In steam cracking the homogeneous pyrolysis of ethane to produce ethylene, $C_2{H}_6{C}_2{H}_4+H_2,$ is

carried out in pipe heated to $850C$ at an ethane atmospheric pressure of $1$atm. The mechanism of the

reaction is thought to be as follows:

$C_2{H}_6{k}_1{C}_2{H}_5*+H.$

$C_2{H}_6+H*{?}^{k_2}{C}_2{H}_5*+H_2$

$C_2{H}_5*longrightarro{w}^{k_3}{C}_2{H}_4+H*$

$2C_2{H}_5*{?}^{k_4}{C}_4{H}_{10}$

a$.$ Which of reactions is the initiation step, the termination step and the propagation step?

b$.$ Applying PSSH where necessary, develop the rate law for the production of $H_2(r_{H_2}).$

c$.$ Your rate law from part $($b$)$ will be of the form $r_{H_2}=k_1{C}_{C_2{H}_6}+k{C}_{C_2{H}_6}^{0\mathrm{.}5},$ where $k$ is a

combination of $k\text{'}$s in the individual reactions.

If the activation energy for reaction $1(E_1)$ is $94$kca$\frac{l}{m}ol,$ the second and third reactions have zero

activation energies $($that is $E_2=0$ and $E_3=0),$ and the activation energy for fourth reaction is $E_4)$

is $25$kca$\frac{l}{m}ol.$ What should be the activation energy of the rate constant, $k?$