Calculate ∆G°, ∆H°, and ∆S° for the following acid–base reactions. Rationalize the value of ∆H° based on the structure of the conjugate bases. [Assume T = 298 K.]
(c)

Verified step by step guidance

1. Step 1: Begin by identifying the acid and base in the given reaction. Write the chemical equation for the acid-base reaction, including the conjugate acid and conjugate base formed.
2. Step 2: Use the relationship between Gibbs free energy (∆G°), enthalpy (∆H°), and entropy (∆S°) given by the equation: $∆G=∆H-T∆S$. Rearrange this equation to solve for any missing variable if needed.
3. Step 3: To calculate ∆G°, use the equilibrium constant (K) for the reaction and the equation: $∆G=-RTlnK$, where R is the gas constant (8.314 J/mol·K) and T is the temperature in Kelvin (298 K).
4. Step 4: Rationalize the value of ∆H° by analyzing the structure of the conjugate bases. Consider factors such as resonance stabilization, electronegativity, and bond strength in the conjugate bases to explain why the enthalpy change occurs.
5. Step 5: Calculate ∆S° using the relationship $∆S=(∆H-∆G)/T$. Ensure all values are in consistent units (e.g., J or kJ) before performing the calculation.

Key Concepts

Gibbs Free Energy (∆G°)

Gibbs Free Energy (∆G°) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is crucial for predicting the spontaneity of a reaction; a negative ∆G° indicates a spontaneous process, while a positive value suggests non-spontaneity. The relationship between ∆G°, enthalpy (∆H°), and entropy (∆S°) is given by the equation ∆G° = ∆H° - T∆S°, where T is the temperature in Kelvin.

Enthalpy (∆H°)

Enthalpy (∆H°) is a measure of the total heat content of a system and reflects the energy changes during a chemical reaction. It can be either exothermic (releasing heat, ∆H° < 0) or endothermic (absorbing heat, ∆H° > 0). The value of ∆H° can be rationalized by examining the stability and structure of the reactants and products, particularly the strength of bonds broken and formed, which influences the overall energy change.

Entropy (∆S°)

Entropy (∆S°) is a measure of the disorder or randomness in a system. In chemical reactions, an increase in entropy (∆S° > 0) typically favors spontaneity, as systems tend to evolve towards greater disorder. The change in entropy can be influenced by factors such as the number of molecules, phase changes, and the complexity of the molecular structures involved in the reaction, which are essential for understanding the thermodynamic favorability of acid-base reactions.