Phosphorus pentachloride forms from phosphorus trichloride and chlorine: PCl₃(g) + Cl₂(g) → PCl₅(g) (b) Estimate the temperature at which the reaction will become nonspontaneous.

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Determine the standard enthalpy change (\( \Delta H^\circ \)) for the reaction using standard enthalpies of formation.

Determine the standard entropy change (\( \Delta S^\circ \)) for the reaction using standard molar entropies.

Use the Gibbs free energy equation \( \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \) to find the temperature at which \( \Delta G^\circ = 0 \), indicating the reaction is at equilibrium and thus nonspontaneous.

Rearrange the equation to solve for temperature: \( T = \frac{\Delta H^\circ}{\Delta S^\circ} \).

Substitute the values of \( \Delta H^\circ \) and \( \Delta S^\circ \) into the equation to estimate the temperature.

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주요 개념

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Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a reaction. A reaction is spontaneous at constant temperature and pressure if the change in Gibbs Free Energy (ΔG) is negative. The relationship between ΔG, enthalpy (ΔH), and entropy (ΔS) is given by the equation ΔG = ΔH - TΔS, where T is the temperature in Kelvin.

Entropy (S)

Entropy is a measure of the disorder or randomness in a system. In chemical reactions, an increase in entropy typically favors spontaneity. For the reaction of phosphorus trichloride and chlorine to form phosphorus pentachloride, understanding how the number of gas molecules changes can help assess the change in entropy and its impact on the reaction's spontaneity.

Enthalpy (ΔH)

Enthalpy is a measure of the total heat content of a system and is crucial for understanding energy changes during a reaction. The change in enthalpy (ΔH) can be either exothermic (releasing heat) or endothermic (absorbing heat). For the reaction in question, knowing whether it is exothermic or endothermic will help determine the temperature at which the reaction becomes nonspontaneous, as it influences the Gibbs Free Energy equation.

Phosphorus pentachloride forms from phosphorus trichloride and chlorine: PCl3(g) + Cl2(g) → PCl5(g) (b) Estimate the temperature at which the reaction will become nonspontaneous.