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.
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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QUANTUM BIOLOGY - EXAMPLE 33.2 : (a) In a biomolecule, ATP hydrolysis will produce 3 kcal / mol to 60 kcal / mol of energy, according to energy scale. Find the range of such energy generation if 2 moles of molecules involved. (b) A formula is given by ln P = ln a + b ln W where P = metabolic rate, W = body size, a = dependent of taxa, b = scaling exponent. If b is approximately 1 for plant, and b is approximately 0.75 for animal, find the relationship of P as a function of a and W in plant.
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CHEMICAL FLUID MECHANIC - EXAMPLE 3.1 : Water flows through a pipe with circular cross sectional area at the rate of V / t = 80 L / s where V is the volume and t is time. Let Av = 80 L / s where A is cross sectional area and v is velocity of fluid. For point 1, the radius of the pipe is 16 cm. For point 2, the radius of the pipe is 8 cm. Find (a) the velocity at point 1; (b) the velocity at point 2; (c) the pressure at point 2 by using Bernoulli's equation where P + Rgy + 0.5 RV = constant. P is the pressure, R = density of fluid, V = square of fluid's velocity, g = gravitational constant of 9.81 N / kg and y = 2 m = difference of height at 2 points. The pressure of point 1 is 180 kPa.
ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.25 : (a) If an engineering company has a policy to maintain A % debt ratio, it will limit its total debt B, to A % of all company assets with total assets C. Find the value of A as a function of B and C. (b) An engineering consultancy that designs biochemical processing plants has a beginning balance in a bank of value D. The interest paid by the bank to the consultancy for the saving is E. The consultancy withdraws F amount of money from the bank to cover the project cost. (i) Calculate the end balance in a bank of the consultancy by using the symbols of D, E and F etc. (ii) Find the value of the principal due to E and F.
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ENGINEERING ECONOMY - EXAMPLE 7.1 : In engineering economy, the future value of first year is FV = PV (1 + i). For second year it is FV = PV (1 + i) (1 + i). For third year it is FV = PV (1 + i) (1 + i)(1 + i) where FV = future value, PV = present value, i = interest rate per period, n = the number of compounding periods. By induction, what is the future value of $1000 for 5 years at the interest rate of 6 %?