Ch. 5 - Chemical Reaction Analysis: Thermodynamics and Kinetics

Mullins - Organic Chemistry: A Learner Centered Approach 1st Edition

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Mullins 1st Edition

Ch. 5 - Chemical Reaction Analysis: Thermodynamics and Kinetics

Problem 24f

Chapter 4, Problem 24f

For the following acid–base reaction, (f) calculate ∆G° at 373 K.

Verified step by step guidance

Identify the acid and base in the reaction and determine the pKa values of the acid and conjugate acid. This will help in calculating the equilibrium constant (K).

Use the relationship between the equilibrium constant (K) and the pKa values: \( K = 10^{\text{pKa (acid)} - \text{pKa (conjugate acid)}} \). Substitute the appropriate pKa values into this equation to calculate K.

Recall the relationship between the standard Gibbs free energy change (\( \Delta G^\circ \)) and the equilibrium constant: \( \Delta G^\circ = -RT \ln K \), where \( R \) is the gas constant (8.314 J/mol·K) and \( T \) is the temperature in Kelvin (373 K in this case).

Substitute the calculated value of \( K \), the gas constant \( R \), and the temperature \( T \) into the equation \( \Delta G^\circ = -RT \ln K \). Ensure that the units are consistent (e.g., \( R \) in J/mol·K and \( T \) in Kelvin).

Simplify the expression to calculate \( \Delta G^\circ \). This will give the standard Gibbs free energy change for the reaction at 373 K.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 a crucial concept in predicting the spontaneity of a reaction; a negative ∆G indicates a spontaneous process, while a positive ∆G suggests non-spontaneity. The standard Gibbs free energy change (∆G°) is calculated under standard conditions, providing a reference point for reactions.

Acid-Base Reactions

Acid-base reactions involve the transfer of protons (H⁺ ions) between reactants. In these reactions, acids donate protons, while bases accept them. Understanding the strength of acids and bases, as well as their dissociation constants (Ka and Kb), is essential for calculating the equilibrium position and the Gibbs free energy change associated with the reaction.

Temperature Dependence of ∆G

The Gibbs free energy change (∆G) is temperature-dependent, and its calculation at different temperatures requires consideration of the enthalpy (∆H) and entropy (∆S) changes of the reaction. The relationship is given by the equation ∆G = ∆H - T∆S, where T is the absolute temperature in Kelvin. At 373 K, it is important to accurately determine ∆H and ∆S to compute ∆G°, reflecting how temperature influences the spontaneity of the reaction.

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Related Practice

Textbook Question

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.]

(b)

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Textbook Question

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.]

(a)

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Textbook Question

For the following acid–base reaction, (c) calculate the ratio of butan-2-ol to 2-butoxide.

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Textbook Question

For the following acid–base reaction, (e) calculate ∆G° at 273 K.

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Textbook Question

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)

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Textbook Question

For the following acid–base reaction, (d) calculate ∆G° at 298 K.

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