A certain reaction `A + B rarr` Products is first order w.r.t. each reactant with `k = 5.0 xx 10^(-3) M^(-1) s^(-1)`. Calculate the concentration of `A` remaining after `100s` if the initial concentration of `A` was `0.1 M` and that of `B` was `6.0 M` State any approximation made in obtaining your result.

Explanation

Since `[B] = 6.0 M`, we can conisder that its concentration remains constant theoughout. Thus,
Rtae `= k[A][B]`
`= k[A] xx 6 M = 6k[A]`
`= k'[A]`
where `k' (=6k)` is new constant and reaction under this conditions is supposed to follow first order kinetics.
`k' = (2.303)/(t)log.(a)/(a-x)`
`:. log.(a)/(a-x) = (k't)/(2.303) = (6kt)/(2.303)`
`log.(a)/(a-x) = (6 xx 5.0 xx 10^(-3) xx 100)/(2.303) = 1.3026`
`((a)/(a-x)) = 20`
`(a-x)/(a) = (1)/(20)`
`(a-x) = (a)/(20) = (0.1)/(20) = 0.0050 M`
Hence, the concentration of reactant `A` after `100 s` is `0.005 M`.