BrO₃⁻][Br⁻][H⁺]².
  • The rate constant has a value of 1.2 x 10³ L³M⁻³s⁻¹.

Qualitative Understanding of Reaction Rate

• Reaction rate involves the qualitative measure of how quickly reactants are consumed and how fast a reaction reaches completion.
• When concentration of reactant is doubled, the reaction rate also doubles which indicates a first order reaction with respect to the reactant.
• Given a rate law rate = k[A]²[B][C]: The units of the rate constant k are M⁻³s⁻¹.

Radioactive Decay and Half-Life

• With radioactive iodine which decays following first-order kinetics:
  • First-order reactions provide a linear relationship on a specific graph and allows determination of reaction rate/order etc.
  • The half-life is approximately 8.15 days based on the rate constant.
  • The time it would take for 100 grams of ¹³¹I to decompose to 50 grams: The time is equivalent to one half-life, which is 8 days.

Temperature, Collision Theory, and Reaction Rates

• At higher temperatures molecules gain energy and move faster, resulting in more collisions with sufficient energy to react.
• Higher reactant concentration increases collisions and therefore reaction rate.

Kinetics Experiment

• Kinetic experiment studying the reaction S₂O₈²⁻(aq) + 3I⁻(aq) → 2SO₄²⁻(aq) + I₃⁻(aq).
  • Determining reaction order with respect to S₂O₈²⁻: Experiments 1 and 2 show doubling the S₂O₈²⁻ doubles the reaction rate, indicating a first order reaction.
  • Determining reaction order with respect to I⁻: Comparing experiments 2 and 3, doubling the concentration of I⁻ doubles the reactions rate which indicates it follows a first order relationship.
  • The rate law is rate = k[S₂O₈²⁻][I⁻].
  • The calculated rate constant: k= 0.0061.
  • To predict the reaction rate with new concentrations: When [S₂O₈²⁻] = 0.083 M and [I⁻] = 0.052 M, the computed rate is 2.65 x 10⁻⁵ M/s.

Energy Diagrams and Reaction Mechanisms

• Diagrams for exothermic reactions visualize the energy pathway from reactants to products, including the activation energy. The energy change, delta H, is also illustrated.
• First order reactions plot linearly.

Applying Kinetics to Reaction Mechanisms

• Sulfur 38 emits beta particles and is first order.
  • Overall order: first order.
  • Half life constant value is 0.693/t1/2.
• Temperature and rate constant.
  • The Arrhenius equation is written for plotting data.
  • The slope and intercept can be used for activation energy and frequency factor calculations.

Rate Laws and Reaction Mechanisms

• Reaction: 2 N₂O₅(g) → 4 NO₂(g) + O₂(g): Initial rate is halved when the concentration of N₂O₅(g) is halved, means it is a first order reaction .
  • Rate law: rate = k[N₂O₅].
  • For initial concentrations: 1.0 M, 0.5 M, 0.25 M, 0.125 with k = 3.21 x 10⁻² s⁻¹, yields respective initial rates of 3.21 x 10⁻² M s⁻¹,1.605 x 10⁻² M s⁻¹,0.803 x 10⁻² M s⁻¹,0.401 x 10⁻² M s⁻¹.
  • Linear graph shows first order reactions.
• First order reaction rate follows: rate (1st order) = k[N₂O₅] second order follows rate (2nd order) = k[N₂O₅]². The rate is larger for higher temperatures
• Given reaction is: O₃(g) + 2 NO₂(g) → N₂O₅(g) + O₂(g): Is is first order in respect to O3 and NO2.
  • The rate law is rate = k[O₃][NO₂].
• Mechanisms:
  • Consistent rate law must match the experimental rate law

Equilibrium and Reaction Rates

• An antibiotic decomposes according to first-order kinetics with a given rate constant.
  • Half life: t12 = 0.693/k
• Reactions involving hydrogen and oxygen may not proceed due to minimal energy for a reaction to start occurring.
• Effects on Reactants on Equilibrium.
• If there are the same number of moles per side nothing happens when pressure is increased.

Equilibrium Calculations and Reaction Quotient

• Reaction of sulfuric acid: 2SO₂(g) + O₂(g) ⇄ 2SO₃(g): Is key for sulfuric acid and shows a forward reaction.
  • An equilibrium can be determined via an equation.
  • At equilibrium a new equation must be used .
• Applying the reaction quoeient
  • Must proceed to reach equilibrium
  • Reaction quotient is derived to find the equilibrium

Equilibrium Pressures

• Given H₂+ 2 Cl(g) ⇄ 2H(g) at equilibrium it changes.
• Pressrure calculation
  • Keq equilibrium is at a lower end. H2O(g) + CH₄(g) --> 3 H₂(9)+CO(g)