91Ó°ÊÓ

Gibbs Free Energy, often denoted as \( \Delta G \), is a thermodynamic potential that measures the maximum reversible work that can be performed by a thermodynamic system at a constant temperature and pressure. In the context of acid dissociation, it helps determine the spontaneity of a chemical reaction.

• If \( \Delta G < 0 \), the process occurs spontaneously.
• If \( \Delta G > 0 \), the process is non-spontaneous.
• If \( \Delta G = 0 \), the system is in equilibrium.

In the calculation of the second acid dissociation constant \( K_a \) for sulfuric acid, the change in Gibbs Free Energy is calculated by summing the free energy changes of products and reactants. This value is crucial because it determines how readily the bisulfate ion \( \text{HSO}_4^- \) will dissociate into sulfate \( \text{SO}_4^{2-} \) and a proton \( \text{H}^+ \). The formula used in this calculation is:\[ \Delta_r G = \Delta_{f} G[\mathrm{SO}_4^{2-}] + \Delta_{f} G[\mathrm{H}^+] - \Delta_{i} G[\mathrm{HSO}_4^-] \]This equation reflects the change from reactants to products, signifying the energy involved in the transition.

Sulfuric acid is a strong acid commonly used in various industries and chemical processes. It is noteworthy due to its ability to donate two protons (\( \text{H}^+ \)) in aqueous solutions, making it a diprotic acid. The dissociation occurs in two steps:

• The first dissociation: \( \text{H}_2\text{SO}_4 \rightarrow \text{HSO}_4^- + \text{H}^+ \)
• The second dissociation: \( \text{HSO}_4^- \rightarrow \text{SO}_4^{2-} + \text{H}^+ \)

The first dissociation is nearly complete in water, while the second dissociation is less so, which is why calculating the second dissociation constant, \( K_a \), is crucial. This constant gives insight into the strength and behavior of the bisulfate ion \( \text{HSO}_4^- \) in solution. Understanding this process aids in predicting the acid's behavior in various chemical settings, ensuring proper handling and use.

Thermodynamics calculations in this context focus on determining the acid dissociation constants using essential principles and formulas. Here, we're primarily concerned with the free energy change (\( \Delta_r G \)) and how it relates to equilibrium constants, specifically the second acid dissociation constant \( K_a \) for sulfuric acid.
To calculate \( \Delta_r G \) for the dissociation, we use:\[ \Delta_r G = \Delta_{f} G[\mathrm{products}] - \Delta_{f} G[\mathrm{reactants}] \]For the reaction \( \mathrm{HSO}_4^- \rightarrow \mathrm{SO}_4^{2-} + \mathrm{H}^+ \), the calculation becomes inserting the given values:\[ \Delta_r G = (-744.53 + 0) - (-755.91) = 11.38, \text{ kJ/mol} \]Using the relationship \( \Delta_r G = -RT\ln K_a \), where \( R \) is the gas constant \( 8.314 \text{ J/mol} \cdot \text{K} \), we solve for \( K_a \):\[ \ln K_a = -\frac{11.38}{2.47988} \]This reveals \( K_a = e^{-4.59} \equiv 0.0101 \).
These calculations not only provide the dissociation constant but also offer insights into the thermodynamic feasibility of the reaction, contributing to a broader understanding of chemical equilibria and reaction spontaneity.