Exercise 4.8: Nonconstant density with a liquid-phase reaction Propylene glycol is produced by the hydrolysis of propylene oxide according to the following reaction H₂ C- CH–CH, + H2O - CHE T

OH OH propylene oxide propylene glycol In the presence of excess water, the reaction has been found to be first-order in propylene oxide and the rate constant is [6] 180 r = kcpo k= koe-Ea/RT ko 4.71 x 109 s-1 E = 18.0 kcal/mol K Methanol is added as a solvent, and the reaction is performed in a 1000 L CSTR operating at 60°C. The feed conditions and physical properties are as follows [15]: Component -CH-CH3 T propylene oxide water The Material Balance for Chemical Reactors Density Mol. wt. Inlet feedrate (g/cm³) (g/mol) 0.859 58.08 1.000 18.02 76.11 32.04 propylene glycol 1.0361 methanol 0.7914 Assume the mixture is ideal so that (L/hr) 1300 6600 0 1300 1-Σαν; in which V; = M;lp; are the pure component specific molar volumes. Neglect any change in the pure component densities with temperature in the temper- ature range 25-60°C. (a) Compute the steady-state concentrations of all components, Q, and VR for the following two situations. 1. A float in the top of the tank is used to adjust Q to maintain reactor volume constant at 1000 L. 2. The reactor is initially charged with pure solvent, and a differential pressure measurement is used to adjust Q to maintain constant reactor mass. Which operation do you recommend, constant volume or constantmass? Look at the conversion of propylene oxide and production rate of propy. lene glycol for the two cases. What are you wasting in constant mass operation? (b) Resolve the constant reactor volume operation under the assumption that all densities are equal to water. How much error in the conversion and production rate do you commit under this assumption?