A laboratory still is charged with 10 L of a methanol-water mixture containing 0.70 mole fraction methano1. This is to be distilled batchwise without reflux at 1 atm pressure until 5 L of liquid remains in the still, that is, 5 L has been boiled off. The rate of heat input is constant at 4 kW. The partial molar volumes are 40.5 cm3/g mol for methanol and 18 cm3/g mol for water. Neglecting any volume changes on mixing and using an average heat of vaporization of 40 kJ/g mol, calculate
(a) the time tT required to boil off 5 L;
(b) the mole fraction of methanol left in the still at times tT/2, 3tT/4, and tT;
(c) the average composition of the total distillate at time tT' Equilibrium data for the system methanol-water are given in Table 18.6.