A research chemist evaluates the energetic profile of the following multistep pathway that converts liquid methanol, CH₃OH(l), at 25 °C into gaseous formaldehyde, HCHO(g), at 200 °C and 1 atm.
Step 1 CH₃OH(l, 25 °C) → CH₃OH(l, 64.7 °C) (heating to the normal boiling point)
Step 2 CH₃OH(l, 64.7 °C) → CH₃OH(g, 64.7 °C) (vaporization)
Step 3 CH₃OH(g, 64.7 °C) → CH₃OH(g, 200 °C) (heating of the vapor)
Step 4 CH₃OH(g, 200 °C) → HCHO(g, 200 °C) + H₂(g, 200 °C) (dehydrogenation)
The following data are provided:
• Specific heat capacity of CH₃OH(l): 2.53 J g⁻¹ °C⁻¹
• Specific heat capacity of CH₃OH(g): 1.98 J g⁻¹ °C⁻¹
• Molar heat of vaporization of CH₃OH at 64.7 °C: 37.0 kJ mol⁻¹
• Enthalpy change for Step 4 at 200 °C: +85.0 kJ mol⁻¹
• Molar mass of CH₃OH: 32.0 g mol⁻¹
(a) Calculate the enthalpy change for each of the first three steps, expressed in kJ mol⁻¹.
(b) Construct a quantitatively accurate energy diagram for the complete four-step pathway, showing relative positions of reactants, intermediates, and products on the enthalpy axis. Label each vertical change with its calculated value and sign.
(c) Using your diagram, rank the four individual steps from the most exothermic to the most endothermic. Provide a brief justification referencing numerical values.
(d) Suppose the process is modified so that Step 2 occurs at 40 °C under reduced pressure instead of at 64.7 °C. Predict qualitatively how this change would affect the overall enthalpy of the pathway and the ranking you gave in part (c). Explain your reasoning.