Gibbs Free Energy and Thermodynamics

Gibbs Free Energy and Thermodynamics Overview

• Learning Outcomes:

  • Mathematically express the laws of thermodynamics.

  • Explain entropy and its relation to spontaneous change.

  • Predict changes in entropy for processes.

  • Evaluate spontaneity from $ riangle H°$ and $ riangle S°$ values.

  • Calculate $ riangle G°$ using thermodynamic data.

  • Determine $ riangle G$ under non-standard conditions.

  • Understand differences between $ riangle G$ and $ riangle G°$.

  • Derive equilibrium constants from thermochemical data.

  • Calculate $ riangle G°$ and $K_{eq}$ at varying temperatures.

Laws of Thermodynamics

• First Law:

  • Energy cannot be created or destroyed.

  • Change in universal energy: $riangle E<em>{universe} = riangle E</em>{system} + riangle E_{surroundings} = 0$

• Second Law:

  • For any spontaneous process, the entropy of the universe increases.

  • Change in entropy: riangle S{universe} = riangle S{system} + riangle S_{surroundings} > 0

• Third Law:

  • The entropy of a perfect crystal at absolute zero (0 K) is zero.

Spontaneity in Chemical Reactions

• Definition: A spontaneous reaction/process occurs naturally under certain conditions.

  • Key Point: Spontaneous does not equal instantaneous.

  • Nonspontaneous processes require continuous external energy.

• Influences on Spontaneity:

  • Exothermic (\Delta H<0rocesses typically favor spontaneity, but exceptions exist: endothermic reactions can also be spontaneous.

Entropy

• Entropy (S): Describes the distribution of energy in a system.

  • Higher $S$ indicates greater disorder/configuration possibilities.

  • Mathematical definition:

  • Microstate: specific arrangement of energy in the system.

  • Number of microstates (W): $S = k<em>B imes ext{ln}(W)$ where $kB$ is Boltzmann's constant.

  • Entropy increases with increased microstates.

Factors Increasing Entropy

• Processes leading to increased entropy:

  • Melting and evaporation.

  • Increase in temperature.

  • Reactions where the number of gas moles increases (e.g., $2NH<em>4NO</em>3(s) <br>ightarrow 2N<em>2(g) + 4H</em>2O(g) + O_2(g)$).

Entropy and Enthalpy

• For a melting/freezing process, entropies change due to heat exchange.

• Example: When water freezes, riangle S{system} < 0 while riangle S{surroundings} > 0 due to heat loss to surroundings.

Gibbs Free Energy

• Gibbs Free Energy ($ riangle G_{system}$):

  • $riangle G<em>{sys} = riangle H</em>{sys} - T riangle S_{sys}$

  • Determines spontaneity:

  • If riangle G < 0, spontaneous.

  • If riangle G > 0, non-spontaneous.

  • If $riangle G = 0$, the system is at equilibrium.

Criteria for Reaction Spontaneity

• Analyze combinations of $ riangle H$ and $ riangle S$:

  1. riangle H > 0, riangle S > 0
     ightarrow ext{spontaneous at high T}

  2. riangle H < 0, riangle S < 0
     ightarrow ext{spontaneous at low T}

Non-standard Conditions and $ riangle G$

• For non-standard conditions, use the equation:

  • $riangle G = riangle G° + RT ext{ln}(Q)$

• Where R is the gas constant and Q is the reaction quotient.

• If $Q = K$, then $riangle G = 0$.

Relationship Between $ riangle G$ and Equilibrium Constant (K)

• $riangle G° = -RT ext{ln}(K)$

  • If $K < 1$, $riangle G°$ is positive (reverse direction is spontaneous).

  • If $K > 1$, $riangle G°$ is negative (forward direction is spontaneous).

Final Thoughts on Gibbs Free Energy

• Differentiate between $ riangle G°$ (standard conditions) and $ riangle G$ (actual conditions).

  • $ riangle G°$ indicates the inherent tendency of a reaction to occur.

  • $ riangle G$ shows the distance from equilibrium state.