The change of state from liquid H₂O to gaseous H₂O has ∆H = +9.72 kcal/mol(+40.7 kJ/mol) and ∆S = -26.1 cal/(mol • K) [-109 J/(mol •K)].
a. Is the change from liquid to gaseous H2O favored or unfavored by ∆H? By ∆S?

Verified step by step guidance

1. Step 1: Understand the problem. The question asks whether the phase change from liquid H2O to gaseous H2O is favored or unfavored by enthalpy (∆H) and entropy (∆S). Positive ∆H indicates an endothermic process, while the sign of ∆S indicates whether the system's disorder increases or decreases.
2. Step 2: Analyze ∆H. The given value of ∆H is +9.72 kcal/mol (+40.7 kJ/mol). A positive ∆H means that energy is absorbed during the phase change, making the process endothermic. This suggests that the change is not energetically favored because it requires an input of energy.
3. Step 3: Analyze ∆S. The given value of ∆S is -26.1 cal/(mol • K) [-109 J/(mol • K)]. A negative ∆S indicates that the system's disorder decreases during the phase change. This is unexpected for a liquid-to-gas transition, as gases are typically more disordered than liquids. This suggests that the change is not entropically favored.
4. Step 4: Summarize the findings. Based on the analysis, the phase change from liquid H2O to gaseous H2O is not favored by ∆H because it requires energy input (endothermic), and it is also not favored by ∆S because the system's disorder decreases (negative entropy change).
5. Step 5: Note the broader context. While the process is not favored by ∆H or ∆S individually, the overall spontaneity of the process depends on the Gibbs free energy change (∆G = ∆H - T∆S). This equation considers both enthalpy and entropy contributions at a given temperature.

Key Concepts

Enthalpy (∆H)

Enthalpy, represented as ∆H, is a measure of the heat content of a system at constant pressure. A positive ∆H indicates that the process is endothermic, meaning it absorbs heat from the surroundings. In the context of the phase change from liquid to gas, a positive ∆H (+9.72 kcal/mol) suggests that the transition requires energy input, which typically makes the process less favorable.

Entropy (∆S)

Entropy, denoted as ∆S, quantifies the degree of disorder or randomness in a system. A negative ∆S value indicates a decrease in disorder, which is the case when liquid water transitions to gas, as gas molecules are generally more disordered than liquid molecules. The negative ∆S (-26.1 cal/(mol • K)) suggests that this phase change is unfavorable in terms of increasing disorder.

Gibbs Free Energy (∆G)

Gibbs Free Energy, represented as ∆G, combines the effects of enthalpy and entropy to determine the spontaneity of a process. The relationship is given by the equation ∆G = ∆H - T∆S, where T is the temperature in Kelvin. A negative ∆G indicates a spontaneous process, while a positive ∆G indicates non-spontaneity. In this case, both a positive ∆H and a negative ∆S suggest that the transition from liquid to gaseous H2O is not favored.