   Chapter 14, Problem 22PS

Chapter
Section
Textbook Problem

The dimerization of butadiene, C4H6, to form 1,5-cyclooctadiene is a second-order process that occurs when the diene is heated. In an experiment, a sample of 0.0087 mol of C4H6 was heated in a 1.0-L flask. After 600. seconds, 21% of the butadiene had dimerized. Calculate the rate constant for this reaction.

Interpretation Introduction

Interpretation: The rate constant for the reaction 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 second order reactions:

Taking in the example of following reaction,

aAproducts

And the reaction follows second order rate law,

Then the relationship between the concentration of A and time can be mathematically expressed as,

1[A]t=kt+1[A]0

The above expression is called as integrated rate for second order reactions.

Explanation

The rate constant for the reaction is calculated as,

-Δ[R]Δt = k[R]2,The realtion can be transformed into,1[R]t - 1[R]0 = ktGiven:Initialconcentration,[butadiene]0 = 0.0087mol1L = 0.0087 mol/LInitially, 100% of buatadiene is present and during process, 21% of butadiene had dimerized.So,100%-21% =79%ofbutadieneis presentas[butadiene]t.79%of butadiene=79100×[butadiene]079 100×0

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