7. Consider the following process, in which AH® is 44.0 kJ/mol at 25°C and 40.6 kJ/mol at 100 °C H2O() → H2O(g) (a) If the entropy S® for H2O(!) and H2O(g) are 70.0 J.mol'.K' and 188.9 J.mol"'.K', respectively, calculate AS,ys and ASgsurr, each with appropriate algebraic sign at 25°C and at 100 °C. (b) Calculate ASuniv at 25°C and at 100 °C, and predict whether the evaporation of water is spontaneous at each temperature if PH20 = 1 atm.

Chemistry
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**Problem 7: Thermodynamics of Water Evaporation**

Consider the following process, in which the standard enthalpy change (\(\Delta H^\circ\)) is 44.0 kJ/mol at 25°C and 40.6 kJ/mol at 100°C:

\[ \text{H}_2\text{O(l)} \rightarrow \text{H}_2\text{O(g)} \]

**(a)** If the standard entropy (\(S^\circ\)) for H\(_2\)O(l) and H\(_2\)O(g) are 70.0 J/mol·K and 188.9 J/mol·K, respectively, calculate the change in entropy of the system (\(\Delta S_{sys}\)) and the surroundings (\(\Delta S_{sur}\)), each with the appropriate algebraic signs at 25°C and at 100°C.

**(b)** Calculate the change in entropy of the universe (\(\Delta S_{univ}\)) at 25°C and at 100°C, and predict whether the evaporation of water is spontaneous at each temperature if \(P_{\text{H}_2\text{O}} = 1\) atm.
Transcribed Image Text:**Problem 7: Thermodynamics of Water Evaporation** Consider the following process, in which the standard enthalpy change (\(\Delta H^\circ\)) is 44.0 kJ/mol at 25°C and 40.6 kJ/mol at 100°C: \[ \text{H}_2\text{O(l)} \rightarrow \text{H}_2\text{O(g)} \] **(a)** If the standard entropy (\(S^\circ\)) for H\(_2\)O(l) and H\(_2\)O(g) are 70.0 J/mol·K and 188.9 J/mol·K, respectively, calculate the change in entropy of the system (\(\Delta S_{sys}\)) and the surroundings (\(\Delta S_{sur}\)), each with the appropriate algebraic signs at 25°C and at 100°C. **(b)** Calculate the change in entropy of the universe (\(\Delta S_{univ}\)) at 25°C and at 100°C, and predict whether the evaporation of water is spontaneous at each temperature if \(P_{\text{H}_2\text{O}} = 1\) atm.
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