The entropy change for a certain nonspontaneous reaction at 50 °C is 104 J/K. (a) Is the reaction endothermic or exothermic? (b) What is the minimum value of ∆H (in kJ) for the reaction?

Verified step by step guidance

1. Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature (50 °C).
2. Use the Gibbs free energy equation: \( \Delta G = \Delta H - T \Delta S \). Since the reaction is nonspontaneous, \( \Delta G > 0 \).
3. Rearrange the equation to find \( \Delta H \): \( \Delta H = \Delta G + T \Delta S \).
4. Since \( \Delta G > 0 \) for a nonspontaneous reaction, the minimum value of \( \Delta H \) occurs when \( \Delta G = 0 \). Therefore, \( \Delta H = T \Delta S \).
5. Substitute the values of \( T \) (in Kelvin) and \( \Delta S \) (104 J/K) into the equation to find the minimum \( \Delta H \) in joules, then convert it to kilojoules by dividing by 1000.

Key Concepts

Entropy (S)

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of ways a system can be arranged, with higher entropy indicating greater disorder. For reactions, changes in entropy can help predict spontaneity; a positive change in entropy often favors spontaneity, while a negative change suggests nonspontaneity.

Gibbs Free Energy (G)

Gibbs Free Energy is a thermodynamic potential that helps predict whether a reaction will occur spontaneously at constant temperature and pressure. It is defined as G = H - TS, where H is enthalpy, T is temperature, and S is entropy. A reaction is spontaneous if the change in Gibbs Free Energy (∆G) is negative, which can be influenced by both enthalpy and entropy changes.

Enthalpy (H)

Enthalpy is a measure of the total heat content of a system and is used to describe energy changes during chemical reactions. It can be either endothermic (absorbing heat, ∆H > 0) or exothermic (releasing heat, ∆H < 0). The relationship between enthalpy and entropy changes is crucial for determining the spontaneity of a reaction, especially when combined with temperature.