Chemical Kinetics: Reaction Rates and Factors

Chemical Kinetics

• Reaction kinetics studies the rates of chemical processes.
• It examines how experimental conditions impact reaction speed.
• It can reveal information about reaction mechanisms and transition states.
• Mathematical models can be constructed to describe chemical reaction characteristics.

Factors Affecting Reaction Rates

• Reaction rate often correlates with reactant concentration.
• Reactions commonly speed up with increased temperature, providing more system energy.
• Reactions occur at phase boundaries, so surface area matters when reactants are in different phases.
• Solvents can affect reaction rates in solutions.
• Catalysts increase reaction rate by offering alternative, lower activation energy pathways and are not consumed.
• Light can provide the energy to start a reaction.

Reaction Rate

• For the reaction $aA + bB \rightarrow cC + dD$, the rate is expressed as: $Rate = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt}$
• $[A]$, $[B]$, $[C]$, $[D]$ represent the concentrations of reactants and products.
• $a$, $b$, $c$, $d$ are the stoichiometric coefficients.
• $t$ represents time.

Rate Law

• The rate law equation links reaction rate to reactant concentrations.
• For the reaction $aA + bB \rightarrow cC + dD$, the rate law is: $Rate = k[A]^m[B]^n$
• $k$ is the rate constant.
• $m$ is the order of reaction with respect to $A$.
• $n$ is the order of reaction with respect to $B$.
• The overall order of the reaction is $m + n$.
• Exponents $m$ and $n$ are experimentally determined and not necessarily equal to stoichiometric coefficients $a$ & $b$.

Zero Order Reactions

• Rate is independent of concentration: $Rate = k$
• Altering reactant concentration does not affect reaction rate.

First Order Reactions

• Rate relies linearly on one reactant concentration: $Rate = k[A]$

Second Order Reactions

• The overall reaction order is two.
• Rate is proportional to the square of one reactant's concentration or the product of two reactants' concentrations: $Rate = k[A]^2$ or $Rate = k[A][B]$

Arrhenius Equation

• Describes temperature dependence of reaction rates: $k = Ae^{-\frac{E_a}{RT}}$
• $k$ is the rate constant.
• $A$ is the pre-exponential or frequency factor.
• $E_a$ is the activation energy.
• $R$ is the gas constant.
• $T$ is the absolute temperature.

Algorithmes gloutons (Greedy Algorithms)

• These are a method of solving optimization problems.
• At each step, a locally optimal choice is made, hoping for a globally optimal solution.

Examples

• Rendu de monnaie (Change Making): Select the highest value coin possible at each step without exceeding the remaining amount.
• Problème du sac à dos (Knapsack Problem): A set of objects each with a weight and value are given and a max capacity for the bag, maximize the items in the bag. Sort the objects by decreasing value/weight ratio, adding if capacity allows,
• Ordonnancement de tâches (Task Scheduling): Minimize the max task delay, sort by increasing due date and execute in that order (Earliest Due Date algorithm).

Advantages

• Simple design and implementation.
• Algorithmic complexity is often low.

Disadvantages

• Optimal solution is not guaranteed.
• Optimality of the solution requires proof.

General Scheme

• Starting from an empty solution add objects if they are possible.

Illustration: Change Making

• Example:* Return 17€32 with the following
• Bills: 5€, 10€
• Coins: 1 cent, 2 cent, 5 cent, 10 cent, 20 cent, 50 cent, 1€, 2€

Illustration : Knapsack Problem

• You have objects with values and weights

• The max capacity is 50kg, which objects maximize total value?
  • Greedy Solution
    • Calculate value and weight ratio for items
    • Sort by decrasing amount value/weight = A, B, C
    • Add A (10kg) value 60, total weight 10kg
    • Add B (20kg) value 160, total weight 30kg
    • Cannot add C (30kg) since total weight >50kg
• Greedy Solution: A and B, total value = 160€, total weight 30kg
  • Optimal solution
    • A and B replaced with C total value is 120€ but weight is 30kg.
    • B and C total value 220 for 50kg
  • Greedy solution is not optimal in this instance