$6\mathrm{.}18$ F$.$ J$.$ Dumez and G$.$ F$.$ Froment $[$Ind$.$ Eng. Chem. Process

Des. Dev., $15,291(1976)]$ studied the kinetics of the

dehydrogenation of $1-$butene over a $C{r}_2\frac{O_3}{A}{l}_2{O}_3$ catalyst at

$490$ to $600C$ :

$C_4{H}_{8}harr{H}_2+C_4{H}_6$

or

$Bharr{H}_2+D$

They carried out a number of experimental studies in an

attempt to discriminate among several Hougen$-$Watson mod$-$

els that were proposed to explain the observed kinetics. A

few of these models are summarized below. Derive the corre$-$

sponding Hougen$-$Watson rate expression for each of these

models.

$($a$)$ Atomic dehydrogenation; surface recombination of

hydrogen

$(1)B+harr{B}_{},K_B$

$(2)B_{}+harr(C_4{H}_7{)}_{}+H_{},k_f,k_r$

$(3)(C_4{H}_7{)}_{}+harr{D}_{}+H_{},K_3$

$(4)D+harr{D}_{},K_D$

$(5)2H_{}$harr$(H_2{)}_{}+,K_5$

$(6)H_2+harr(H_2{)}_{},K_{H_2}$

Consider the case where the second reaction is rate con$-$

trolling.

$($b$)$ Atomic dehydrogenation; gas$-$phase recombination of

hydrogen

$(1)B+harr{B}_{},K_B$

$(2)B_{}+harr(C_4{H}_7{)}_{}+H_{},k_f,k_r$

$(3)(C_4{H}_7{)}_{}+harr{D}_{}+H_{},K_3$

$(4)D+harr{D}_{},K_D$

$(5)H_2+2harr2H_{},K_{H_2}$

$($c$)$ Molecular dehydrogenation

$(1)B+harr{B}_{},K_B$

$(2)B_{}+harr{D}_{}+(H_2{)}_{},k_f,k_r$

$(3)D+harr{D}_{},K_D$

$(5)H_2+harr(H_2{)}_{},K_{H_2}$

What sorts of kinetic experiments could be utilized

to discriminate between the models proposed? In what

manner should initial rate data be plotted to assess the

validity of each of the three proposed mechanisms?