12.11 Using values for $\Delta_{ ext {fus }} H^{\circ}$ and $\Delta_{ ext {fus }} S^{\circ}$ at 298 kelvins, estimate the standard boiling point of mercury, $\Delta_{\mathrm{f}} H^{\circ}=$ $61.4 \mathrm{~kJ} / \mathrm{mol}$ and $S^{\circ}=175.0 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}$ for $\mathrm{Hg}(g)$. Determine the vapor pressure of mercury at $25^{\circ} \mathrm{C}$.

Question

12.11 Using values for $\Delta_{	ext {fus }} H^{\circ}$ and $\Delta_{	ext {fus }} S^{\circ}$ at 298 kelvins, estimate the standard boiling point of mercury, $\Delta_{\mathrm{f}} H^{\circ}=$ $61.4 \mathrm{~kJ} / \mathrm{mol}$ and $S^{\circ}=175.0 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}$ for $\mathrm{Hg}(g)$. Determine the vapor pressure of mercury at $25^{\circ} \mathrm{C}$.

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Use the Gibbs free energy equation for phase transition**: To estimate the standard boiling point of mercury, we can use the Gibbs free energy equation $\Delta G = \Delta H - T\Delta S$. At the boiling point, $\Delta G$ for the phase transition is zero. ‖ ‖ 2 ⋮ **Solve for the boiling point**: Setting $\Delta G = 0$ for the boiling point, we get $0 = \Delta_{ ext{f}} H^{\circ} - T_{ ext{b}} \Delta_{ ext{fus}} S^{\circ}$. We can solve for the boiling temperature $T_{ ext{b}}$ by rearranging the equation: $T_{ ext{b}} = \frac{\Delta_{ ext{f}} H^{\circ}}{\Delta_{ ext{fus}} S^{\circ}}$. ‖ ‖ 3 ⋮ **Calculate the boiling point**: Plugging in the values, $T_{ ext{b}} = \frac{61.4 imes 10^3 ext{ J/mol}}{175.0 ext{ J/mol} \cdot ext{K}} = 350.857 ext{ K}$. ‖ ‖ 4 ⋮ **Determine the vapor pressure at $25^{\circ}C$**: To find the vapor pressure at $25^{\circ}C$ (or $298 ext{ K}$), we can use the Clausius-Clapeyron equation, which relates the vapor pressure at two temperatures. However, we need the heat of vaporization and the vapor pressure at another known temperature, which are not provided. Without this information, we cannot calculate the vapor pressure at $25^{\circ}C$. ‖ ∻Answer∻ ⚹ The standard boiling point of mercury is approximately 350.857 K. The vapor pressure at $25^{\circ}C$ cannot be determined with the given information. ⚹ ∻Key Concept∻ ⚹ The boiling point of a substance can be estimated using the Gibbs free energy equation for phase transitions. ⚹ ∻Explanation∻ ⚹ At the boiling point, the Gibbs free energy change for the phase transition from liquid to gas is zero, allowing us to solve for the boiling temperature using the enthalpy and entropy of fusion. ⚹◊What is the equation used to calculate the vapor pressure of a substance at a given temperature?⍭ Generate me a similar question◊

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