Question

In a first order reaction, the concentration of product 'x' at time 't' is given by the expression:

(where,a $=$ initial concentration, k $=$ rate constant, n $=$ order)

• A. $x=a(1-e^{-kt})$
• B. $x=\frac{1}{(a-x)}$
• C. $x=\frac{1}{2^{n-1}}$
• D. $x=\frac{a}{(a-x)}$

Answer 1

The correct option is A $x=a(1-e^{-kt})$

The integrated rate law for the first order reaction is $\left[A\right]=[A{]}_0{e}^{-kt}$.

Substituting the value of $\left[A\right]=a-x$ and $[A{]}_0=a$ in the above expression.

We get, $a-x=a{e}^{-kt}$.

Rearrange above expression, $x=a(1-e^{-kt})$.