Neco 2019 Chemistry Question 20

The solid allotropes of sulfur, rhombic S\(_8\) and monoclinic S\(_8\), interconvert according to the reaction\n\\(\text{rhombic}\,\text{S}_{8}\rightleftharpoons\text{monoclinic}\,\text{S}_{8}\\).\nAt 298 K the standard enthalpy of formation of rhombic sulfur is defined as 0 kJ·mol\(^{-1}\), and the enthalpy change for the transition to monoclinic at this temperature is +2.0 kJ·mol\(^{-1}\). At 400 K the equilibrium constant for the transition is K = 3.0. Assuming the enthalpy change is temperature‑independent, (a) calculate the standard enthalpy change \(\Delta H^{\circ}\) for the transition (in kJ·mol\(^{-1}\)), (b) determine the temperature at which K = 0.5, and (c) if 0.050 mol of rhombic sulfur is heated to that temperature in a sealed container, calculate the amount (in mol) of monoclinic sulfur present at equilibrium.