An industrial dryer is used to remove methanol from a process stream by vaporizing the liquid solvent. During one hour of operation, the dryer supplies 125 MJ of thermal energy, but only 65.0 % of that energy is actually absorbed by the methanol; the rest is lost to the surroundings. The methanol enters the dryer as a saturated liquid at its normal boiling point.
Relevant data for methanol (CH₃OH):
• molar enthalpy of vaporization: 35.3 kJ mol⁻¹
• molar mass: 32.0 g mol⁻¹
• initial mass of liquid methanol in the dryer: 500 kg
(a) Calculate the mass of methanol that is converted to vapor during this one-hour period, accounting for the stated efficiency.
(b) Determine the number of methanol molecules that enter the gas phase during the same period.
(c) If engineering improvements raise the energy-transfer efficiency to 80.0 %, compute the new mass of methanol that would be vaporized and discuss how this change would impact overall solvent recovery.