For a particular reaction, ΔH = -32 kJ and ΔS = -98 J>K. Assume that ΔH and ΔS do not vary with temperature. (a) At what temperature will the reaction have ΔG = 0? (b) If T is increased from that in part (a), will the reaction be spontaneous or nonspontaneous?

Verified step by step guidance

1. Step 1: Recall the Gibbs free energy equation: \( \Delta G = \Delta H - T \Delta S \). For part (a), set \( \Delta G = 0 \) and solve for temperature \( T \).
2. Step 2: Convert \( \Delta S \) from J/K to kJ/K to match the units of \( \Delta H \). This is done by dividing \( \Delta S \) by 1000.
3. Step 3: Substitute \( \Delta H = -32 \text{ kJ} \) and the converted \( \Delta S \) into the equation \( 0 = \Delta H - T \Delta S \) and solve for \( T \).
4. Step 4: For part (b), consider the sign of \( \Delta G \) when \( T \) is increased. Since \( \Delta G = \Delta H - T \Delta S \), increasing \( T \) will affect the term \( -T \Delta S \).
5. Step 5: Analyze the sign of \( \Delta S \) to determine the effect on \( \Delta G \) as \( T \) increases. If \( \Delta S < 0 \), increasing \( T \) makes \( -T \Delta S \) more positive, thus \( \Delta G \) becomes positive, indicating nonspontaneity.

Key Concepts

Gibbs Free Energy (ΔG)

Gibbs Free Energy (ΔG) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It 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 indicates nonspontaneity.

Enthalpy (ΔH)

Enthalpy (ΔH) is a measure of the total heat content of a system and reflects the energy required to break and form bonds during a chemical reaction. A negative ΔH value, such as -32 kJ, indicates that the reaction is exothermic, meaning it releases heat to the surroundings. This factor can influence the spontaneity of a reaction, especially when combined with entropy changes.

Entropy (ΔS)

Entropy (ΔS) is a measure of the disorder or randomness in a system. A negative ΔS value, like -98 J/K, suggests that the reaction leads to a decrease in disorder, which can affect the spontaneity of the reaction. In the context of Gibbs Free Energy, the interplay between ΔH and ΔS at a given temperature determines whether a reaction will be spontaneous or nonspontaneous.