Acetaldehyde decomposes at 750 K : CH3 CHO →CO+CH4^-The reaction is first order in acetaldehyde

Name: Problem 57, Chapter 8: Physical Chemistry for IIT JEE
Uploaded: 2022-02-01T22:18:24-08:00
Duration: 2 min 55 s
Channel: Nikhil Kumar
Description: Acetaldehyde decomposes at 750 K : CH3 CHO →CO+CH4^-The reaction is first order in acetaldehyde and the half life of the reaction is found to be 530 seconds. What is the rate constant for the reaction at this temperature? a. 3.7 ×10^-3 s^-1 b. 3.13 ×10^3 s^-1 c. 1.3 ×10^-3 s^-1 d. 2.3 ×10^-3 s^-1

step 1 Hi everyone in this equation we have given the half life of the equation and we have to find the

Question

Acetaldehyde decomposes at $750 \mathrm{~K}$ : $\mathrm{CH}_{3} \mathrm{CHO} \rightarrow \mathrm{CO}+\mathrm{CH}_{4^{-}}$The reaction is first order in acetaldehyde and the half life of the reaction is found to be 530 seconds. What is the rate constant for the reaction at this temperature? a. $3.7 \times 10^{-3} \mathrm{~s}^{-1}$ b. $3.13 \times 10^{3} \mathrm{~s}^{-1}$ c. $1.3 \times 10^{-3} \mathrm{~s}^{-1}$ d. $2.3 \times 10^{-3} \mathrm{~s}^{-1}$

   Acetaldehyde decomposes at $750 \mathrm{~K}$ :
$\mathrm{CH}_{3} \mathrm{CHO} \rightarrow \mathrm{CO}+\mathrm{CH}_{4^{-}}$The reaction is first order
in acetaldehyde and the half life of the reaction is found to be 530 seconds. What is the rate constant for the reaction at this temperature?
a. $3.7 \times 10^{-3} \mathrm{~s}^{-1}$
b. $3.13 \times 10^{3} \mathrm{~s}^{-1}$
c. $1.3 \times 10^{-3} \mathrm{~s}^{-1}$
d. $2.3 \times 10^{-3} \mathrm{~s}^{-1}$

Physical Chemistry for IIT JEE

Atul Singha 1st Edition

Chapter 8, Problem 57

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Solved by Expert Nikhil Kumar

02/01/2022

Step 1

Step 1: The integrated rate law for a first order reaction is given by: \[a = a_0 e^{-kt}\] where $a$ is the concentration of the reactant at any time $t$, $a_0$ is the initial concentration of the reactant, and $k$ is the rate constant. Show more…

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Acetaldehyde decomposes at $750 \mathrm{~K}$ : $\mathrm{CH}_{3} \mathrm{CHO} \rightarrow \mathrm{CO}+\mathrm{CH}_{4^{-}}$The reaction is first order in acetaldehyde and the half life of the reaction is found to be 530 seconds. What is the rate constant for the reaction at this temperature? a. $3.7 \times 10^{-3} \mathrm{~s}^{-1}$ b. $3.13 \times 10^{3} \mathrm{~s}^{-1}$ c. $1.3 \times 10^{-3} \mathrm{~s}^{-1}$ d. $2.3 \times 10^{-3} \mathrm{~s}^{-1}$

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Key Concepts

First Order Reaction Kinetics

In first order reactions, the rate of reaction is directly proportional to the concentration of the reactant. The mathematical expression is given by the exponential decay law, where the concentration decreases as a function of time according to the equation ln([A]?/[A]) = kt.

Half-Life

The half-life is defined as the time required for the concentration of a reactant to reduce to one-half of its initial value. For first order reactions, the half-life is constant and related to the rate constant by the formula t?/? = ln 2/k.

Rate Constant

The rate constant, denoted by k, is a fundamental parameter in chemical kinetics that determines the speed at which a reaction proceeds. In first order reactions, it can be calculated directly from the half-life using the relationship k = ln 2/t?/?, quantifying the reaction's dependency on time.

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