For the following values of ∆H° , ∆S°, and T, tell whether the process would be favored.
(d) ∆H° = -8.3 kcal/mol ; ∆S° = -12 cal/mol•K ; T = 298 K

Verified step by step guidance

1. Step 1: Recall the Gibbs free energy equation: ΔG = ΔH - TΔS. This equation determines whether a process is thermodynamically favored. A negative ΔG indicates a favored process.
2. Step 2: Convert all units to be consistent. Here, ΔH° is given in kcal/mol, and ΔS° is given in cal/mol•K. Convert ΔH° to cal/mol by multiplying by 1000: ΔH° = -8.3 kcal/mol × 1000 = -8300 cal/mol.
3. Step 3: Calculate the TΔS term. Multiply the temperature (T = 298 K) by ΔS° (-12 cal/mol•K): TΔS = 298 × (-12) = -3576 cal/mol.
4. Step 4: Substitute the values into the Gibbs free energy equation: ΔG = ΔH - TΔS. Using the converted ΔH° (-8300 cal/mol) and calculated TΔS (-3576 cal/mol), plug them into the equation.
5. Step 5: Analyze the sign of ΔG. If ΔG is negative, the process is thermodynamically favored. If ΔG is positive, the process is not favored. Perform the subtraction ΔG = -8300 - (-3576) and determine the sign of the result.

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 formula 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 that the process is favored.

Enthalpy (ΔH)

Enthalpy (ΔH) is a measure of the total heat content of a system. A negative ΔH value, such as -8.3 kcal/mol, indicates that the process is exothermic, meaning it releases heat. Exothermic reactions are generally favored because they contribute to a decrease in the system's energy, promoting spontaneity.

Entropy (ΔS)

Entropy (ΔS) is a measure of the disorder or randomness in a system. A negative ΔS value, like -12 cal/mol•K, suggests that the process leads to a decrease in disorder. While processes that increase entropy are favored, a negative ΔS can be offset by a sufficiently negative ΔH at high temperatures, affecting the spontaneity of the reaction.