A laboratory still is charged with 10 L of a methanol-water mixture containing 0.70 mole fraction methanol. 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 t_ɣ required to boil off 5 L;

(b) The mole fraction of methanol left in the still at times t_ɣ/2. 3t_ɣ/4. and t_ɣ;

(c) The average composition of the total distillate at time t_ɣ Equilibrium data for the system methanol-water are given in Table 21.6.

Table 21.6

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TABLE 21.6 System acetone-methanol Temperature, "C 64.5 53,6 62.5 60.2 58.65 57.55 Mole fraction acetone Vapor 0.000 0.102 0.186 0.322 0428 0.513 Liquid 0.00 0.05 0.10 0.20 0.30 0.40 Temperature, "C 56.7 56.0 55.3 55.05 56.1 Mole fraction acetone Vapor 0.586 0.656 0.725 0.80 1.00 Liquid 0.50 0.60 0.70 0.80 1.00