Phosgene (COCl₂) is formed by CO and Cl₂ reacting in the presence of activated charcoal:

At T = 303:8 K the rate of formation of phosgene in the presence of 1 gram of charcoal is

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 CP(t) be the concentration of phosgene at an arbitrary time t, derive relations for C_CO and C_Cl2 in terms of C_P.

(b) Write a differential balance on phosgene and show that it simplifies to

Provide an initial condition for this equation.

(c) A plot of C_P versus t starts at C_P = 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 Simpson’s 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 n_p is an odd number, and then to evaluate the integral using Simpson’s rule. Perform the calculation for n_p = 5; 21; and 51. What can you conclude about the number of points needed to obtain a result accurate to three significant figures?

Transcribed Image Text:

CO + Cl2 → COC2