Calculate the change in Gibbs free energy for each of the sets of ΔH_rxn, ΔS_rxn, and T given in Problem 42. Predict whether or not each reaction is spontaneous at the temperature indicated. (Assume that all reactants and products are in their standard states.)

검증된 단계별 안내

Identify the formula for Gibbs free energy change: \( \Delta G = \Delta H - T \Delta S \).

Substitute the given values for \( \Delta H \), \( \Delta S \), and \( T \) into the formula.

Ensure that the units are consistent, typically converting \( \Delta S \) from J/mol·K to kJ/mol·K by dividing by 1000.

Calculate \( \Delta G \) using the substituted values.

Determine spontaneity: if \( \Delta G < 0 \), the reaction is spontaneous; if \( \Delta G > 0 \), it is non-spontaneous.

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주요 개념

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

Gibbs Free Energy (G)

Gibbs free energy is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is defined by the equation G = H - TS, where H is enthalpy, T is temperature, and S is entropy. A negative change in Gibbs free energy (ΔG < 0) indicates that a reaction is spontaneous, while a positive change (ΔG > 0) suggests non-spontaneity.

Enthalpy (ΔH)

Enthalpy is a measure of the total heat content of a system and is used to quantify the energy changes during chemical reactions. The change in enthalpy (ΔH) can be either positive or negative, indicating whether a reaction absorbs heat (endothermic, ΔH > 0) or releases heat (exothermic, ΔH < 0). This value is crucial for determining the spontaneity of a reaction when combined with entropy changes.

Entropy (ΔS)

Entropy is a measure of the disorder or randomness in a system. The change in entropy (ΔS) during a reaction reflects how the distribution of energy changes, with positive ΔS indicating increased disorder and negative ΔS indicating decreased disorder. In the context of Gibbs free energy, a positive ΔS can favor spontaneity, especially at higher temperatures, as it contributes to a more negative ΔG.

Calculate the change in Gibbs free energy for each of the sets of ΔHrxn, ΔSrxn, and T given in Problem 42. Predict whether or not each reaction is spontaneous at the temperature indicated. (Assume that all reactants and products are in their standard states.)