Question

$A\left(g\right)\to 2B\left(g\right)$ is a first order reaction with respect to $A\left(g\right)$. Which of the following is correct ($[A{]}_0$ being the initial concentration of $A$)?

• A. $\left[B\right]=[A{]}_0{e}^{-kt}$
• B. $\left[B\right]=\left[A{]}_0\right(1-e^{-kt})$
• C. $\left[B\right]=\left[A{]}_0\right(e^{-kt}-1)$
• D. $\left[B\right]=2\left[A{]}_0\right(1-e^{-kt})$

Answer 1

The correct option is D $\left[B\right]=2\left[A{]}_0\right(1-e^{-kt})$

$A\left(g\right)\to 2B\left(g\right)$
at t=0 $[A{]}_0$ 0
at t=t $[A{]}_0-x$ $2x$

Let, $[A{]}_0-x=[A]$

At time 't' ,
$x=[A{]}_0-[A]$
and we know for a first order reaction, $\left[A\right]=[A{]}_0{e}^{-kt}$
Substituting we get,
$x=[A{]}_0-[A{]}_0{e}^{-kt}$
$x=\left[A{]}_0\right(1-e^{-kt})$
and the concentration of $\left[B\right]$ at time 't' is $=2x$
So, $\left[B\right]=2\left[A{]}_0\right(1-e^{-kt})$