The slope of a graph lo g [ A ] t versus ' t ' for first order reaction is − 2.5 × 1 0 − 3 s − 1 . Find rate constant of the reaction?

Question

The slope of a graph lo g [ A ] t ​ versus ' t ' for first order reaction is − 2.5 × 1 0 − 3 s − 1 . Find rate constant of the reaction?

TestHub · Accepted Answer

For a first order reaction, the integrated rate law is given by:

$k = \frac{2.303}{t} lo g \frac{[ A ] _{0}}{[ A ] _{t}}$

Rearranging the equation in the form of a straight line $y = m x + c$ :

$lo g [A]_{t} = - \frac{k}{2.303} t + lo g [A]_{0}$

The graph of $lo g [A]_{t}$ versus $t$ is a straight line with slope $m = - \frac{k}{2.303}$ .

Given slope $= - 2.5 \times 1 0^{- 3} s^{- 1}$ .

$- \frac{k}{2.303} = - 2.5 \times 1 0^{- 3}$

$k = 2.303 \times 2.5 \times 1 0^{- 3}$

$k = 5.7575 \times 1 0^{- 3} s^{- 1}$

Answer: $5.757 \times 1 0^{- 3} s^{- 1}$

Chemistry - Chemical Kinetics Question with Solution | TestHub

Options:

Doubts & Discussion