Problem $3\mathrm{.}5.$ Chlorination of Carbon Monoxide to Phosgene Over Activated

Carbon.

The reaction CO $+$ CI$2=>$ COCI$2$ has been studied over an activated carbon

catalyst. The following data has been collected at a given temperature from a labscale reactor system.

The overall goal is to identify which step is rate$-$controlling, and what form of the

rate equation gives the best representation to the data. Answer the following

questions.

a$.$ Postulate at least three rate equations that are consistent with the overall

reaction.

b$.$ Rewrite each of the rate equations in a linearized form so they could utilize

the given data to identify the unknown kinetic and adsorption equilibrium

parameters.

c$.$ Identify the various kinetic rate and adsorption equilibrium parameters

using the Excel function LINEST. Include the option where the various

statistical measures that define the goodness$-$of$-$fit are provided. Next,

create an Excel table that compares the kinetic rate equation parameters

and the various statistical measures for goodness$-$of$-$fit. Which rate

equation is the recommended form?

d$.$ For each rate equation, create a parity plot that shows the experimental

values for the rate versus the model$-$predicted values. Included the

numerical values for the coefficient of determination, the regression sumof$-$squares, and the residual sum$-$of$-$squares on each chart.

rate x $103$

$,$ gmol$/($g cat$-$hr$)$ CO Cl$2$ COCl$2$

$4\mathrm{.}410\mathrm{.}4060\mathrm{.}3520\mathrm{.}226$

$4\mathrm{.}400\mathrm{.}3960\mathrm{.}3630\mathrm{.}231$

$2\mathrm{.}410\mathrm{.}3100\mathrm{.}3200\mathrm{.}356$

$2\mathrm{.}450\mathrm{.}2870\mathrm{.}3330\mathrm{.}376$

$1\mathrm{.}570\mathrm{.}2530\mathrm{.}2180\mathrm{.}522$

$3\mathrm{.}900\mathrm{.}6100\mathrm{.}1130\mathrm{.}231$

$2\mathrm{.}000\mathrm{.}1790\mathrm{.}6080\mathrm{.}206$

Partial pressures, atm

CHEN $5333$

Homework $3$

Page $8$

e$.$ Using the preferred rate equation from step c$,$ perform a nonlinear

regression analysis of the reaction rates using the Excel function SOLVER to

minimize an objective function based on $($a$)\%$ absolute error and $($b$)\%$

relative errors. Use the kinetic rate and adsorption parameters from the

linearized analysis as the initial parameter estimates.

f$.$ Compare the final values for the kinetic and adsorption parameters from

the linear and nonlinear analysis along with numerical values for the

coefficient of determination, the regression sum$-$of$-$squares, and the

residual sum$-$of$-$squares.

g$.$ What can you conclude from the final form of the rate equation and the

two approaches for determining the rate equation kinetic and adsorption

parameters?