REACTION ENGINEERING - EXAMPLE 13.2 : A batch reactor is designed for the system of the irreversible, elementary liquid-phase hydration of butylene oxide that produces butylene glycol. At the reaction temperature T = 323 K, the reaction rate constant is k = 0.00083 L / (mol - min). The initial concentration of butylene oxide is 0.25 mol / L = Ca. The reaction is conducted using water as the solvent, so that water is in large excess. (a) Let the molecular weight of water is 18 g / mol and the mass of 1 kg in 1 L of water, calculate the molar density of water, Cb in the unit of mol / L. (b) Determine the final conversion, X of butylene oxide in the batch reactor after t = 45 min of reaction time. Use the formula X = 1 - 1 / exp [ kt (Cb) ] derived from material balance. (c) Find the equation of t as a function of X.
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REACTION ENGINEERING - ANSWER 13.2 : (a) Cb = (1000 g / L) / (18 g / mol) = 55.556 mol / L. (b) X = 1 - 1 / exp [ kt (Cb) ] = 1 - 1 / exp (0.00083 x 45 x 55.556) = 0.8744. (c) X = 1 - 1 / exp [ kt (Cb) ], 1 / exp [ kt (Cb) ] = 1 - X, exp [ kt (Cb) ] = 1 / (1 - X), (Cb) kt = ln [ 1 / (1 - X) ], t = 1 / [ k (Cb) ] ln [ 1 / (1 - X) ] = ln [ 1 / (1 - X) ] / [ k (Cb) ]. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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