Question

For the given first order reaction
$A\to \text{Products}$

Which of the following represents the correct graph between $\left[A\right]v/st$

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

For a first order reaction:
$A\to \text{Products}t=0at=ta-x$
a is intial concentration and (a-x) is the concentration at time t
$-\frac{d\left[A\right]}{dt}=k\left[A\right]$
$-\frac{d(a-x)}{dt}=k(a-x)$
a is a constant value
$\frac{dx}{dt}=k(a-x)$
$\frac{dx}{a-x}=k.dt$
$-\underset{0}{\overset{x}{\int }}\frac{dx}{a-x}=k\underset{0}{\overset{t}{\int }}dt$
$ln\frac{a}{a-x}=kt$
$2.303log\frac{a}{a-x}=kt$
This is the integrated rate law of first order reaction
$ln\frac{[A{]}_0}{\left[A\right]}=kt$
$\Rightarrow \left[A\right]=[A{]}_0{e}^{-kt}$
So, the correct option is (a)