Question

What does the Gibbs function of formation \(\bar{g}_{f}^{\circ}\) of a compound represent?

Short answer

Answer: The Gibbs function of formation is the change in Gibbs free energy when a compound is formed from its constituent elements under standard conditions. It helps in predicting the spontaneity of chemical reactions, as reactions with negative ΔG values are spontaneous, while those with positive ΔG values are non-spontaneous. The Gibbs function of formation is also used in calculating equilibrium constants and determining the feasibility of industrial processes.

Step-by-step solution

Definition of Gibbs Function of Formation

The Gibbs function of formation, denoted as \(\bar{g}_{f}^{\circ}\), represents the change in Gibbs free energy (\(\Delta G\)) when a compound is formed from its constituent elements at standard conditions (e.g., at a pressure of 1 bar and a specific temperature, typically 298.15 K). It is an important property in the field of thermodynamics and is widely used in studying chemical reactions, equilibria, and determining the spontaneity of processes.

Significance of Gibbs Function of Formation

The Gibbs function of formation of a compound helps us understand the energy changes associated with the formation of the compound from its elements. It aids in predicting the spontaneity of chemical reactions, as reactions with negative \(\Delta G\) values are spontaneous, while those with positive \(\Delta G\) values are non-spontaneous. Furthermore, it is used in calculating equilibrium constants and determining the feasibility of industrial processes.

Calculation of Gibbs Function of Formation from Enthalpy and Entropy

Since the Gibbs free energy (\(G\)) is related to the enthalpy (\(H\)) and entropy (\(S\)) of a system by the equation \(G = H - TS\), the change in Gibbs free energy during a reaction can be expressed as \(\Delta G = \Delta H - T\Delta S\). Thus, the Gibbs function of formation of a compound can be calculated using its enthalpy of formation (\(\Delta H_f^{\circ}\)) and entropy (\(S^{\circ}\)) at standard conditions using the following formula: \(\bar{g}_{f}^{\circ} = \Delta H_f^{\circ} - T S^{\circ}\)

Using Standard Gibbs Function of Formation in Calculating Gibbs Free Energy Change in Reaction

The standard Gibbs function of formation can be used to calculate the Gibbs free energy change of chemical reactions. For a balanced chemical reaction, the overall change in Gibbs free energy (\(\Delta G^{\circ}\)) can be determined by summing the products' standard Gibbs function of formation and subtracting the sum of the reactants' standard Gibbs function of formation, according to the equation: \(\Delta G^{\circ} =\Sigma n_p\bar{g}_{f,p}^{\circ} - \Sigma n_r\bar{g}_{f,r}^{\circ}\) where \(n_p\) and \(n_r\) represent the stoichiometric coefficients of the products and reactants, respectively, and \(\bar{g}_{f,p}^{\circ}\) and \(\bar{g}_{f,r}^{\circ}\) represent the standard Gibbs function of formation of the products and reactants, respectively. In conclusion, the Gibbs function of formation is a key thermodynamic property that represents the change in Gibbs free energy when a compound is formed from its elements under standard conditions. It helps us predict the spontaneity of chemical reactions, calculate equilibrium constants, and assess the feasibility of industrial processes.