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Posted about 1 month ago

12.11 Using values for Δfus H\Delta_{\text {fus }} H^{\circ} and Δfus S\Delta_{\text {fus }} S^{\circ} at 298 kelvins, estimate the standard boiling point of mercury, ΔfH=\Delta_{\mathrm{f}} H^{\circ}= 61.4 kJ/mol61.4 \mathrm{~kJ} / \mathrm{mol} and S=175.0 J/molKS^{\circ}=175.0 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} for Hg(g)\mathrm{Hg}(\mathrm{g}). Determine the vapor pressure of mercury at 25C25^{\circ} \mathrm{C}.
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Answer from Sia
Posted about 1 month ago
Identify the given values: The problem provides the enthalpy of fusion (ΔfusH\Delta_{\text{fus}} H^{\circ}) and the entropy of fusion (ΔfusS\Delta_{\text{fus}} S^{\circ}) for mercury at 298 K. These values are ΔfusH=61.4kJ/mol\Delta_{\text{fus}} H^{\circ} = 61.4 \, \text{kJ/mol} and ΔfusS=175.0J/molK\Delta_{\text{fus}} S^{\circ} = 175.0 \, \text{J/mol} \cdot \text{K}
Calculate the standard boiling point: The standard boiling point can be estimated using the formula Tb=ΔfusHΔfusST_b = \frac{\Delta_{\text{fus}} H^{\circ}}{\Delta_{\text{fus}} S^{\circ}}. Converting ΔfusH\Delta_{\text{fus}} H^{\circ} to J/mol: 61.4kJ/mol=61400J/mol61.4 \, \text{kJ/mol} = 61400 \, \text{J/mol}. Then, Tb=61400J/mol175.0J/molK=350.29KT_b = \frac{61400 \, \text{J/mol}}{175.0 \, \text{J/mol} \cdot \text{K}} = 350.29 \, \text{K}
Determine the vapor pressure at 25°C: Use the Clausius-Clapeyron equation: ln(P2P1)=ΔHvapR(1T11T2)\ln \left( \frac{P_2}{P_1} \right) = \frac{\Delta H_{\text{vap}}}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right). Assuming P1P_1 is the vapor pressure at the boiling point (1 atm), T1=350.29KT_1 = 350.29 \, \text{K}, T2=298KT_2 = 298 \, \text{K}, and ΔHvapΔfusH=61400J/mol\Delta H_{\text{vap}} \approx \Delta_{\text{fus}} H^{\circ} = 61400 \, \text{J/mol}. Solving for P2P_2 at 25C25^{\circ} \text{C}: ln(P21atm)=614008.314(1350.291298)\ln \left( \frac{P_2}{1 \, \text{atm}} \right) = \frac{61400}{8.314} \left( \frac{1}{350.29} - \frac{1}{298} \right)
The standard boiling point of mercury is approximately 350.29 K. The vapor pressure of mercury at 25°C can be calculated using the Clausius-Clapeyron equation.
Key Concept
The Clausius-Clapeyron equation relates the vapor pressure of a substance to its temperature and enthalpy of vaporization.
By using the enthalpy and entropy of fusion, we can estimate the boiling point. The Clausius-Clapeyron equation then allows us to determine the vapor pressure at a different temperature.

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