For the following values of ∆H° , ∆S°, and T, tell whether the process would be favored.
(b) ∆H° = +7.34 kcal/mol ; ∆S° = +43 cal/mol•K ; T = 325 K

Verified step by step guidance

1. Step 1: Recall the Gibbs free energy equation: G = ΔH - TΔS. This equation determines whether a process is thermodynamically favored. A negative value of ΔG indicates a favored process.
2. Step 2: Ensure the units are consistent. Here, ΔH° is given in kcal/mol, while ΔS° is in cal/mol•K. Convert ΔH° to cal/mol by multiplying by 1000: ΔH° = 7.34 kcal/mol × 1000 = 7340 cal/mol.
3. Step 3: Substitute the given values into the Gibbs free energy equation. Use ΔH° = 7340 cal/mol, ΔS° = +43 cal/mol•K, and T = 325 K. The equation becomes: G = 7340 - (325 × 43).
4. Step 4: Analyze the sign of ΔG. If the result of the calculation is negative, the process is thermodynamically favored. If it is positive, the process is not favored.
5. Step 5: Consider the temperature dependence. Since ΔH° is positive (endothermic) and ΔS° is positive (increase in entropy), the process may become favored at higher temperatures. Evaluate whether the given temperature (325 K) is sufficient to make ΔG negative.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict whether a process will occur spontaneously 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 process, while a positive ΔG suggests non-spontaneity.

Enthalpy (ΔH)

Enthalpy (ΔH) is a measure of the total heat content of a system. A positive ΔH indicates that the process is endothermic, meaning it absorbs heat from the surroundings. This can affect the spontaneity of a reaction, as higher energy input may be required to drive the process, especially if the entropy change is not favorable.

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. In the context of the Gibbs Free Energy equation, a larger positive ΔS can offset a positive ΔH, potentially leading to a negative ΔG and making the process more favorable at higher temperatures.