12: Chemical Kinetics and Catalysts

Lecture 12 Announcements

• Topics Covered: Chemical Equilibrium, the Concept of Equilibrium, the Equilibrium Constant, Understanding and Working with Equilibrium Constants, Calculating Equilibrium Constants, Le Châtelier's Principle, Free Energy and the Equilibrium Constant
• Assigned Readings: Brown Chapter 15
• Problem Sets: Problem Set 11 due before Exercise #12 tomorrow, Problem Set 12 due before Exercise #13 next week. Both problem sets are posted on Moodle
• 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, 8:30-10:30

Lecture 13

• Topics Covered: Acid-Base Equilibria, the Autoionization of Water, The pH Scale, Strong Acids and Bases, Weak Acids, Weak Bases, Additional Aspects of Aqueous Equilibria, The Common-Ion Effect, Buffers
• Assigned Readings: Brown Chapter 16 and Chapter 17

Red Thread (Last Three Weeks)

• Concepts: Properties, Kinetics, Catalysis, Acid-Base, Equilibrium, Christmas!, Batteries

Review of Lecture 11

• Kinetics: Role of temperature in kinetics, the Arrhenius equation (k(T) = A exp(-Ea/RT)), activation energy (Ea), factors affecting reaction rate (Ea can be large or small
• Spontaneous Reactions: Why some spontaneous reactions are fast and others are slow (activation energy, independent of enthalpy change)
• Rate Laws: Rate = k[A]m[B]n[C]p, what do m, n, p represent (stoichiometric coefficients for multistep reactions of elementary reactions), molecularity, elementary reactions

Why High Pressure is Needed to Produce NH3 (Haber-Bosch Process)

• Haber-Bosch Process: Reaction to convert N2 and H2 to NH3.
• Spontaneity vs. Kinetics: Reaction is spontaneous at room temperature, but slow due to high activation energy.
• Catalysts: Catalysts lower activation energy, but still require high temperature to get reasonable reaction rates.
• Pressure: Increasing pressure shifts the reaction towards products

Today: Equilibrium (Dynamic Equilibrium in Chemical Reactions)

• Definition of dynamic equilibrium: reaction and reverse processes balance, no net change in concentrations
• Examples of dynamic equilibrium: saturated solutions, Henry's Law, vapor pressure.
• Dynamic Equilibrium: Molecules leaving/entering gas phase in equilibrium.
• Equilibrium is dynamic: even though the concentrations are stable, molecules are still reacting in both directions.
• Assumption of Reactions: Reaction that go only forward or reverse reactions only.
• Equilibrium is reached in both directions simultaneously

Chemical Equilibrium

• Equilibrium occurs when forward and reverse rates are equal.
• Rate constants: kf (forward) and kr (reverse)
• Equilibrium Constant: The ratio of product concentrations to reactant concentrations at equilibrium, which is written mathematically as K.
• [B]/[A] = K

Equilibrium Constant (K)

• Equilibrium constant, K, relates the concentrations of products to reactants.
• K depends on temperature (T).
• K for Reaction in Reverse: K is 1/K for the reverse reaction
• Multiple reaction: K is the product of the individual reaction constants.

Equilibrium Constant and Pressure

• The equilibrium constant in terms of partial pressure, Kp
• General case Kp ≠ Kc;Kp = Kc * (RT)Δn, where R= gas constant ,T= absolute temperature. Δn = The difference between the number of moles of gaseous products and the number of moles of gaseous reactants

Important Considerations About Kc and Kp

• K is unitless.
• Relating K to Equilibrium concentration, Activity: The ratio of concentration to a reference concentration or pressure.
• Units of K, depend on stoichiometry and whether pressure measurements are in bars or atmospheres.
• Magnitude of equilibrium constant K:
  -If K > 1: Equilibrium lies towards products- products dominate the system. -If K < 1: Equilibrium lies towards reactants -reactants dominate the system.
• Reaction Quotient (Q) : For calculating position of reaction away from Equilibrium.

Equilibrium Math

• Equilibrium constant K for a reaction written in reverse is inverted. (if a reaction is written in reverse , then the equilibrium constant for the new reaction is 1/original reaction equilibrium constant).
• If reaction written with multiple of a constant n, the equilibrium constant will be raised to the power of n. (Example; if a reaction is multiplied by 3, then equilibrium constant is raised to power 3 )
• Equilibrium constant K for a multistep reaction is the product of the equilibrium constants of the individual reactions

Equilibrium Considerations: Solids and Pure Liquids

• In Heterogeneous Equilibria: Removing pure solids and pure liquids from K expressions.
• Equilibrium Constant for Solid and/or Liquid: Concentrations of pure solids and pure liquids are considered to be constant; therefore are omitted from Equilibrium constant expressions.
• Solubility product: for saturate solutions of low solubility ionic solids

Implications of Equilibrium in a Closed System

• Product yield is limited by closed system, open system might yield more products.
• Equilibrium sets maximum amount product obtainable.

Le Chatelier's Principle

• If system at equilibrium is disturbed by changes in temperature (T), pressure (P), or concentration, the system will shift its equilibrium to counteract the change, to approach back to new equilibrium in a closed system.

Concentration Changes at Equilibrium

• Adding more reactant or product shifts system to re-establish equilibrium
• Adding more Reactant pushes the reaction to the right, creating more product
• Adding more Product pushes the reaction to the left, making more reactant.

Temperature Changes at Equilibrium

• In Exothermic reaction, increasing temperature will cause the equilibrium to shift toward the reactants and vice-versa.
• In endothermic reaction, increasing temperature will cause the equilibrium to shift toward the products and vice versa.

Catalysts and Equilibrium

• Catalyst: A substance that increases the rate of a chemical reaction without itself undergoing a permanent chemical change.
• Effect on Equilibrium: Catalysts do not affect the equilibrium constant, K; they only speed up the rate by which equilibrium is achieved.

Equilibrium, Thermodynamics & Free Energy

• Relation between K (Equilibrium constant) and Thermodynamic parameters: The relationship of equilibrium constant K to Gibbs free energy G.
• Equilibrium and Spontaneity: Spontaneous reactions, when ∆G is negative.
• Equilibrium and Rate: Equilibrium constant and reaction rates

Gibbs Free Energy, AG

• ∆G = Free energy change, a product of T (Temperature), and R (Ideal gas constant), and ∆G°
• Standard Free Energy Change:∆ G°
• Equilibrium constant and Gibbs free energy AG: AG = −RT ln K

Relationship Between ∆G° and K

• ∆G° and K relationship: If ∆G° is negative (-), K is greater than 1 (equilibrium lies toward products).
• ∆G° and K relationship: If ∆G° is positive (+), K is less than 1 (equilibrium favor reactants).

Summary of Key Concepts in Equilibrium

• Dynamic equilibrium
• Equilibrium constant (Kc,Kp)
• Reaction quotient (Q)
• Le Chatelier's Principle
• Catalyst effects
• Relation between ∆G and K
• Equilibrium, Thermodynamics, and free Energy
• Significance of K

Test your understanding of chemical kinetics, catalysts, and the Haber–Bosch process. This quiz covers key concepts, such as the role of catalysts, reaction rates, and the activity of species in chemical reactions. Dive into the principles that govern the energy barriers and equilibrium in reactions.