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Use the following data to calculate AvapHo for water at 298 K. Avap Ho for water at 373 K is 40.7 kJ/mole. Cp is 75.2 J/Kmol for liquid and 33.6 J/Kmol for gaseous water. Is the value of Avap Ho higher or lower than at 373 K? Can you give a reason why?

Use the following data to calculate AvapHo for water at 298 K. Avap Ho for water at 373 K is 40.7 kJ/mole. Cp is 75.2 J/Kmol for liquid and 33.6 J/Kmol for gaseous water. Is the value of Avap Ho higher or lower than at 373 K? Can you give a reason why?

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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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**Title: Calculating the Standard Enthalpy of Vaporization for Water at 298 K** --- **Objective:** To determine the standard enthalpy of vaporization (\( \Delta_{\text{vap}}H^o \)) for water at 298 K using provided data. **Data Provided:** - \( \Delta_{\text{vap}}H^o \) for water at 373 K is 40.7 kJ/mole. - Heat capacity (\( \bar{C}_P \)) values: - Liquid water: 75.2 J/Kmol - Gaseous water: 33.6 J/Kmol **Task:** Determine whether the standard enthalpy of vaporization (\( \Delta_{\text{vap}}H^o \)) at 298 K is higher or lower than that at 373 K. Provide a reason for the observed difference. --- **Explanation:** To calculate \( \Delta_{\text{vap}}H^o \) at a different temperature, use Kirchhoff’s Law, which accounts for the temperature dependence of enthalpy changes. It involves integrating the change in heat capacity over the temperature range. The basic approach is as follows: 1. Use the given heat capacities to determine the change in \( \Delta_{\text{vap}}H^o \) between the two temperatures. 2. Apply the formula: \[ \Delta_{\text{vap}}H^o(T_2) = \Delta_{\text{vap}}H^o(T_1) + \int_{T_1}^{T_2} \Delta \bar{C}_P \, dT \] where \( \Delta \bar{C}_P = \bar{C}_P(\text{gas}) - \bar{C}_P(\text{liquid}) \). **Outcome Analysis:** Analyze the signs and magnitudes to determine if \( \Delta_{\text{vap}}H^o \) increases or decreases: - **Higher at 298 K:** If the integrated term increases \( \Delta_{\text{vap}}H^o \). - **Lower at 298 K:** If the integrated term decreases \( \Delta_{\text{vap}}H^o \). **Reasoning:** Consider how the difference in heat capacities and temperature affects the energy required for vaporization, discussing molecular interactions and energy distributions. --- **
Transcribed Image Text:**Title: Calculating the Standard Enthalpy of Vaporization for Water at 298 K** --- **Objective:** To determine the standard enthalpy of vaporization (\( \Delta_{\text{vap}}H^o \)) for water at 298 K using provided data. **Data Provided:** - \( \Delta_{\text{vap}}H^o \) for water at 373 K is 40.7 kJ/mole. - Heat capacity (\( \bar{C}_P \)) values: - Liquid water: 75.2 J/Kmol - Gaseous water: 33.6 J/Kmol **Task:** Determine whether the standard enthalpy of vaporization (\( \Delta_{\text{vap}}H^o \)) at 298 K is higher or lower than that at 373 K. Provide a reason for the observed difference. --- **Explanation:** To calculate \( \Delta_{\text{vap}}H^o \) at a different temperature, use Kirchhoff’s Law, which accounts for the temperature dependence of enthalpy changes. It involves integrating the change in heat capacity over the temperature range. The basic approach is as follows: 1. Use the given heat capacities to determine the change in \( \Delta_{\text{vap}}H^o \) between the two temperatures. 2. Apply the formula: \[ \Delta_{\text{vap}}H^o(T_2) = \Delta_{\text{vap}}H^o(T_1) + \int_{T_1}^{T_2} \Delta \bar{C}_P \, dT \] where \( \Delta \bar{C}_P = \bar{C}_P(\text{gas}) - \bar{C}_P(\text{liquid}) \). **Outcome Analysis:** Analyze the signs and magnitudes to determine if \( \Delta_{\text{vap}}H^o \) increases or decreases: - **Higher at 298 K:** If the integrated term increases \( \Delta_{\text{vap}}H^o \). - **Lower at 298 K:** If the integrated term decreases \( \Delta_{\text{vap}}H^o \). **Reasoning:** Consider how the difference in heat capacities and temperature affects the energy required for vaporization, discussing molecular interactions and energy distributions. --- **
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