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 25a

Chapter 4, Problem 25a

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)

Verified step by step guidance

Step 1: Understand the relationship between ∆G°, ∆H°, and ∆S° using the Gibbs free energy equation:

∆G° = ∆H° - T∆S°

. Here, T is the temperature in Kelvin (given as 298 K). This equation will help you calculate ∆G° once ∆H° and ∆S° are determined.

Step 2: Identify the acid-base reaction provided in the problem. Write the balanced chemical equation for the reaction, including the acid, base, conjugate acid, and conjugate base. This will help you analyze the structural changes and thermodynamic properties.

Step 3: Use experimental data or provided values (such as bond dissociation energies, enthalpies of formation, or entropy values) to calculate ∆H° (change in enthalpy) and ∆S° (change in entropy) for the reaction. For ∆H°, consider the bond strengths and structural differences between the acid and its conjugate base.

Step 4: Substitute the calculated values of ∆H° and ∆S° into the Gibbs free energy equation to determine ∆G°. Ensure that units are consistent (e.g., convert ∆S° to kJ/K·mol if ∆H° is in kJ/mol).

Step 5: Rationalize the value of ∆H° by analyzing the structure of the conjugate bases. Consider factors such as resonance stabilization, electronegativity, and the ability of the conjugate base to delocalize charge. These structural features influence the enthalpy change during the reaction.

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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 calculated using the equation ∆G° = ∆H° - T∆S°, where ∆H° is the change in enthalpy and ∆S° is the change in entropy. A negative ∆G° indicates a spontaneous reaction, while a positive value suggests non-spontaneity.

Enthalpy (∆H°)

Enthalpy (∆H°) is a measure of the total heat content of a system, reflecting the energy required to break and form bonds during a chemical reaction. In acid-base reactions, ∆H° can be influenced by the stability of the conjugate bases formed. A more stable conjugate base typically corresponds to a more negative ∆H°, indicating that the reaction is exothermic and releases heat.

Entropy (∆S°)

Entropy (∆S°) is a measure of the disorder or randomness in a system. In the context of acid-base reactions, changes in entropy can arise from the number of molecules and their states (solid, liquid, gas) before and after the reaction. A positive ∆S° indicates an increase in disorder, which can favor spontaneity in conjunction with a negative ∆G°.

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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

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

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Textbook Question

Within the following pairs, pick which reaction you would expect to be faster based on having a higher value of the frequency factor (A).

(a)

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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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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)

Verified video answer for a similar problem:

Key Concepts

Gibbs Free Energy (∆G°)

Enthalpy (∆H°)

Entropy (∆S°)

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)