Solid carbon dioxide (dry ice) sublimates at –78.5 °C and 1 atm with a molar enthalpy of sublimation ΔH_sub = 25.2 kJ mol⁻¹. At 5 atm the substance instead melts at –56.6 °C (ΔH_fus = 8.4 kJ mol⁻¹) and then boils at –29.8 °C (ΔH_vap = 16.8 kJ mol⁻¹).
A sealed, evacuated chamber is maintained at 0.50 atm. Two moles of dry ice at –90 °C are placed inside the chamber. The molar heat capacities are:
C_solid = 37 J mol⁻¹ K⁻¹ C_liquid = 58 J mol⁻¹ K⁻¹ (liquid exists only above the triple point).
(a) At 0.50 atm, predict whether the first phase transition the sample undergoes upon heating will be melting or sublimation. Justify your answer with reference to the given data.
(b) Calculate the total heat (in kJ) required to convert the 2.00 mol sample from –90 °C solid to gas at –78.5 °C while the pressure remains at 0.50 atm.
(c) Suppose instead that the chamber pressure is increased to 5 atm before any heating occurs. Calculate the total heat required to convert the same sample from –90 °C solid to gas at –29.8 °C under this higher pressure.
(d) Compare the heats calculated in parts (b) and (c). Explain, in terms of the sequence of phase changes and the intermolecular forces disrupted, why the required energies differ.