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)]. What are the values of ∆H and ∆S (in kcal/mol and kJ/mol) for the change from gaseous to liquid H2O?

Verified step by step guidance

1. Identify that the process described is the reverse of the given process, which is the condensation of gaseous H2O to liquid H2O.
2. Recognize that reversing a process changes the sign of both \( \Delta H \) and \( \Delta S \).
3. For \( \Delta H \), change the sign from +9.72 kcal/mol to -9.72 kcal/mol and from +40.7 kJ/mol to -40.7 kJ/mol.
4. For \( \Delta S \), change the sign from -26.1 cal/(mol \cdot K) to +26.1 cal/(mol \cdot K) and from -109 J/(mol \cdot K) to +109 J/(mol \cdot K).
5. Conclude that the values for the condensation process are \( \Delta H = -9.72 \text{ kcal/mol} \) and \( \Delta S = +26.1 \text{ cal/(mol \cdot K)} \) or \( \Delta H = -40.7 \text{ kJ/mol} \) and \( \Delta S = +109 \text{ J/(mol \cdot K)} \).

Key Concepts

Enthalpy Change (∆H)

Enthalpy change (∆H) refers to the heat absorbed or released during a chemical reaction or phase change at constant pressure. In this context, the positive value of ∆H for the transition from liquid to gas indicates that the process is endothermic, meaning it requires energy input. For the reverse process, from gas to liquid, ∆H will be negative, reflecting the release of energy.

Entropy Change (∆S)

Entropy change (∆S) measures the degree of disorder or randomness in a system. A negative value of ∆S, as seen in the transition from liquid to gas, indicates a decrease in disorder, as gas molecules are more dispersed than liquid molecules. Conversely, when transitioning from gas to liquid, ∆S will be positive, signifying an increase in order as the gas condenses into a liquid.

Thermodynamic Relationships

Thermodynamic relationships, particularly the Gibbs free energy equation (∆G = ∆H - T∆S), help predict the spontaneity of a process. In this case, understanding how ∆H and ∆S change during phase transitions is crucial for calculating the values for the reverse process. The temperature (T) plays a significant role in determining the overall energy changes and spontaneity of the phase change.