Q$1$: The dimethyl ether $($DME$)$ can be thermally decomposed in the gas phase. One student team performed this reaction and measured the increase in the pressure at constant volume batch reactor. At $500C$ and initial pressure of $312mmHg,$ the following data where obtained:

$t,$ sec $,39077711953155$

$P_{\text{t}\text{o}\text{t}\text{a}\text{l}},mmHg408488562779931$

Assuming that only DME was present initially and that the reaction is

$(C{H}_3{)}_{2}OlongrightarrowC{H}_4+H_2+CO$

Hint: test for the rate dependence on the reactant DME providing a graph as art of your answer. This require you to find the partial pressure of DME at each time from the total pressure, knowing that $N_{\text{t}\text{o}\text{t}\text{a}\text{l}}=N_{\text{D}\text{M}\text{E}}+N_{CH4}+N_{H2}+N_{CO},$ also assuming ideal gas

$($a$)$ Determine the rate equation for the decomposition $($ the order and the rate constant$)$

$($b$)$ What reactor is suitable for such reaction?

$($c$)$ Explain what steps you should do if you decide to use a packed bed reactor filled with catalyst for that reaction

$($d$)$ What are the codes of ethics implemented in that decomposition reaction?