For the following values of ∆H° , ∆S°, and T, tell whether the process would be favored.
(c) ∆H° = -21.3 kcal/mol ; AS° = -51 cal/mol•K ; T = 373 K

Verified step by step guidance

1. Step 1: Recall the Gibbs free energy equation: $\Delta G°\; =\; \Delta H°\; -\; T\Delta S°$. This equation determines whether a process is thermodynamically favored. A negative value of $\Delta G°$ indicates a favored process.
2. Step 2: Ensure the units of $\Delta H°$ and $\Delta S°$ are consistent. Here, $\Delta H°$ is given in kcal/mol, and $\Delta S°$ is in cal/mol•K. Convert $\Delta H°$ to cal/mol by multiplying by 1000: $\Delta H°\; =\; -21.3\; imes\; 1000\; =\; -21300\; ext\{\; cal/mol\}$.
3. Step 3: Substitute the given values into the Gibbs free energy equation: $\Delta G°\; =\; (-21300)\; -\; (373)(-51)$. Be careful with the negative sign in $\Delta S°$.
4. Step 4: Simplify the equation by calculating the term $T\Delta S°$. Multiply the temperature (373 K) by $\Delta S°$ (-51 cal/mol•K): $T\Delta S°\; =\; 373\; imes\; -51$. Then, subtract this value from $\Delta H°$.
5. Step 5: Analyze the sign of the resulting $\Delta G°$. If $\Delta G°$ is negative, the process is thermodynamically favored. If it is positive, the process is not favored.

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, while a positive ΔG suggests it is not.

Enthalpy (ΔH)

Enthalpy (ΔH) is a measure of the total heat content of a system. A negative ΔH value, such as -21.3 kcal/mol, indicates that the process is exothermic, meaning it releases heat. This release of energy can favor the spontaneity of a reaction, especially when combined with the entropy change.

Entropy (ΔS)

Entropy (ΔS) is a measure of the disorder or randomness in a system. A negative ΔS value, like -51 cal/mol•K, suggests that the process leads to a decrease in disorder, which can hinder spontaneity. In the Gibbs Free Energy equation, a negative ΔS can counteract the favorable effects of a negative ΔH, especially at higher temperatures.