Gibbs Free Energy

Gibbs free energy, denoted by \( \Delta G \), is a thermodynamic quantity that determines whether a process is spontaneous at constant temperature and pressure.

The formula is:

\[ \Delta G = \Delta H - T\Delta S \]

\( \Delta G \): Gibbs free energy change (J)
\( \Delta H \): Enthalpy change (J)
\( T \): Temperature in Kelvin (K)
\( \Delta S \): Entropy change (J/K)

Spontaneity Criteria:

\( \Delta G < 0 \): Reaction is spontaneous
\( \Delta G = 0 \): Reaction is at equilibrium
\( \Delta G > 0 \): Reaction is non-spontaneous

This equation shows how both enthalpy and entropy influence the spontaneity of a process.

Gibbs free energy can also be written as

\(G = - RTlnK\)
\(G = -nFE\)

Where:

R = Universal Gas Constant
T = Temperature
K = Equilibrium Constant
n = Number of Moles
F = Faraday's Constant
E = Electrochemical Potential

At room temperature (298 K), ice melts spontaneously. Let's consider the thermodynamic values:

\( \Delta H = +6.01 \, \text{kJ/mol} \)
\( \Delta S = +22.0 \, \text{J/mol·K} \)

Convert \( \Delta S \) to kJ: \( 22.0 \, \text{J/mol·K} = 0.022 \, \text{kJ/mol·K} \)

\[ \Delta G = 6.01 - (298 \times 0.022) = 6.01 - 6.556 = -0.546 \, \text{kJ/mol} \]

Conclusion: Since \( \Delta G < 0 \), melting is spontaneous at 298 K.

The thermal decomposition of calcium carbonate:

\[ \text{CaCO}_3 (s) \rightarrow \text{CaO} (s) + \text{CO}_2 (g) \]

\( \Delta H = +178 \, \text{kJ/mol} \)
\( \Delta S = +160 \, \text{J/mol·K} = 0.160 \, \text{kJ/mol·K} \)

At 298 K:

\[ \Delta G = 178 - (298 \times 0.160) = 178 - 47.68 = 130.32 \, \text{kJ/mol} \]

Conclusion: Since \( \Delta G > 0 \), this reaction is non-spontaneous at room temperature.

Written by Thenura Wickramaratna