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

검증된 단계별 안내

Step 1: Identify the acid and base in the reaction. Determine the conjugate acid and conjugate base formed after the reaction. This will help in understanding the equilibrium of the reaction.

Step 2: Use the pKa values of the acid and conjugate acid to calculate the equilibrium constant (K_eq) for the reaction. The relationship between pKa and K_eq is given by \( K_{eq} = 10^{\Delta pKa} \), where \( \Delta pKa = pKa_{acid} - pKa_{conjugate acid} \).

Step 3: Recall the relationship between \( \Delta G^\circ \) and \( K_{eq} \): \( \Delta G^\circ = -RT \ln K_{eq} \). Here, \( R \) is the gas constant (8.314 J/mol·K), \( T \) is the temperature in Kelvin (298 K), and \( K_{eq} \) is the equilibrium constant calculated in Step 2.

Step 4: Substitute the values of \( R \), \( T \), and \( K_{eq} \) into the equation \( \Delta G^\circ = -RT \ln K_{eq} \). Ensure that \( K_{eq} \) is expressed in a form suitable for logarithmic calculation.

Step 5: Perform the calculation to determine \( \Delta G^\circ \). The result will be in joules per mole (J/mol). If needed, convert the value to kilojoules per mole (kJ/mol) by dividing by 1000.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 (1 atm, 1 M concentration, and 298 K).

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. The reaction's direction and extent can significantly influence the overall energy change.

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction. It is related to the standard Gibbs free energy change by the equation ∆G° = -RT ln(K), where R is the universal gas constant and T is the temperature in Kelvin. Knowing K allows for the calculation of ∆G° and provides insight into the favorability of the reaction under standard conditions.