Phosgene (COCl2) is formed by CO and Cl2 reacting in the

QUESTION:

Phosgene (COCl2) is formed by CO and Cl2 reacting in the presence of activated charcoal: CO Cl2 ! COCl2 At T 303:8 K the rate of formation of phosgene in the presence of 1 gram of charcoal is Rfmol=min 8:75CCOCCl2 1 58:6CCl2 34:3CCOCl2 2 where C denotes concentration in mol/L. (a) Suppose the charge to a 3.00-liter batch reactor is 1.00 g of charcoal and a gas initially containing 60.0 mole% CO and the balance Cl2 at 303.8 K and 1 atm. Calculate the initial concentrations (mol/L) of both reactants, neglecting the volume occupied by the charcoal. Then, letting CPt be the concentration of phosgene at an arbitrary time t, derive relations for CCO and CCl2 in terms of CP. BIOENGINEERING Equipment Encyclopedia batch reactor www.wiley.com/college/felder 600 CHAPTER 10 Balances on Transient Processes WEBC10 06/04/2015 22:57:0 Page 601 (b) Write a differential balance on phosgene and show that it simplifies to dCP dt 2:920:02407 CP0:01605 CP 1:941 24:3CP 2 Provide an initial condition for this equation. (c) A plot of CP versus t starts at CP 0 and asymptotically approaches a maximum value. Explain how you could predict that behavior from the form of the equation of Part (b). Without attempting to solve the differential equation, determine the maximum value of CP. (d) Starting with the equation of Part (b), derive an expression for the time required to achieve a 75% conversion of the limiting reactant. Your solution should have the form t a definite integral. (e) The integral you derived in Part (d) can be evaluated analytically; however, more complex rate laws than the one given for the phosgene formation reaction would yield an integral that must be evaluated numerically. One procedure is to evaluate the integrand at a number of points between the limits of integration and to use a quadrature formula such as the trapezoidal rule or Simpsons rule (Appendix A.3) to estimate the value of the integral. Use a spreadsheet to evaluate the integrand of the integral of Part (c) at np equally spaced points between and including the limits of integration, where np is an odd number, and then to evaluate the integral using Simpsons rule. Perform the calculation for np 5; 21; and 51. What can you conclude about the number of points needed to obtain a result accurate to three significant figures?