   # The compound Xe(CF 3 ) 2 decomposes in a first-order reaction to elemental Xe with a half-life of 30. minutes. If you place 7.50 mg of Xe(CF 3 ) 2 in a flask, how long must you wait until only 0.25 mg of Xe(CF 3 ) 2 remains? ### 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 28PS
Textbook Problem
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## The compound Xe(CF3)2 decomposes in a first-order reaction to elemental Xe with a half-life of 30. minutes. If you place 7.50 mg of Xe(CF3)2 in a flask, how long must you wait until only 0.25 mg of Xe(CF3)2 remains?

Interpretation Introduction

Interpretation: The time taken for the amount of Xe(CF3)2 has to be givem

Concept Introduction:

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=-Δ[A]Δt=k[A]

The integrated rate law equation can be given as,

ln[A]t[A]o=-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 time taken for the amount of SO2Cl2 is calculated as,

Reactionrate = k [Xe(CF3)2]1.Given:t1/2=30 mins;t1/2=0.693kk=0.69330 mins=0.0231min1[Xe(CF3)2]0=7.50mg[Xe(CF3)2]t=0.25mgTherefore,First order rate law,ln[Xe(CF3)2]t=-kt + ln[Xe(CF3)2]0ln[0

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