Among the following statements,the correct st | vedclass

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

Question

(A) For a first order reaction,the integrated rate law is given by $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.At half-life,$t = t_{1/2}$ and $[A]_

Vedclass · Accepted Answer

Independent of concentration

Vedclass · Answer

(A) For a first order reaction,the integrated rate law is given by $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.At half-life,$t = t_{1/2}$ and $[A]_t = \frac{[A]_0}{2}$.Substituting these values into the equation:$k = \frac{2.303}{t_{1/2}} \log \frac{[A]_0}{[A]_0 / 2} = \frac{2.303}{t_{1/2}} \log 2$.Since $\log 2 \approx 0.3010$,we get $k = \frac{2.303 	imes 0.3010}{t_{1/2}} = \frac{0.693}{t_{1/2}}$.Therefore,$t_{1/2} = \frac{0.693}{k}$.This expression shows that the half-life of a first order reaction is independent of the initial concentration of the reactant.

Among the following statements,the correct statement about the half-life period for a first order reaction is

Similar Questions

The rate constant of a first order reaction is $1.15 \times 10^{-3} \ s^{-1}$. How long will $5 \ g$ of reactant take to reduce to $3 \ g$ (in $s$)?

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 $......... \ min$.

The reaction $X \rightarrow$ products is a first order reaction. In $40 \ min$,the concentration of $X$ changes from $1.0 \ M$ to $0.25 \ M$. What is the rate of reaction when $[X] = 0.1 \ M$? $(\log 4 = 0.60)$

The rate constant of the decomposition of hydrogen peroxide is $0.0204 \text{ min}^{-1}$. Calculate the half-life of the reaction. (in $\text{ min}$)

At $500\,^oC$,cyclopropane isomerizes to propene. This reaction is first order with a rate constant of $6.7 \times 10^{-4}\,s^{-1}$. If the initial concentration of cyclopropane is $0.05\, M$,what will be the molarity of cyclopropane after $30\, min$ (in $, M$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module