For the overall reaction between `A` and `B` to yield `C` and `D`, two mechanism are proposed:
`{:(I,A+BrarrAB^(**)rarr C + D,,k'_(1) = 1 xx 10^(-5)M^(-1)s^(-1),),(II,A rarrA^(**)rarrE,,,k_(1) = 1 xx10^(-4)s^(-1),),(,E+BrarrC+D,,,k'_(1) = 1 xx 10^(-10)s^(-1),):}`
a. Write the rate law expresison fr each mechanism when initial concentration of each is `0.1 M`.
b. At that concentration of `A` and/or `B`, will the inherent rates be equal?

Explanation

`Rate_(I) = k'_(1)[A][B] = 1 xx 10^(-5)(0.1)(0.1) = 1 xx 10^(-7) M s^(-1)`
`Rate_(II) = k_(1)[A] = 1 xx 10^(-4) xx 0.1`
`= 1 xx 10^(-5)Ms^(-1)`
(Its second step is fast and first step is slow as evident `k_(1)` and `k_(2)` values)
If rates are equal, then `k'_(1)[A][B] = k_(t)[A]`
`:. k'_(1)[A] = k_(t)`
`:. [B] = (k_(1))/(k'_(1)) = (1 xx 10^(-4)s^(-1))/(1 xx 10^(-5)M^(-1)s^(-1)) = 10 M`