   # The rate equation for the decomposition of N 2 O 5 (giving NO 2 and O 2 ) is Rate = k [N 2 O 5 ]. The value of k is 6.7 × 10 −5 s −1 for the reaction at a particular temperature. (a) Calculate the half-life of N 2 O 5 . (b) How long does it take for the N 2 O 5 concentration to drop to one tenth of its original value? ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 14, Problem 25PS
Textbook Problem
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## The rate equation for the decomposition of N2O5 (giving NO2 and O2) is Rate = k[N2O5]. The value of k is 6.7 × 10−5 s−1 for the reaction at a particular temperature. (a) Calculate the half-life of N2O5. (b) How long does it take for the N2O5 concentration to drop to one tenth of its original value?

(a)

Interpretation Introduction

Interpretation: The half-life of N2O5 has to be calculated

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time.  The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of mol/(L.s).

Integrated rate law for first order reaction:

Consider A as substance, that gives the product based on the equation,

aAproducts

Where a= stoichiometric co-efficient of reactant A.

Consider the reaction has first-order rate law,

Rate=-ΔAΔt=kA

The integrated rate law equation can be given as,

lnAtAo=-kt

The above expression is called integrated rate law for first order reaction.

Half life for first order reactions:

The half life for the first order reaction is constant and it is independent of the reactant concentration.

Half life period of first order reaction can be calculated using the equation,

t1/2=0.693k

### Explanation of Solution

The half-life is calculated as,

Reactionrate = k N2O51Given:k=6.7×105s1Therefore,t1/20.693k     = 0

(b)

Interpretation Introduction

Interpretation:

The time duration taken for N2O5 to drop to one tenth of its original value has to be given.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time.  The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of mol/(L.s).

Integrated rate law for first order reaction:

Consider A as substance, that gives the product based on the equation,

aAproducts

Where a= stoichiometric co-efficient of reactant A.

Consider the reaction has first-order rate law,

Rate=-ΔAΔt=kA

The integrated rate law equation can be given as,

lnAtAo=-kt

The above expression is called integrated rate law for first order reaction.

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