Chemical Kinetics: Reaction Rates

Chapter 14: Chemical Kinetics

Overview

• Chemical kinetics includes rates of reaction and its relation to the following:
• Concentration: rate laws
• Integrated rate laws and half-lives
• Temperature
• Reaction mechanisms
• Catalysis

14.1 Rates of Reaction

• Objectives:
• Describe factors that affect reaction rates
• Express reaction rates in relation to reaction stoichiometry.
• Calculate relative reaction rates using stoichiometric reaction rate expressions.

14.1: Factors that Affect Reaction Rates

• Chemical kinetics describes the rate of reactions, and is affected by:
• Particle size of solid reactants; greater surface area increases reaction rate
• Reactions with solids proceed quicker when surface area is increased
• Solids ground into a powder have a larger surface area
• Reactant concentrations; higher the concentration, the faster the reaction proceeds
• Higher concentrations lead to more collisions between molecules
• Temperature; affects reaction rates by increasing frequency and energy of collisions
• At higher temperatures, collisions are more frequent
• Rate ∝ collision frequency ∝ temperature
• Rate ∝ collision energy ∝ temperature
• Physical state of reactants
• Homogeneous reactions involve all liquid or all gaseous reactants
• Heterogeneous reactions involve reactants in different phases
• Presence of a catalyst influences the energy needed to initiate a reaction
• Catalysts increase the reaction rate by:
• Lowering the energy required for the reaction to occur
• Providing an alternate reaction pathway
• Catalysts are not consumed; they're regenerated at the end of the reaction.

14.1: Reaction Rates and Stoichiometry

• Reaction rate is the change in concentration per unit of time, with always positive values
• For a reaction aA + bB → cC + dD
• Rate of A = -(1/a) * (Δ[A]/Δt)
• Rate of B = -(1/b) * (Δ[B]/Δt)
• Rate of C = (1/c) * (Δ[C]/Δt)
• Rate of D = (1/d) * (Δ[D]/Δt)
• Overall Rate = (1/a) * (Δ[Α]/Δt) = -(1/b) * (Δ[Β]/Δt) = (1/c) * (Δ[C]/Δt) = (1/d) * (Δ[D]/Δt)
• Reaction rates are measured as:
• Instantaneous rates, which is the slope of the line tangent to the concentration vs. time plot, where the instantaneous rate at t=0 is the initial rate
• Average rates, which equals the concentration difference between two points divided by the change in time

14.2 Reaction Rates and Concentration: Rate Laws

Objectives

• Rate laws and reaction orders are described and written.
• Rate laws for chemical reactions are derived from experimental data.
• Reaction rate calculation are performed for reactions with specific concentrations with the determined rate law.

14.2: Measuring Concentrations – Beer's Law

• Many substances posses the ability to absorb electromagnetic radiation or light
• Colorless solutions typically absorb UV light (< 400 nm)
• Colored substances are able to absorb visible light (400 - 700 nm)
• Absorbance measurements utilize a spectrophotometer
• Light from polychromatic source that goes through a wavelength selection device isolates the single wavelength of interest.
• Monochromatic light is passed through a sample and is detected by the detector.
• Beer's Law
• Provides a relationship between the absorbance of light and the concentration of a substance.
• Αλ = Exbc, where:
• A = absorbance (unitless)
• E = molar absorptivity (M-1cm-1)
• b = pathlength (cm)
• c = concentration of absorbing species (M)
• *Molar absorptivity is wavelength-dependent.
• Beer's Law is accurate when:
• Monochromatic light is absorbed
• Concentration of absorbing substance is dilute
• A linear correlation exists between absorbance (A) and concentration (c)

14.2: Reaction Rates and Concentration

• Changes in absorption can be correlated to changes in concentration for kinetics
• For kinetics, changes in absorption of an analyte can be be correlated to changes in concentration over time.
• dA/dt = eb * dc/dt

14.2: Reaction Rates and Rate Laws

• Rate Law
• Experimentally determined descriptions that link reactant concentrations to the reaction rate
• aA + bB → cC + dD
• Rate = k[A]^m[B]^n, where:
• m and n are the "orders" of the reactants
• Common Values of orders are 0, 1, or 2
• 0 = zero order
• 1 = first order
• 2 = second order
• *Orders are "with respect to" the individual reactants

14.2: Reaction Rates and Rate Laws

• Zero-Order
• There is no effect on the reaction rate when the the concentration is changed
• A → product; Rate = k[A]0 = k
• First-Order
• Concentration of the reactant is directly proportional to the reaction rate.
• A → product; Rate = k[A]
• Ex. In reaction that is first order with respect to A:
  • A → product
  • Rate = k[A]
• Second order
• Reaction rate is directly proportional to the square of the reactant concentration.
• If the concentration of [A] doubles, rate increases by 4x
• Ex. a reaction that is 2nd order with respect to A:
• A → product
• Rate = k[A]^2

14.2: Reaction Rates and Rate Laws

• The coefficients in a balanced reaction do not necessarily relate to the orders m and n
• Overall Reaction Order = the sum of the orders with respect to each reactant.
• Example: Rate = k[A][B]^2; m=1 and n=2
• Reaction is 1st order with respect to the reactant A, 2nd order with respect to B, and 3rd order overall
• Rate Laws
• Include a proportionally constant called the rate constant, or k
• is determined experimentally with units depending on rate law
• Value of the Rate Constant
• Is temperature dependent based on the reaction
• Small k = slower reaction, while Larger k = faster reaction

14.2: Reaction Rates and Rate Laws

• Using sets of reactant concentrations to determine reaction rates to calculate the orders of reactants, m and n, in the rate law, and the constant, k.
• To determine the rate law:
• A + 2B -> C + D
• Rate = k[A]^m[B]^n

14.2: Reaction Rates and Rate Laws

• Summary of prior section...
• For the reaction of A + 2B → C + D
• Rate = k[A][B]
• Reaction is first order with respect to A
• Reaction is first order with respect to B
• Reaction is second order overall Determine the rate constant (k)
• Good: Pick any of the experiments. Rate = k[A][B]
• Better: k can be determined for all experiments and averaged.
• Using Experiment 1, Rate * 1 / [A][B] = k

14.2: Reaction Rates and Rate Laws

• In some rate constant calculations, finding m or n is not easy.
• For the case of a = b^m
• log a = m log b
• log a / log b = m

14.3 Integrated Rate Laws and Half-Lives

• Objectives include:
• Calculating concentrations, times, and constant rates with 0, 1st, and 2nd order integrated rate laws
• Calculating half-lives and concentrations
• Indentifying the order of a reaction using graphical data

14.3: Integrated Rate Law – 0 Order

• Defines zero-order reactions as independent from the reactant concentration
• A -> Products (Zero-Order Reaction) :
  • d[A]/dt = k - d[A] = - kdt
  • Rate = -(Δ[Α]/Δt) = k[A]^0 = k
  • Δ[Α] ∫^t_t=0 = - k ∫^t_t=0 dt
    • [A] t-[A]o=-kt
• The integrated rate law is zero-order:
  • [A]t = - kt + [A]o

14.3: Integrated Rate Law – 1st Order

• Reactions of the first-order depends on the concentration of a single reactant raised to the first power.
  • A -> Products (First-Order Reaction) : - -(d[A]/dt) = k[A] - d[A]/[A]) = -kdt - ∫^t_to d[A]/([A] = - k ∫^t_to dt - ln [A]t - ln [A]o = -kt
• The integrated rate law is [A]t + ln [A]o = -kt

14.3: Integrated Rate Law - 2nd Order

• Second-order reactions has a rate that depends on either:
• One raised reactant concentration to the second power
• Reaction: A -> Products Rate = k[A]^ 2 , where:
• d[A]/dt = k[A]^2
• d[A]/[A]^2 = kdt
• Limits: ∫^t_to d[A]/[A]^2 = k ∫^t_to dt - 1/[A]t -1/([A])=kt
• The concentrations of two reactants, each raised to the first power. i.e. - Reaction: A + B -> Products Rate = k[A]*[B]:
• The integrated rate law is 1/[𝐀]t = kt + 1/[𝐀]o

14.3: Determining Reaction Orders

Uses A graphical Method

• The integrated rates for processes of 0, 1st, and 2nd order can be made to fit a linear graph
• y = mx + b

14.3: Half Life - 0 Order

Zero order reaction:

• [A]t = - kt + [A]o
• Half-life of a zero-order is directly proportional to the initial reaction concentration
• Half-life of an inversely of zero-order is proportional to the rate constant
• In simpler terms, a smaller reaction(lowerk) = longer half life. conversely, a faster reaction is the opposite

14.3: Half-Life – 1st Order

First-Order

• Half-life of first order is proportional to k or the rate constant

14.3: Half-Life – 2nd Order

Second-order

• Half-life of 2nd order is inverse to both the rate constant and initial reaction.
• Over time a 2nd order reaction is subject to change the rate constant and the initial reactant concentration in the reaction processes
• For a second-order reaction, on each successive one the half life is doubles longer from the perceeding.

14.4 Reaction Rates and Temperature

• Define Activation Energy
• Using Graphs
  • Reaction progression diagrams
  • Identify reactant transition states
  • Understand the terminology in the collision theory
  • Calculations using the Arrhenius equation

14.4: The Collision Model - Concentration Factor

• Reactions are reliant on the molecules in a chemical reaction to collide together
• Reaction rate is directly related and dependent on the amounts of collision occurring in that second.
• The number of collision increases when reactant concentration goes up = faster reaction

14.4: The Collision Model - Orientation Factor

• Collisions do not immediately result in a reaction
• Bonds can form under a condition where molecules are oriented as they contact each other

14.4: The Collision Model-Energy Factor

• Molecule's Kinetic Energy is related to Absolute Temperature
• Higher Temperature cause molecules to process more power which is needed in the reaction
• Reactions speed up and increase with Temperature Reactants double in temperature with approximate 10 degree celcius increases

14.4: Reaction Rates and Temperature - Activation Energy

• Activation ENergy is the minimum Energy to create a chemical reaction to occur
• Molecules use energy from highest points, to start rearrangement
• Higher energy in reactions cause bonds to break
• magnitude of high magnitude directly related in relation to Reaction constants

14.4: Arrhenius Equation

• For reactions with increase rates and non linear temperatures
• Use to find rate equation in the realtion to temperature:
  • k = Ae^-Ea/RT
    • k (Rate Constant)
    • A frequency Factor
    • Constant 8.31
• graphing the action energy constant is found by algebraically manipulating the Arrhenius Equation.
• In K = E/R (1/T) + In A
  • y = mx+b

14.4: Arrhenius Equation

• Is used to find two point equation rates in different temperatures
• Calculating activation energy:
  • In* K2/K1 = E/R (* 1/T2-1/T1)

14.5 Reaction Mechanism

• Reaction Mechanisms are the way reactants create products - A collection of molecular steps
• Elementary reactions are steps composed of reactions, and the reactants are provided in exponents
• Add everything to have the correct chemical reaction

14.5: Reaction Mechanisms

• The intermediate is in middle, in the next Step

14.5: Rate-Determining Step

• To have highest energy in multistep reactions, speed needs to have slow elementary reaction
• The steps are limited by the slowest reaction
• Reactions are slower when highest Ea

14.5: Reaction mechanisms - slow initial step

Overall, 2NO(g) + F2(g) +2NO2 F(g)

• Rate will have same rate as for Step 1. or Rate = k[No2][F2]

14.5: Reaction Mechanisms - Fast Initial Step

• To get rate and concentrations
• Constant of intermediate is resolved by assumption, the fast stpe is followed by a slow, the concentration in reaction
  • Rate of forward reaction = Rate of reverse reaction (K1[No][O2] = K-1[No3])

14.6 Catalysis

• change is reaction, no chemical change
• speed is change, so speed increases:
  • decrease energy during activation steps or reactions -or- provide the replacement pathway
  • catalyst can affect the constant rate - both at same time
  • catalyst turns smaller to larger - rate decreases as larger. faster is the best

14.6: Catalysis

• Catalyst types:
• Homogeneous - catalyst is in the same phase as the reactants
• Hetrogeneous - catalyst has reactants in a seperate phase
• Properties for great Catalysis:
• Sufficent longitivity. has lots of cycles doing it
• Catalysis of decompostion is veyr small
• speed it up and add bromide

14.6: Catalysis

• Hetrogenois Catalysis is when Molecules are in a different phase
• Initial adsorption has reactant on cataclyst to determine the rate
• Solid Cataclytic will start Hgas2 and C2H4 gas for carbon
• In this part, adsoprtion reaction on catalyze start