Tell whether reactions with the following values of ΔH and ΔS are spontaneous or nonspontaneous and whether they are exothermic or endothermic. (a) ΔH = -128 kJ; ΔS = 35 J/K at 500 K (b) ΔH = +67 kJ; ΔS = -140 J/K at 250 K (c) ΔH = +75 kJ; ΔS = 95 J/K at 800 K

Verified step by step guidance

Step 1: Understand the relationship between spontaneity, enthalpy (ΔH), and entropy (ΔS) using the Gibbs free energy equation: ΔG = ΔH - TΔS, where T is the temperature in Kelvin.

Step 2: Convert the entropy change (ΔS) from J/K to kJ/K by dividing by 1000, since ΔH is given in kJ.

Step 3: Calculate the Gibbs free energy change (ΔG) for each reaction using the equation ΔG = ΔH - TΔS, substituting the given values for ΔH, ΔS, and T.

Step 4: Determine spontaneity: If ΔG < 0, the reaction is spontaneous; if ΔG > 0, the reaction is nonspontaneous.

Step 5: Determine if the reaction is exothermic or endothermic: If ΔH < 0, the reaction is exothermic; if ΔH > 0, the reaction is endothermic.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a reaction at constant temperature and pressure. The change in Gibbs Free Energy (ΔG) is calculated using the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates a spontaneous reaction, while a positive ΔG suggests nonspontaneity.

Enthalpy (ΔH)

Enthalpy (ΔH) is a measure of the total heat content of a system. It indicates whether a reaction is exothermic (releases heat, ΔH < 0) or endothermic (absorbs heat, ΔH > 0). Understanding the sign of ΔH is crucial for determining the energy changes associated with a reaction and its impact on spontaneity when combined with entropy changes.

Entropy (ΔS)

Entropy (ΔS) is a measure of the disorder or randomness in a system. A positive ΔS indicates an increase in disorder, which generally favors spontaneity, while a negative ΔS suggests a decrease in disorder. The relationship between entropy and temperature is essential for evaluating the overall spontaneity of a reaction, as it influences the Gibbs Free Energy calculation.