(C) For a first order reaction,the rate constant $k$ is given by $k = \frac{1}{t} \ln \frac{[A]_0}{[A]_t}$.Given $[A]_0 = 1.0 \ M$,$[A]_t = 0.25 \ M$,

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

(C) For a first order reaction,the rate constant $k$ is given by $k = \frac{1}{t} \ln \frac{[A]_0}{[A]_t}$.Given $[A]_0 = 1.0 \ M$,$[A]_t = 0.25 \ M$,and $t = 10 \ hours$.$k = \frac{1}{10} \ln \frac{1.0}{0.25} = \frac{\ln 4}{10} \ h^{-1}$.The half-life $t_{1/2}$ is given by $t_{1/2} = \frac{\ln 2}{k}$.Substituting the value of $k$: $t_{1/2} = \frac{\ln 2}{(\ln 4) / 10} = \frac{10 \ln 2}{2 \ln 2} = 5 \ hours$.

Class 12 Chemistry Chemical Kinetics First Order reaction

Easy

What is the half-life of a first order reaction if the time required to decrease the concentration of the reactant from $1.0 \ M$ to $0.25 \ M$ is $10 \ hours$ (in $hours$)?

MHT CET 2021 All MHT CET

A
$12$
B
$4$
C
$5$
D
$10$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Chemistry Questions

Chapter

Chemical Kinetics

Subtopic

First Order reaction

Previous Year

MHT CET 2021 Paper All MHT CET years →

Identify True $(T)$ and False $(F)$ statements of the following for a first order reaction $R \rightarrow P$.
$(i) \ t_{1/2} \propto [R]_0^0$
$(ii) \ t_{1/2} = \frac{0.693}{k}$

Easy

View Solution

Time required for $90 \%$ completion of a first order reaction is $t$. What is the time required for $99.9 \%$ completion of reaction?

MediumMHT CET 2022

View Solution

For the $1^{st}$ order reaction,the half-life is $5 \ minutes$ when $[A] = 0.1 \ M$. If the concentration of $[A]$ becomes twice,then the half-life becomes:

Easy

View Solution

Find the rate constant of a first-order reaction in $sec^{-1}$ having a half-life of $2.5 \ hours$.

EasyMHT CET 2022

View Solution

For the first-order gaseous reaction $A_{(g)} \to 2B_{(g)} + C_{(g)}$,the expression for the rate constant $K$ in terms of initial pressure $P_0$ and total pressure $P_t$ at time $t$ is:

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

What is the half-life of a first order reaction if the time required to decrease the concentration of the reactant from $1.0 \ M$ to $0.25 \ M$ is $10 \ hours$ (in $hours$)?

Similar Questions

Identify True $(T)$ and False $(F)$ statements of the following for a first order reaction $R \rightarrow P$.$(i) \ t_{1/2} \propto [R]_0^0$$(ii) \ t_{1/2} = \frac{0.693}{k}$

Time required for $90 \%$ completion of a first order reaction is $t$. What is the time required for $99.9 \%$ completion of reaction?

For the $1^{st}$ order reaction,the half-life is $5 \ minutes$ when $[A] = 0.1 \ M$. If the concentration of $[A]$ becomes twice,then the half-life becomes:

Find the rate constant of a first-order reaction in $sec^{-1}$ having a half-life of $2.5 \ hours$.

For the first-order gaseous reaction $A_{(g)} \to 2B_{(g)} + C_{(g)}$,the expression for the rate constant $K$ in terms of initial pressure $P_0$ and total pressure $P_t$ at time $t$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Identify True $(T)$ and False $(F)$ statements of the following for a first order reaction $R \rightarrow P$.
$(i) \ t_{1/2} \propto [R]_0^0$
$(ii) \ t_{1/2} = \frac{0.693}{k}$