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

`A + B rarr` products
Given : Rate `= k[A][B]" "(2^(nd)` Order reaction)
Now, since `[B] gt gt [A], [B]` can be assumed to remain constant throughout the reation. Thus, the rate law for the reaction, becomes :
Rate `~~ k_(0)[A]`
where `k_(0) =k[B]=5.0xx10^(-3)xx6.0 s^(-1)=3.0xx10^(-2) s^(-1)`
Thus, the reaction is now of first order.
Using, `2.303 log_(10)"" (A_(0))/(A)=k_(0)t`
`rArr 2.303 log_(10)""(0.1)/(A) =k_(0)t=3`
`rArr log_(e)""(0.1)/(A) =3" "[therefore" log x =2.303 log"_(10)x]`
`rArr A=(0.1)/(e^(3))=5xx10^(-3) M`