A first order reaction is 60% complete in 20 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a first order reaction, the rate constant $k$ is given by $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.For $60\%$ completion, $[A]_t = [A]_0

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(C) For a first order reaction, the rate constant $k$ is given by $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.For $60\%$ completion, $[A]_t = [A]_0 - 0.60[A]_0 = 0.40[A]_0$ and $t = 20 	ext{ min}$.$k = \frac{2.303}{20} \log \frac{[A]_0}{0.40[A]_0} = \frac{2.303}{20} \log(2.5) \approx \frac{2.303 	imes 0.3979}{20} \approx 0.0458 	ext{ min}^{-1}$.For $84\%$ completion, $[A]_t = [A]_0 - 0.84[A]_0 = 0.16[A]_0$.$t = \frac{2.303}{k} \log \frac{[A]_0}{0.16[A]_0} = \frac{2.303}{0.0458} \log(6.25)$.Since $\log(6.25) = 2 \log(2.5) \approx 2 	imes 0.3979 = 0.7958$.$t = \frac{2.303 	imes 0.7958}{0.0458} \approx 40 	ext{ min}$.

$t/min$	Pressure of system at time $t/mm \ Hg$
$10$	$160$
$\infty$	$240$

$A$ first order reaction is $60\%$ complete in $20 \text{ minutes}$. How long will the reaction take to complete $84\%$ (in $\text{ min}$)?

Similar Questions

Identify True $(T)$ and False $(F)$ statements for the following expressions regarding a first-order reaction $R \rightarrow P$:
Statement $I$: $\text{Rate} = -\frac{d[R]}{dt} = k[R]$
Statement $II$: $\text{Rate} = -\frac{d[R]}{dt} = -k[R]$

Which of the following is an example of a first-order reaction?

Calculate the rate constant of a first-order reaction having a half-life of $1 \text{ minute } 40 \text{ seconds}$.

Reaction $A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$ is a first order reaction. It was started with pure $A$.
$t/min$ Pressure of system at time $t/mm \ Hg$
$10$ $160$
$\infty$ $240$
Which of the following option is incorrect?

The rate constant for a first order reaction is $60 \text{ s}^{-1}$. How much time (in seconds) will it take to reduce the initial concentration of the reactant to its $1/16^{th}$ value?

Vedclass Test Series

Exam Paper Generator

Online Exam Module