11: Chemical Kinetics II

Lecture 11 Announcements

• Today's Topics: Chemical Kinetics II (Brown Ch. 14)
  • Temperature and Rate (14.5)
  • Reaction Mechanisms (14.6)
  • Catalysis (14.7)
• Problem Set 10: Due before Exercise #11 tomorrow; upload on Moodle link
• Problem Set 11: Posted on Moodle; due before Exercise #12 next week
• Study Center: Wednesdays 18:00–20:00 in ETA F 5
• Office Hours: Prof. Norris and Brisby, Thursdays 17:00–18:00 in LEE P 210
• Final Exam: Monday, February 3, 2025, at 8:30–10:30

Lecture 12 Next Week

• Topics: Brown Ch. 15 Chemical Equilibrium
  • 15.1 The Concept of Equilibrium
  • 15.2 The Equilibrium Constant
  • 15.3 Understanding and Working with Equilibrium Constants
  • 15.4 Calculating Equilibrium Constants
  • 15.5 Le Châtelier's Principle
  • 19.7 Free Energy and the Equilibrium Constant

Red Thread

• Topics progression: Properties → Kinetics → Equilibrium → Acid-Base → Catalysis → Christmas! → Batteries

Review

• Chemical Kinetics: Studies the speed of reactions/processes, quantified by reaction rate
• Reaction Rate: Depends on reactant concentrations (Rate = k[A]m[B]n[C]p...); determined by experiment
• Reaction Order: Determined by experiment; can be zero-, first-, second-order, etc.
• Half-life (t1/2): Time when half the initial reactant is gone

Important Open Questions

• Rate Law: What do terms m, n, p mean in Rate = k[A]m[B]n[C]p…?
• Reaction Speed: Why can one spontaneous reaction be fast and another slow?
• Reaction Activation: Why are reactions often heated?
• Temperature Influence: What role does temperature play in kinetics?

Speed of Ants versus Temperature

• Ants as Model: Ants are "cold-blooded", body temperature changes with the environment
• Experiment: A classic experiment revealed doubling of ant speed with a 10°C rise in temperature
• Relevance: This relates to analogous concepts in chemistry

Why Heat Chemical Reactions?

• Collision Model: Molecules must collide to react; reaction rate is proportional to collision frequency
• Collision Frequency: Depends on both concentration and temperature.
• Kinetic Energy and Orientation: Molecules must collide with proper kinetic energy and orientation for reaction

Why Does Orientation Matter?

• Correct Collision: Correct molecular orientation is crucial for reaction; a "hit from the wrong side" will not form product
• Kinetic Energy: Proper kinetic energy must also be present at the collision point

Why Does Kinetic Energy Matter?

• Activation Energy (Ea): Minimum energy needed for molecules to react
• Reactants Stability: Reactants are generally stable molecules
• Products Stability: Products are generally stable molecules
• Transition State: Molecules in the unstable transition state during reaction

Activation Energy, Ea

• Chemical Bonds: In transition state, bonds are half broken and half formed; relatively unstable
• Energy Barrier: Energy required to achieve transition state is the activation energy; the "hill" to overcome
• Transition State/Complex: At peak reactants are in transition state/activated complex.

Implications of Activation Energy, Ea

• Energy Effect: High activation energy results in slow reaction because only a small fraction of molecules have enough kinetic energy to reach transition state; in simpler terms, a high hill means less success
• Temperature effect: At higher temperatures, the number of molecules with kinetic energy exceeding activation energy will increase
• Kinetics: Increasing temperature will generally speed up a reaction by increasing the fraction of molecules with kinetic energy sufficient to make it over the energy barrier

Temperature Dependence of Rate Law

• Rate Constant (k): Rate constant depends on temperature, thus often called a rate coefficient
• Arrhenius Equation: k(T) = A exp(-Ea/RT) = A exp[-Ea/RT].
• Frequency Factor: A is a temperature-independent constant that includes collision frequency.
• Exponential term: exp[-Ea/RT] is the Boltzmann factor, shows temperature dependence

Arrhenius Equation

• Natural Log: Taking natural log of both sides gives ln[k] = ln(A) - Ea/RT
• Linear Relationship: This gives a linear relationship useful for determining Ea graphically from plotting ln(k) vs. 1/T

Ants at +10°C?

• Rate constants at different temperatures: k1(T1) = Aexp(-Ea/RT1) ; k2(T2) = Aexp(-Ea/RT2); k1/k2 = exp(-Ea/R(1/T1 - 1/T2))
• Rule of thumb: Reaction rate doubles for a 10°C increase in temperature - a rough idea of temperature effect

Role of ΔE

• Reaction rate: ΔE (change in enthalpy/energy) does not directly affect reaction rate itself
• Reverse reaction: ΔE does affect reverse reaction rate.

Reaction Mechanisms

• Elementary Reactions: Simple reactions that are fundamental steps in a chemical reaction; reactions that occur in single steps.
• Overall Reaction: Summation of elementary reactions.
• Molecularity: Number of molecules participating in an elementary reaction (unimolecular, bimolecular, termolecular).

Rate Laws for Elementary Reactions

• Rate Law vs. Molecularity: m and n in rate law are not always equal to stoichiometric coefficients a and b - depends on the molecularity of the elementary reaction.

Elementary Reactions and Their Rate Laws

• Rate Laws for different molecularities: Summary table for elementary reactions of different molecularities and their associated rate laws - unimolecular, bimolecular, termolecular.

Notes

• Complexity of Reactions: Not all reactions are elementary, as many are multi-step processes
• Rate Law Determination: Rate laws for complex reactions cannot always be determined by inspection; requires analysis of elementary reactions and steps
• Multistep Reactions: Multistep reactions (including intermediates) are common

Process to Determine Reaction Mechanism

• Procedure: Measuring rates, proposing a mechanism, and checking consistency with measured laws to determine reaction mechanism
• Identifying intermediates: Rate-determining step (slowest step) is the key to determine the overall reaction rate.

Rate Law of Proposed Mechanism

• Rate expressions: Combining rate expressions for each step can yield an expression for the overall rate
• Rate Limiting Step: One step (typically slowest step) is rate-limiting; sets overall reaction rate.

Rate Law of Proposed - 2

• Comparison: Compare proposed rate law with experimentally measured rate law
• Inconsistency: If not consistent, propose an alternate mechanism and repeat the process

Catalysts

• Effect on Reaction Rate: Substances that speed up reactions without being consumed themselves
• Mechanism: Catalysts may alter reaction path, leading to a lower activation energy. They may also help reactants come together in the right way or orientation
• Effect on Rate Law: Catalysts affect reaction rate by changing the rate constant (k) often by affecting activation energy

Catalysts: Graphically

• Reaction Coordinate: Catalysis can influence reaction paths and transition states; catalysed pathways with multiple steps show multiple transition state peaks.

Catalysts: Types

• Homogeneous: Reactants, products, and catalysts are in the same phase (like acid catalysis).
• Heterogeneous: Reactants, products, and catalysts are in different phases (like solid catalysts for gas phase reactions)

Natural Catalysts: Enzymes

• Biological Role: Enzymes lower activation energies and are essential for biological processes.
• Example: Nitrogen fixing enzyme nitrogenase plays a role in fertilizers

The Crisis

• Historical Concern: William Crookes predicted widespread starvation in the 1930s due to fertilizer shortages; the prediction came true.
• Background on Agriculture: Plants require nitrogen-based nutrients, and traditional methods used crop rotation, manure composting, etc., to maintain soil fertility.

Fertilizers

• Historical Sources: Early sources of nitrogen based fertilizers (bird guano, Chilean salts).
• Need of solutions: Crookes predicted shortage of natural sources; needing alternative sources

Fritz Haber and Carl Bosch

• Development: Developed a process to produce synthetic ammonia, a crucial fertilizer; fixed nitrogen efficiently
• Scaled up production: Significant engineering challenges overcome in scaling up the Haber-Bosch process
• Industrial Significance: Crucial for producing ammonia based fertilizers; this process became a major factor in feeding the growing population

Synthetic Fertilizers

• Ammonium-based fertilizers: Different types of synthetic fertilizers, like ammonium sulfate and nitrate, their composition, and nitrogen content
• Nitric Acid: Produced from ammonia using the Ostwald process; also used to produce explosives like TNT.

Oppau Plant

• Disaster: Explosion at BASF plant in Oppau, Germany, highlights some hazards associated with ammonia based fertilizer production
• Cause: Poor mixing of nitrogen fertilizers combined with moisture; caused explosion

But Why Is High Pressure Needed for NH3?

• Kinetics of Haber process: The reaction forming ammonia is exothermic at room temperature but very slow due to high activation energy
• Pressure Effect: High pressure improves reaction rates by effectively increasing concentration and thus collisions, needed to overcome the kinetics barrier.

What We Learned

• Arrhenius Equation: Summarizes the relationship between rate constant, temperature, and activation energy; important for understanding temperature impacts
• Activation Energy Difference: Different activation energies can affect speed of reaction.
• Reaction mechanisms: Defined molecularity clarifies rate laws for elementary reactions