Q$2.$ The thermal decomposition of ethane to ethylene, methane, butane, and hydrogen is believed to proceed in the following sequence:

Initiation:

$C_2{H}_{6}2C{H}_3**$

Propagation:

$C{H}_3**+C_2{H}_{6}C{H}_4+C_2{H}_5**$

$C_2{H}_5**C_2{H}_4+H**$

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

Termination:

$2C_2{H}_5**C_4{H}_{10}$

Use the PSSH to derive a rate law for the rate of formation of ethylene. $k_1,k_2,k_3,k_4,$ and $k_5$ are the rate constants for reactions $1$ to $5,$ respectively.