$3\mathrm{.}10$ Rate Data Analysis for a Catalytic Reforming Reaction

$3\mathrm{.}10\mathrm{.}1$ Concepts Demonstrated

Evaluation of catalytic reaction rate expressions for experimental data.

$3\mathrm{.}10\mathrm{.}2$ Numerical Methods Utilized

Linear and nonlinear regression, transformation of data for regression, and calculations with comparisons involving confidence intervals, residual plots and sum of squares.

$3\mathrm{.}10\mathrm{.}3$ Excel Options and Functions Demonstrated

Quanch and Rouleau ${?}^7$ investigated different models for the reversible catalytic reforming reaction

$C{H}_4+2H_{2}OharrC{O}_2+4H_2$

The experimental results of reaction rate as function of partial pressure of the products at $350C$ are given in Table $3-10.$

Table $3-10$ Reaction Rate Data for Catalytic Reforming Reaction

$\backslash$table$[[$Partial Pressure $($atm$),\backslash$table$[[$Reaction Rate$],[$of $C{O}_2$One of several models for this catalytic reaction, in which methane is adsorbed

on the catalyst surface, is given by

$r_{C{O}_2}=\frac{k_g{K}_{C{H}_4}(P_{C{H}_4}{P}_{H_{2}O}^2-\frac{P_{C{O}_2}{P}_{H_2}^4}{K_P})}{1+K_{C{H}_4{P}_{C{H}_4}}}$

where the overall equilibrium constant is known from thermodynamic calcula$-$

tion to be $K_P=5\mathrm{.}051{10}^{-5}at{m}^2.$ Thus there are only two parameters which need

to be evaluated for this catalytic rate expression.

Another simpler model is simply for a reversible reaction in which there is

no component adsorption on the catalyst. This rate expression is given by

$r_{C{O}_2}=k_1(P_{C{H}_4}{P}_{H_{2}O}^2-\frac{P_{C{O}_2}{P}_{H_2}^4}{K_P})$

where there is only one parameter, $k_1.$

Note that the rate, $r_{C{O}_2},$ is the positive net generation of $C{O}_2,$ and that the

rate of $C{H}_4$ would be the negative of this same rate.

$($a$)$ Find the values of parameters $k_s$ and $K_{C{H}_4}$ using nonlinear regression

on the data from Table $3-10.$

$($b$)$ Determine the value of parameter $k_1.$

$($c$)$ Which of these two rate equations best represents the given data set?

Justify your selection.

The problem data file is found in directory Chapter $3$ with file name

P$3-10.$POL. pleasegive me the response and solve using excel and python