$P3-13$ A $($a$)$ Write the rate law for the following reactions assuming each reaction follows an elementary rate law. Give the units of $k_A$ for each, keeping in mind some are homogeneous and some reactants are heterogeneous.

$C_2{H}_6{C}_2{H}_4+H_2$

$(C{H}_3{)}_3\frac{C}{O}OC(C{H}_3{)}_3{C}_2{H}_6+2C{H}_{3}COC{H}_3$

$n{C}_4{H}_{10}i{C}_4{H}_{10}$

$C{H}_3\frac{C}{O}O{C}_2{H}_5+C_4{H}_{9}OHC{H}_3\frac{C}{O}O{C}_4{H}_9+C_2{H}_{5}OH$

$2C{H}_{3}N{H}_2{}_{\text{c}\text{a}\text{t}}(C{H}_3{)}_{2}NH+N{H}_3$

$(C{H}_{3}CO{)}_{2}O+H_{2}O2C{H}_3\frac{C}{O}OH$