Spontaneity of reactions Knowledge-Based Study

Study notes

1. What Is a Spontaneous Process?

   In thermodynamics, a spontaneous process is one that occurs naturally under specified conditions without requiring an ongoing input of external energy. Spontaneity indicates whether a reaction can proceed in the forward direction on its own, but it provides no information about the reaction rate (kinetics).

   The Second Law of Thermodynamics

   The fundamental criterion for spontaneity in the universe is expressed by the Second Law of Thermodynamics:

   • A process is spontaneous if the entropy of the universe increases: $\Delta S_{\text{univ}} > 0$.
   • Here, $\Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}}$.
   • Because heat transferred to or from the surroundings at constant temperature satisfies $\Delta S_{\text{surr}} = -\frac{\Delta H_{\text{sys}}}{T}$, tracking surroundings directly can be inconvenient.

   The Criterion of Gibbs Free Energy

   To evaluate spontaneity solely using system variables at constant temperature and pressure, chemists use the Gibbs free energy change ($\Delta G$):

   $$\Delta G = \Delta H - T\Delta S$$

   where $T$ is absolute temperature in kelvins, $\Delta H$ is the enthalpy change, and $\Delta S$ is the entropy change of the system.

   Interpreting the Sign of $\Delta G$

   • $\Delta G < 0$: The process is spontaneous in the forward direction.
   • $\Delta G = 0$: The system is at dynamic equilibrium.
   • $\Delta G > 0$: The process is non-spontaneous in the forward direction (the reverse process is spontaneous).

   Enthalpy and Entropy Driving Forces

   The sign of $\Delta G$ depends on the interplay between enthalpy ($\Delta H$) and entropy ($\Delta S$), modulated by absolute temperature ($T$):

   • Exothermic with increasing entropy ($\Delta H < 0$, $\Delta S > 0$): $\Delta G$ is negative at all temperatures. Spontaneous at all temperatures.
   • Endothermic with decreasing entropy ($\Delta H > 0$, $\Delta S < 0$): $\Delta G$ is positive at all temperatures. Non-spontaneous at all temperatures.
   • Exothermic with decreasing entropy ($\Delta H < 0$, $\Delta S < 0$): The enthalpy term favors spontaneity, while the entropy term opposes it. Spontaneous only at low temperatures where $|\Delta H| > |T\Delta S|$.
   • Endothermic with increasing entropy ($\Delta H > 0$, $\Delta S > 0$): The entropy term favors spontaneity, while the enthalpy term opposes it. Spontaneous only at high temperatures where $T\Delta S > \Delta H$.

   The transition temperature between non-spontaneous and spontaneous behavior occurs at $\Delta G = 0$:

   $$T = \frac{\Delta H}{\Delta S}$$