6.7 Describing a Reaction: Equilibria, Rates, and Energy Changes

Chemical reactions are all about balance and energy. Equilibrium constants tell us where reactions end up, while free energy changes reveal if they'll happen on their own. These concepts help us predict and control reactions in the lab and in nature.

Enthalpy and entropy are the yin and yang of chemistry. Enthalpy deals with heat changes, while entropy measures disorder. Together, they determine if a reaction is favorable. Understanding these helps us design better processes and explain why some reactions occur spontaneously.

Equilibria, Rates, and Energy Changes in Organic Reactions

Equilibrium constants and free energy

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• Equilibrium constant ($K$)
  • Represents the ratio of product concentrations to reactant concentrations when a reaction reaches equilibrium state
  • Calculated using the equation $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ for the reaction $aA + bB \rightleftharpoons cC + dD$ where $a$, $b$, $c$, and $d$ are the stoichiometric coefficients
  • Higher $K$ values signify the reaction favors the formation of products at equilibrium (product-favored) while lower $K$ values indicate the reaction favors reactants (reactant-favored)
  • Le Chatelier's principle explains how the equilibrium position shifts in response to changes in concentration, pressure, or temperature
• Gibbs free energy change ($\Delta G$)
  • Thermodynamic quantity that determines the spontaneity and direction of a reaction at constant temperature and pressure conditions
  • Calculated using the equation $\Delta G = \Delta H - T\Delta S$ where $\Delta H$ represents the change in enthalpy, $T$ is the absolute temperature, and $\Delta S$ is the change in entropy
  • Related to the equilibrium constant $K$ through the equation $\Delta G = -RT\ln K$ where $R$ is the gas constant and $T$ is the absolute temperature
  • Negative $\Delta G$ values ($\Delta G < 0$) indicate a spontaneous reaction that favors the formation of products
  • Positive $\Delta G$ values ($\Delta G > 0$) suggest a non-spontaneous reaction that favors the reactants
  • When $\Delta G = 0$, the system is at equilibrium, and the concentrations of reactants and products remain constant

Enthalpy and entropy in reactions

• Enthalpy ($\Delta H$)
  • Thermodynamic quantity that measures the heat energy change during a reaction at constant pressure
  • Exothermic reactions have a negative $\Delta H$ ($\Delta H < 0$) and release heat energy to the surroundings (combustion reactions)
  • Endothermic reactions have a positive $\Delta H$ ($\Delta H > 0$) and absorb heat energy from the surroundings (photosynthesis)
• Entropy ($\Delta S$)
  • Thermodynamic property that measures the disorder or randomness of a system
  • Reactions that increase disorder (more gas molecules or fewer moles of reactants than products) have a positive $\Delta S$ and are entropically favored
  • Reactions that decrease disorder (fewer gas molecules or more moles of reactants than products) have a negative $\Delta S$ and are entropically disfavored
• Gibbs free energy ($\Delta G$) combines the contributions of enthalpy and entropy to determine reaction favorability
  • Calculated using the equation $\Delta G = \Delta H - T\Delta S$
  • Favorable reactions have a negative $\Delta G$ ($\Delta G < 0$) and are driven by either a decrease in enthalpy (exothermic) or an increase in entropy (more disorder)
  • Unfavorable reactions have a positive $\Delta G$ ($\Delta G > 0$) and are driven by either an increase in enthalpy (endothermic) or a decrease in entropy (less disorder)

Reaction rates vs equilibrium positions

• Reaction rates
  • Measure of the speed at which reactants are converted into products over time
  • Determined by the slowest step in the reaction mechanism, known as the rate-determining step (RDS)
  • Influenced by factors such as temperature (Arrhenius equation), reactant concentrations (rate law), surface area (heterogeneous reactions), and the presence of catalysts
  • Independent of the equilibrium position of the reaction and do not determine the final concentrations of reactants and products
• Equilibrium position
  • Represents the relative concentrations of reactants and products when a reaction reaches a dynamic equilibrium state
  • Determined by the equilibrium constant ($K$) and the Gibbs free energy change ($\Delta G$) of the reaction
  • Achieved when the forward and reverse reaction rates become equal, resulting in no net change in reactant and product concentrations
  • Unaffected by factors that influence reaction rates, such as the presence of catalysts, which only accelerate the attainment of equilibrium without shifting its position
• Relationship between reaction rates and equilibrium
  • Reaction rates govern the time required for a system to reach equilibrium but do not affect the equilibrium position itself
  • The equilibrium position is determined by thermodynamic factors ($\Delta G$, $\Delta H$, and $\Delta S$) and is independent of the reaction rates

Reaction energy profile

• Activation energy: The minimum energy required for a reaction to occur
• Transition state: The highest energy point on the reaction coordinate, representing the unstable intermediate structure between reactants and products
• Reaction coordinate diagram: A graphical representation of the energy changes during a reaction, showing the relationship between reactants, transition state, and products
• Collision theory: Explains how reactions occur when reactant molecules collide with sufficient energy and proper orientation