The following data was obtained by Sinfelt and company for the dehydrogenation of methyl cyclohexane to toluene. Furthermore, they discovered that the partial pressure of toluene has no effect on the rate of reaction. According to the following mechanism: M$+$S$---($MS$)$

$($MS$)---($RS$)$

$($RS$)---$ T$+$H$2+$S

Where M $=$ methyl cyclohexane, T $=$ toluene and H$2=$ diatomic hydrogen. Develop the velocity equation for the following cases: a$)$ Adsorption is the limiting step b$)$ Surface reaction is the limiting step c$)$ Which of the two equations obtained in parts a$)$ and b$)$ presents a best fit based on the experimental data in the table? Present the value of the kinetic parameters with their units and the coefficient of determination $($R $2)$ for each equation. d$)$ Based on the kinetic parameters of the equation that obtained the best fit, determine the activation energy.

$\backslash$table$[[T(C),P_M(atm),P_{H2}(atm),r_p(kmo\frac{l}{k}{g}_{\text{c}\text{a}\text{t}}*h)$