Questions: Elemental sulfur exists in two crystalline forms, rhombic and monoclinic. From the following data, calculate the equilibrium temperature at which monoclinic sulfur and rhombic sulfur are in equilibrium. - Delta Hf°(kJ / mol) and S°(J / K mol): S (rhombic): 0, 31.880 S (monoclinic): 0.30, 32.546 450 K 200 K -200 K -450 K 0 K

Solution Steps

We need to find the equilibrium temperature at which monoclinic sulfur and rhombic sulfur are in equilibrium. This involves using the given enthalpy and entropy values for both forms of sulfur.

The equilibrium temperature can be found using the Gibbs free energy change equation: \[ \Delta G = \Delta H - T \Delta S \] At equilibrium, \(\Delta G = 0\), so: \[ 0 = \Delta H - T \Delta S \] Solving for \(T\): \[ T = \frac{\Delta H}{\Delta S} \]

Given: \[ \Delta H_{\text{f}}^{\circ}(\text{monoclinic}) = 0.30 \, \text{kJ/mol} \] \[ \Delta H_{\text{f}}^{\circ}(\text{rhombic}) = 0 \, \text{kJ/mol} \] \[ S^{\circ}(\text{monoclinic}) = 32.546 \, \text{J/K mol} \] \[ S^{\circ}(\text{rhombic}) = 31.880 \, \text{J/K mol} \]

Calculate the changes: \[ \Delta H = \Delta H_{\text{f}}^{\circ}(\text{monoclinic}) - \Delta H_{\text{f}}^{\circ}(\text{rhombic}) = 0.30 \, \text{kJ/mol} - 0 \, \text{kJ/mol} = 0.30 \, \text{kJ/mol} \] \[ \Delta S = S^{\circ}(\text{monoclinic}) - S^{\circ}(\text{rhombic}) = 32.546 \, \text{J/K mol} - 31.880 \, \text{J/K mol} = 0.666 \, \text{J/K mol} \]

\[ \Delta H = 0.30 \, \text{kJ/mol} \times 1000 \, \text{J/kJ} = 300 \, \text{J/mol} \]

\[ T = \frac{\Delta H}{\Delta S} = \frac{300 \, \text{J/mol}}{0.666 \, \text{J/K mol}} = 450.4505 \, \text{K} \]

Final Answer