Question

In a first order reaction, fraction of the total concentration of the reactant that varies with time 't' is equal to:

• A. $e^{+kt}$
• B. ${10}^{+0.434kt}$
• C. $\frac{1}{2^{-n}}$
• D. $e^{-kt}$

Answer 1

Answer: (D)

$e^{-kt}$

$k=\frac{2.303}{t}\times log\frac{A_0}{A_t}$
where,
$A_0=$ is the initial concentration
$A_t=$ is the concentration at time t
And k is the specific rate constant for the reaction,
$\therefore kt=ln\frac{A_0}{A_t}$
Which can be written in the exponential form as,
$\frac{A_0}{A_t}=e^{kt}$
$\frac{A_t}{A_0}=e^{-kt}$