Question

A certain second-order reaction (B→products) has a rate constant of 1.30×10−3 M−1⋅s−1 at 27 ∘C and an initial half-life of 224 s . What is the concentration of the reactant B after one half-life?

Answer 1

Answer:

       $\large\boxed{\large\boxed{0.291M}}$

Explanation:

By definition one half-life is the time to reduce the initial concentration to half.

For a second order reaction the rate law equations are:

              $\dfrac{d[B]}{dt}=-k[B]^2$

             $\dfrac{1}{[B]}=\dfrac{1}{[B]_0}+kt$

The half-life equation is:

            $t_{1/2}=\dfrac{1}{k[A]_0}$

Thus, substitute the rate constant  $1.30\times 10^{-3}M^{-1}\cdot s^{-1}$ and the half-life time 224s to find [A]₀:

           $224s=\dfrac{1}{1.30\times10^{-3}M^{-1}\cdot s^{-1}[A]_0}$

           $[A]_o=0.291M$