Five hundred kilograms per hour of an aqueous solution containing 20.0mole% sodium acetate (NaC2H3O2) enters an evaporative crystallizer at 60°C. When the solution is exposed to the low pressure in the evaporator 16.9% of the water evaporates, concentrating the remaining solution and causing crystals of sodium acetate trihydrate (NaC2H3O2·3 H2O) to form. The product is an equilibrium mixture of crystals and a saturated aqueous solution containing 15.4 mole% NaC2H3O2. The effluents (crystals, solution, and water vapor) are all at 50°C.
(a) Calculate the feed rate to the crystallizer in k mol/h.
(b) Calculate the production rate (kg/h) of trihydrate crystals and the mass flow rate (kg/h) of the liquid solution in which the crystals are suspended.
(c) Estimate the rate (kJ/h) at which heat must be transferred to or from the crystallizer (state which), using the following physical property data: (Cp) all solutions 3.5 kJ/(kg·°C) (Cp) crystals = 1.2 kJ/(kg·°C) (Cp) H2O (v) = 32.4 kJ/(k mol·°C) (?Hv)H2O = 4.39 x 104 kJ /k mol) Heat of solution of anhydrous sodium acetate: ?Hs (25°C) = —1.71 X 104 kJ/k mol NaC2H3O2 Heat of hydration: NaC2H3O2(s) + 3 H2O (l) ? NaC2H3O2·3 H2O(s) ?H (25°C) = —3.66 x 104 kJ/k mol NaC2H3O2
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