Question

With the help of rate equation show that the first order reaction is never complete

Answer 1

Think of the equations that arise from solving the first-order reaction rate law:

If [A] is the concentration of your reactant which is getting converted to products according to

[A]→products,

then, we have,

d[A]dt=−k[A].

Solving this with the initial condition that the initial concentration of A is [A]0, we get an equation for the concentration of [A] at any time t as:

[A]=[A]0⋅e−kt.

The mathematics says it all! [A] can never be zero, though it can be infinitesimally close to it.

We generally wait till the reaction is 99.something% complete or something and then neglect the rest.

Of course, limt→∞[A]=0, but you literally can never wait that long.