**Calculation of Change in Standard Gibbs Free Energy (\(\Delta G^\circ\))**

A thermodynamically favored process is one that has \(\Delta G ^\circ < 0\). A process is not thermodynamically favored if \(\Delta G ^\circ> 0\). The \( \Delta G ^\circ \) can be calculated using \( \Delta G^\circ = \Delta H^\circ – T\Delta S^\circ\).

**Example 1.**

Calculate \(\Delta G ^\circ \) at \(298 \text{ K}\) for the following process.

\(\require{mhchem}\ce{H2O(l) -> H2O(g)} \;\;\Delta H^\circ = 40.7 \text{ kJ/mol}\;\;\; \Delta S^\circ = 118.8 \text{ J/mol K}\)

A. \(5.29 \text{ kJ/mol}\)

B. \(-78.8 \text{ kJ/mol}\)

C. \(12.0 \text{ kJ/mol}\)

*Solution*

A. \(5.29 \text{ kJ/mol}\)

\(\Delta G^\circ = \Delta H^\circ – T\Delta S^\circ = 40.7\text{ kJ/mol} - (298\text{ K})(0.1188\text{ kJ/mol}\cdot\text{K}) = 5.29\text{ kJ/mol}\)

**Example 2.**

In a thermodynamically favored process, \(\Delta G ^\circ\) _____ \(0\).

A. \(>\)

B. \(<\)

C. \(=\)

*Solution*

B. \(<\)

In a thermodynamically favored process, \(\Delta G ^\circ < 0\).

**Example 3.**

An exothermic reaction has \(\Delta S^ \circ< 0\). What is true about this reaction?

A. It is never thermodynamically favored (at any temperature).

B. It is always thermodynamically favored (at any temperature).

C. It is sometimes thermodynamically favored (at low temperatures).

*Solution*

C. It is sometimes thermodynamically favored (at low temperatures).

An exothermic reaction accompanied by a decrease in entropy can be thermodynamically favored at low temperatures.