SMITH CHEMICAL ENGINEERING KINETICS

$12-3$ The liquid$-$phase hydrogenation of $-$methyl styrene to cumene,

$H_2($dissolved$)+C_6{H}_{5}C(C{H}_3)=C{H}_2(l)C_6{H}_{5}CH(C{H}_3{)}_2(l),$

has been studied in a recycle batch reactor at $80$psia and $55C.$ The reactor was packed with $\frac{1}{8}-$in$.A{l}_2{O}_3$ spheres containing $0\mathrm{.}5wt\%$ palladium on the outer surface as a catalyst. The reaction was followed by analyzing micro$-$samples of reaction liquid at various times. The recycle rate was such that the conversion per pass was very low. The reaction liquid was always saturated

with hydrogen. Data for two runs are as follows:

$($table$)$

$($a$)$ For the integral changes in composition $($during a run$)$ shown, a plot of cumene mole fraction vs time might be expected to be curved; yet the data show a linear relationship. What does this signify about the kinetics of the reaction?

$($b$)$ Calculate rates of hydrogenation from the data given.