Chapter: Equilibria, Rates, and Mechanisms

1. Introduction to Chemical Reactions

• Chemical Reaction: A process that involves the rearrangement of the atomic, ionic, or molecular structure of a substance, usually entailing the breaking and making of chemical bonds, resulting in new substances.
• Driving Forces: Reactions proceed to achieve a more stable state (lower energy), driven by changes in enthalpy (ΔH) and entropy (ΔS), which combine to determine Gibbs Free Energy (ΔG).
  • ΔG=ΔH−TΔS
  • A negative ΔG indicates a spontaneous (exergonic) reaction that will proceed towards products.
  • A positive ΔG indicates a non-spontaneous (endergonic) reaction.
  • ΔG=0 indicates the system is at equilibrium.

2. Chemical Equilibrium

• Reversible Reactions: Most chemical reactions are reversible, meaning products can revert to reactants.
• Chemical Equilibrium: A state in which the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of reactants and products remain constant (though not necessarily equal). It is a dynamic state, not a static one.
• Equilibrium Constant (K): A value that expresses the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their stoichiometric coefficients.
  • For a generic reaction: aA+bB⇌cC+dD
    Kc​=[A]a[B]b[C]c[D]d​
  • If K>1: Products are favored at equilibrium.
  • If K<1: Reactants are favored at equilibrium.
  • If K≈1: Significant amounts of both reactants and products are present at equilibrium.
  • Relationship between ΔG∘ and K: ΔG∘=−RTlnK
    • ΔG∘ is the standard Gibbs free energy change.
    • R is the ideal gas constant.
    • T is the temperature in Kelvin.
• Le Chatelier’s Principle: If a change of condition is applied to a system in equilibrium, the system will shift in a direction that relieves the stress.
  • Change in Concentration: Adding reactant shifts equilibrium to products; adding product shifts to reactants. Removing reactant shifts to reactants; removing product shifts to products.
  • Change in Temperature: For an endothermic reaction (ΔH>0), increasing temperature shifts to products. For an exothermic reaction (ΔH<0), increasing temperature shifts to reactants. (Think of heat as a reactant/product).
  • Change in Pressure (for gases): Increasing pressure (decreasing volume) shifts equilibrium to the side with fewer moles of gas. Decreasing pressure (increasing volume) shifts to the side with more moles of gas.
  • Catalyst: A catalyst increases the rates of both forward and reverse reactions equally, thus it does NOT affect the position of equilibrium (the value of K). It only helps the system reach equilibrium faster.

3. Reaction Rates (Kinetics)

• Reaction Rate: The speed at which reactants are consumed and products are formed over time.
• Rate Law: An equation that describes how the rate of a reaction depends on the concentration of reactants (and sometimes products or catalysts). It is determined experimentally.
  • For aA+bB→Products
    Rate=k[A]x[B]y
    • k: Rate constant (temperature-dependent).
    • x: Order of reaction with respect to A.
    • y: Order of reaction with respect to B.
    • x+y: Overall order of reaction.
• Order of Reaction:
  • Zero-order: Rate is independent of reactant concentration (e.g., Rate=k).
  • First-order: Rate is directly proportional to the concentration of one reactant (e.g., Rate=k[A]).
  • Second-order: Rate is proportional to the square of one reactant concentration or the product of two reactant concentrations (e.g., Rate=k[A]2 or Rate=k[A][B]).
• Factors Affecting Reaction Rate:
  • Concentration of Reactants: Generally, higher concentrations lead to more frequent collisions and thus faster rates. (As expressed in the rate law).
  • Temperature: Increasing temperature increases the kinetic energy of molecules, leading to more frequent and more energetic collisions. This significantly increases the rate constant (k) and thus the overall reaction rate. (Arrhenius equation relates k to T).
  • Presence of a Catalyst: Catalysts increase reaction rates without being consumed. They do this by providing an alternative reaction pathway with a lower activation energy.
  • Surface Area (for heterogeneous reactions): Greater surface area allows for more contact between reactants, increasing the rate.
  • Nature of Reactants: The chemical identity of reactants (bond strengths, molecular complexity) inherently influences how fast they react.

4. Reaction Mechanisms

• Reaction Mechanism: A step-by-step description of how a chemical reaction occurs at the molecular level. It shows the sequence of elementary steps.
• Elementary Step (or Elementary Reaction): A single step in a reaction mechanism that describes an actual molecular event (e.g., a collision, a bond breaking, or a bond forming). The molecularity of an elementary step is the number of reactant molecules involved in that step.
  • Unimolecular: One molecule reacts (e.g., A → products). Rate ∝ [A].
  • Bimolecular: Two molecules react (e.g., A + B → products or 2A → products). Rate ∝ [A][B] or Rate∝[A]2.
  • Termolecular: Three molecules react (rare).
• Intermediates: Species that are formed in one elementary step and consumed in a subsequent elementary step. They do not appear in the overall balanced chemical equation. Intermediates are usually unstable and highly reactive (e.g., carbocations, carbanions, radicals, enolates). They exist for a transient period.
• Transition States (Activated Complexes): High-energy, unstable arrangements of atoms that represent the peak of an energy barrier between reactants and products (or between an intermediate and another species). They cannot be isolated. A reaction mechanism involves at least one transition state per elementary step.
• Rate-Determining Step (RDS) / Rate-Limiting Step: The slowest elementary step in a reaction mechanism. The rate law of the overall reaction is determined by the molecularity of this slowest step and the concentrations of the species involved up to and including that step.
• Energy Diagrams (Reaction Coordinate Diagrams): Visual representations of the energy changes during a reaction.
  • X-axis: Reaction coordinate (progress of the reaction).
  • Y-axis: Potential energy.
  • Reactants and Products: Energy minima.
  • Transition States: Energy maxima (peaks). The energy difference between reactants and the highest energy transition state is the activation energy (Ea​).
  • Intermediates: Local energy minima (valleys between transition states).
  • Activation Energy (Ea​): The minimum energy required for a reaction to occur. A higher Ea​ means a slower reaction rate. Catalysts lower the Ea​.
  • Exothermic Reaction: Products are at a lower energy than reactants (ΔH is negative).
  • Endothermic Reaction: Products are at a higher energy than reactants (ΔH is positive).

5. Types of Mechanisms in Organic Chemistry (Briefly)

• Concerted Mechanism: All bond breaking and bond forming occur simultaneously in a single elementary step (e.g., SN​2 reaction, Diels-Alder reaction). Characterized by a single transition state and no intermediates.
• Stepwise Mechanism: Involves two or more elementary steps, with at least one intermediate formed (e.g., SN​1 reaction, electrophilic addition to alkenes). Characterized by multiple transition states and one or more intermediates.
• Common Mechanistic Patterns:
  • Nucleophilic Attack: An electron-rich species (nucleophile) attacks an electron-deficient species (electrophile).
  • Proton Transfer: Acid-base reactions, involving the donation and acceptance of a proton.
  • Leaving Group Departure: A group leaves a molecule, taking its bonding electrons with it.
  • Rearrangement: A change in connectivity within a molecule, often to form a more stable intermediate (e.g., carbocation rearrangements).
  • Radical Reactions: Involve species with unpaired electrons.

6. Importance of Mechanisms

• Understanding Reactivity: Mechanisms explain why reactions occur at certain rates and how they lead to specific products.
• Predicting Products: Knowing the mechanism allows chemists to predict the products of new reactions and understand stereochemical outcomes.
• Optimizing Reactions: By understanding the rate-determining step and influencing factors, conditions can be optimized to improve reaction yield and rate.
• Designing New Reactions: Insights from mechanisms help in the rational design of novel synthetic methodologies.

Multiple Choice Questions (MCQ) on Equilibria, Rates, and Mechanisms

Instructions: Choose the best answer for each question.

1. A chemical reaction that has a negative Gibbs Free Energy change (ΔG<0) is considered: a) Non-spontaneous b) Endergonic c) Exergonic d) At equilibrium

2. At chemical equilibrium, which of the following statements is true? a) The concentrations of reactants and products are equal. b) The forward reaction rate is zero. c) The rate of the forward reaction equals the rate of the reverse reaction. d) The reaction has stopped.

3. For the reaction 2A+B⇌3C, what is the correct expression for the equilibrium constant Kc​? a) Kc​=[C]3[A]2[B]​ b) Kc​=[A]2[B][C]3​ c) Kc​=[A][B][C]​ d) Kc​=2[A][B]3[C]​

4. If the equilibrium constant (K) for a reaction is much greater than 1 (K≫1), what does this indicate? a) Reactants are favored at equilibrium. b) Products are favored at equilibrium. c) The reaction is very slow. d) The activation energy is very high.

5. According to Le Chatelier’s Principle, if the concentration of a reactant is increased in a system at equilibrium, which way will the equilibrium shift? a) Towards the reactants. b) Towards the products. c) No change will occur. d) The reaction will stop.

6. For an exothermic reaction (ΔH<0), how will increasing the temperature affect the position of equilibrium? a) Shift towards products. b) Shift towards reactants. c) No change in equilibrium position. d) Increase the equilibrium constant K.

7. What is the effect of adding a catalyst to a chemical reaction at equilibrium? a) It shifts the equilibrium position towards the products. b) It increases the equilibrium constant K. c) It only increases the rate of the forward reaction. d) It increases the rates of both forward and reverse reactions equally, reaching equilibrium faster.

8. What does the rate law of a reaction describe? a) The change in Gibbs Free Energy. b) The ratio of products to reactants at equilibrium. c) How the reaction rate depends on the concentration of reactants. d) The overall enthalpy change.

9. For a reaction with the rate law Rate=k[A]2[B]1, what is the overall order of the reaction? a) First-order b) Second-order c) Third-order d) Zero-order

10. What typically happens to the rate constant (k) of a reaction as temperature increases? a) It decreases. b) It remains constant. c) It increases. d) It becomes zero.

11. Which of the following is an elementary step involving only one molecule? a) Bimolecular b) Unimolecular c) Termolecular d) Quaternary

12. What is an intermediate in a reaction mechanism? a) A species that is a reactant in the overall reaction. b) A high-energy, unstable arrangement of atoms that cannot be isolated. c) A species formed in one elementary step and consumed in a subsequent step. d) A catalyst that is consumed during the reaction.

13. A transition state (activated complex) represents: a) A stable product of a reaction. b) A local energy minimum on a reaction coordinate diagram. c) A high-energy, unstable structure at the peak of an energy barrier. d) A reactant that is consumed in the slowest step.

14. What is the rate-determining step (RDS) in a reaction mechanism? a) The fastest elementary step. b) The step that occurs first. c) The slowest elementary step. d) The step that consumes the most reactants.

15. What is the activation energy (Ea​)? a) The overall energy change of a reaction. b) The energy released during a reaction. c) The minimum energy required for a reaction to occur. d) The energy of the products.

16. How does a catalyst increase the rate of a reaction? a) By increasing the concentration of reactants. b) By increasing the kinetic energy of molecules. c) By providing an alternative reaction pathway with a lower activation energy. d) By shifting the equilibrium towards products.

17. In an energy diagram, what do the “valleys” between peaks represent? a) Reactants b) Products c) Transition states d) Intermediates

18. Which type of mechanism involves all bond breaking and bond forming occurring simultaneously in a single elementary step? a) Stepwise mechanism b) Radical mechanism c) Concerted mechanism d) Chain reaction mechanism

19. What is the relationship between the standard Gibbs Free Energy change (ΔG∘) and the equilibrium constant (K)? a) ΔG∘=RTlnK b) ΔG∘=−RTlnK c) ΔG∘=K/RT d) ΔG∘=TΔS−ΔH

20. If a reaction doubles its rate when the concentration of reactant A is doubled (while other concentrations are kept constant), what is the order of reaction with respect to A? a) Zero-order b) First-order c) Second-order d) Cannot be determined

21. For a reaction that proceeds from reactants to products, if the products are lower in energy than the reactants, the reaction is: a) Endothermic b) Exothermic c) At equilibrium d) Inhibited

22. Which of the following is NOT a factor affecting reaction rate? a) Concentration of reactants b) Temperature c) Overall Gibbs Free Energy Change (ΔG) d) Presence of a catalyst

23. What is the molecularity of the elementary step: A+B→C? a) Unimolecular b) Bimolecular c) Termolecular d) Zero-order

24. Which of the following is typically a very unstable and highly reactive species? a) Reactants b) Products c) Intermediates d) Catalysts

25. A reaction with a very high activation energy (Ea​) will generally have a: a) Fast reaction rate. b) Slow reaction rate. c) Large equilibrium constant. d) Small equilibrium constant.

26. If the pressure of a gaseous equilibrium system is increased, and the product side has fewer moles of gas than the reactant side, the equilibrium will shift: a) Towards the products. b) Towards the reactants. c) No change will occur. d) The reaction will stop.

27. In a reaction mechanism, the sum of the elementary steps must equal: a) The rate law. b) The activation energy. c) The overall balanced chemical equation. d) The equilibrium constant.

28. What type of reaction mechanism involves at least one intermediate? a) Concerted mechanism b) Radical mechanism c) Stepwise mechanism d) Pericyclic mechanism

29. If a reaction is spontaneous at standard conditions (ΔG∘<0), what can be said about its equilibrium constant K? a) K<1 b) K=1 c) K>1 d) K=0

30. Which common mechanistic pattern involves an electron-rich species attacking an electron-deficient species? a) Proton transfer b) Leaving group departure c) Nucleophilic attack d) Rearrangement

31. The rate constant (k) for a reaction is dependent on: a) Reactant concentrations. b) Product concentrations. c) Temperature. d) Time.

32. For an endothermic reaction (ΔH>0), how will decreasing the temperature affect the equilibrium? a) Shift towards products. b) Shift towards reactants. c) No change in equilibrium position. d) Increase the value of K.

33. In an energy diagram, what is the energy difference between the reactants and the highest energy transition state? a) ΔH b) ΔG c) Ea​ (Activation Energy) d) Energy of intermediate

34. What is the main purpose of studying reaction mechanisms in organic chemistry? a) To determine the boiling point of compounds. b) To understand and predict reactivity, product formation, and reaction optimization. c) To calculate the molecular weight of compounds. d) To measure the concentration of reactants.

35. If a reaction exhibits zero-order kinetics, how does its rate change if the reactant concentration is doubled? a) It doubles. b) It quadruples. c) It remains the same. d) It halves.

36. A catalyst works by: a) Participating in the reaction to form a new product. b) Increasing the temperature of the reaction. c) Providing an alternative reaction pathway with a higher transition state. d) Providing an alternative reaction pathway with a lower activation energy.

37. Which definition of acids and bases is most applicable when discussing electron pair movement in reaction mechanisms? a) Arrhenius b) Brønsted-Lowry c) Lewis d) All are equally applicable

38. Which term refers to a change in connectivity within a molecule, often occurring to form a more stable intermediate? a) Elimination b) Rearrangement c) Addition d) Substitution

39. If the equilibrium constant K for a reaction is less than 1 (K<1), what is true about ΔG∘ for the reaction? a) ΔG∘>0 b) ΔG∘<0 c) ΔG∘=0 d) ΔG∘ is undefined

40. Why don’t intermediates appear in the overall balanced chemical equation? a) They are too unstable to be detected. b) They are consumed as fast as they are formed. c) They are formed in one step and consumed in a later step. d) They are not involved in the actual reaction.

Answer Key with Explanations

1. c) Exergonic.
   • Explanation: An exergonic reaction is a spontaneous chemical reaction where the change in the Gibbs free energy is negative (ΔG<0), meaning it releases energy and favors product formation.
2. c) The rate of the forward reaction equals the rate of the reverse reaction.
   • Explanation: Chemical equilibrium is a dynamic state where the opposing reactions occur at the same rate, leading to no net change in concentrations.
3. b) Kc​=[A]2[B][C]3​.
   • Explanation: The equilibrium constant is defined as the ratio of the product of the concentrations of the products raised to their stoichiometric coefficients to the product of the concentrations of the reactants raised to their stoichiometric coefficients.
4. b) Products are favored at equilibrium.
   • Explanation: A large K value indicates that at equilibrium, the concentration of products is significantly higher than the concentration of reactants.
5. b) Towards the products.
   • Explanation: According to Le Chatelier’s Principle, increasing the concentration of a reactant stresses the equilibrium, and the system shifts to consume the added reactant, thus favoring product formation.
6. b) Shift towards reactants.
   • Explanation: For an exothermic reaction, heat is a product. Increasing temperature is like adding a product, so the equilibrium shifts to consume that added heat, moving towards the reactants.
7. d) It increases the rates of both forward and reverse reactions equally, reaching equilibrium faster.
   • Explanation: Catalysts accelerate reactions by lowering activation energy but do not alter the relative stabilities of reactants and products, thus having no effect on the position of equilibrium or the value of K.
8. c) How the reaction rate depends on the concentration of reactants.
   • Explanation: The rate law is an experimentally determined expression that quantitatively relates the rate of a reaction to the concentrations of the reactants.
9. c) Third-order.
   • Explanation: The overall order of reaction is the sum of the individual orders with respect to each reactant. Here, 2+1=3.
10. c) It increases.
    • Explanation: Increasing temperature increases the kinetic energy of molecules, leading to more frequent and energetic collisions, which in turn increases the rate constant (k) and the overall reaction rate.
11. b) Unimolecular.
    • Explanation: A unimolecular elementary step involves only one molecule undergoing a transformation (e.g., bond cleavage or rearrangement).
12. c) A species formed in one elementary step and consumed in a subsequent step.
    • Explanation: Intermediates are transient species that are produced and then reacted away within the mechanism. They do not appear in the net chemical equation.
13. c) A high-energy, unstable structure at the peak of an energy barrier.
    • Explanation: A transition state is a fleeting, unstable arrangement of atoms that represents the highest energy point along the reaction pathway between reactants and products (or intermediates).
14. c) The slowest elementary step.
    • Explanation: The rate-determining step (or rate-limiting step) is the slowest elementary step in a multi-step reaction mechanism, as it dictates the overall rate of the reaction.
15. c) The minimum energy required for a reaction to occur.
    • Explanation: Activation energy (Ea​) is the energy barrier that must be overcome for reactants to transform into products.
16. c) By providing an alternative reaction pathway with a lower activation energy.
    • Explanation: Catalysts work by offering a different reaction pathway that has a lower energy barrier (lower Ea​), thus speeding up both the forward and reverse reactions.
17. d) Intermediates.
    • Explanation: In an energy diagram, intermediates are represented by local energy minima (valleys) between transition states (peaks).
18. c) Concerted mechanism.
    • Explanation: A concerted mechanism involves a single elementary step where all bond breaking and bond forming processes occur simultaneously, passing through a single transition state.
19. b) ΔG∘=−RTlnK.
    • Explanation: This fundamental thermodynamic equation relates the standard Gibbs Free Energy change to the equilibrium constant.
20. b) First-order.
    • Explanation: If doubling the concentration of A doubles the rate, the exponent x in the rate law Rate=k[A]x must be 1 (Rate∝[A]1).
21. b) Exothermic.
    • Explanation: In an exothermic reaction, the products have lower potential energy than the reactants, indicating a release of heat.
22. c) Overall Gibbs Free Energy Change (ΔG).
    • Explanation: ΔG determines the spontaneity and equilibrium position of a reaction, but not its rate. Rate is determined by activation energy and factors like concentration and temperature.
23. b) Bimolecular.
    • Explanation: A bimolecular elementary step involves two reactant molecules colliding to form products.
24. c) Intermediates.
    • Explanation: Intermediates are generally unstable, short-lived, and highly reactive species because they often contain incomplete octets or unpaired electrons.
25. b) Slow reaction rate.
    • Explanation: A higher activation energy means a larger energy barrier must be overcome, leading to fewer molecules having sufficient energy to react, resulting in a slower reaction rate.
26. a) Towards the products.
    • Explanation: Increasing pressure shifts the equilibrium to the side with fewer moles of gas to relieve the stress. If products have fewer moles of gas, the shift is towards products.
27. c) The overall balanced chemical equation.
    • Explanation: The individual elementary steps in a reaction mechanism must sum up to give the overall balanced chemical equation for the reaction.
28. c) Stepwise mechanism.
    • Explanation: A stepwise mechanism is characterized by multiple elementary steps and the formation of one or more intermediates.
29. c) K>1.
    • Explanation: If ΔG∘<0 (spontaneous), then from ΔG∘=−RTlnK, it follows that lnK must be positive, which means K>1.
30. c) Nucleophilic attack.
    • Explanation: Nucleophilic attack involves a nucleophile (electron-rich) using its electron pair to form a new bond with an electrophile (electron-deficient).
31. c) Temperature.
    • Explanation: The rate constant (k) is sensitive to temperature, increasing significantly with higher temperatures as described by the Arrhenius equation. It is independent of reactant concentrations.
32. b) Shift towards reactants.
    • Explanation: For an endothermic reaction (ΔH>0, heat is a reactant), decreasing the temperature is like removing a reactant (heat), causing the equilibrium to shift to replace it, moving towards the reactants.
33. c) Ea​ (Activation Energy).
    • Explanation: The activation energy (Ea​) is the energy difference between the reactants’ energy level and the energy level of the transition state.
34. b) To understand and predict reactivity, product formation, and reaction optimization.
    • Explanation: Understanding mechanisms provides fundamental insights into why reactions occur, how products are formed, and allows for rational design and optimization of synthetic routes.
35. c) It remains the same.
    • Explanation: For a zero-order reaction, the rate is independent of the reactant concentration. Doubling the concentration has no effect on the rate.
36. d) Providing an alternative reaction pathway with a lower activation energy.
    • Explanation: Catalysts function by changing the reaction mechanism to one with a lower energy transition state, thereby reducing the activation energy and increasing the reaction rate.
37. c) Lewis.
    • Explanation: The Lewis definition of acids (electron pair acceptors) and bases (electron pair donors) is particularly useful in mechanistic organic chemistry as it describes the movement of electron pairs in bond-forming and bond-breaking steps.
38. b) Rearrangement.
    • Explanation: A rearrangement reaction involves a reorganization of the atoms within a molecule, often driven by the formation of a more stable intermediate (e.g., a more stable carbocation).
39. a) ΔG∘>0.
    • Explanation: If K<1, it means reactants are favored at equilibrium, indicating a non-spontaneous reaction under standard conditions. From ΔG∘=−RTlnK, if lnK is negative (because K<1), then ΔG∘ must be positive.
40. c) They are formed in one step and consumed in a later step.
    • Explanation: Intermediates are short-lived species that are produced and then reacted away within the sequence of elementary steps. They are transient and therefore do not appear in the overall balanced equation.