The rate of a first-order reaction is 0.04 m | 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 $R$ at time $t$ is given by $R = k[A]_t$,where $[A]_t = [A]_0 e^{-kt}$.Thus,$R_t = k[A]_0 e^{-kt} = R_0 e^{-kt

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(C) For a first-order reaction,the rate $R$ at time $t$ is given by $R = k[A]_t$,where $[A]_t = [A]_0 e^{-kt}$.Thus,$R_t = k[A]_0 e^{-kt} = R_0 e^{-kt}$.Given $R_{10} = 0.04 \ mol \ L^{-1} \ s^{-1}$ and $R_{20} = 0.03 \ mol \ L^{-1} \ s^{-1}$.Taking the ratio: $\frac{R_{10}}{R_{20}} = \frac{e^{-k(10)}}{e^{-k(20)}} = e^{10k} = \frac{0.04}{0.03} = 1.333$.Taking natural log on both sides: $10k = \ln(1.333) = 0.2877$.$k = 0.02877 \ s^{-1}$.The half-life period is $t_{1/2} = \frac{0.693}{k} = \frac{0.693}{0.02877} \approx 24.1 \ s$.

The rate of a first-order reaction is $0.04 \ mol \ L^{-1} \ s^{-1}$ at $10 \ s$ and $0.03 \ mol \ L^{-1} \ s^{-1}$ at $20 \ s$ after the initiation of the reaction. The half-life period of the reaction is ......... $s$. (in $.1$)

Similar Questions

Rate of first order reaction $A \rightarrow \text{product}$ is $0.01 \ mol \ dm^{-3} \ s^{-1}$. Calculate the rate constant if the concentration of the reactant is $0.2 \ M$. (in $s^{-1}$)

Which is the correct relation between rate constant and half-life of a first-order reaction?

Thermal decomposition of $HCOOH$ is a first order reaction and the rate constant at $T(K)$ is $4.606 \times 10^{-3} \ s^{-1}$. The time required to decompose $90 \%$ of initial quantity of $HCOOH$ at $T(K)$ in seconds is

Half-life and rate constant for a first-order reaction are related by the equation:

For a first-order reaction,the time taken for the initial concentration to decrease to $1/4$ of its value is $20 \ min$. The time taken for the initial concentration to decrease to $1/16$ of its value will be $......... \ min$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module