   Chapter 12, Problem 54E

Chapter
Section
Textbook Problem

# The rate law for the reaction 2 NOBr ( g )   →   2 NO ( g )   +   Br 2 ( g ) at some temperature is Rate   =   − Δ [ NOBr ] Δ t   =   k [ NOBr ] 2 a. If the half-life for this reaction is 2.00 s when [NOBr]0 = 0.900 M, calculate the value of k for this reaction.b. How much time is required for the concentration of NOBr to decrease to 0.100 M?

(a)

Interpretation Introduction

Interpretation: The rate law reaction of decomposition of NOBr and half-life is given. The rate constant for the given value of half life is to be calculated. Also, the time required for the given change in the concentration of NOBr is to be calculated.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

To determine: The rate constant for 2.00s half life.

Explanation

The half-life is 2.00s .

The given reaction is,

2NOBr(g)2NO(g)+Br2(g)

The formula of rate of reaction is,

Rate=Δ[NOBr]Δt=k[NOBr]2

Where,

• k is rate constant.
• Δ[NOBr] is change in concentration of [NOBr] .
• Δt is change in time.

The given equation belongs to second order reaction. Hence,

[NOBr]0=0.900M[NOBr]=0.1M

Where,

• [NOBr]0 is initial concentration.
• [NOBr] is concentration at time t .

Formula:

The half-life is calculated using the formula,

t12=1k[A]0

Where,

• t12 is half life

(b)

Interpretation Introduction

Interpretation: The rate law reaction of decomposition of NOBr and half-life is given. The rate constant for the given value of half life is to be calculated. Also, the time required for the given change in the concentration of NOBr is to be calculated.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

To determine: The time taken by 0.900M NOBr to decrease to a concentration to 0.100M .

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