   # When healed lo a high temperature, cyclobutane, C 4 H 8 decomposes to ethylene: C 4 H 8 (g) → 2 C 2 H 4 (g) The activation energy, E a , for this reaction is 260 kJ/mol. At 800 K, the rate constant k = 0.0315 s −1 . Determine the value of k at 850 K. ### 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 39PS
Textbook Problem
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## When healed lo a high temperature, cyclobutane, C4H8 decomposes to ethylene:C4H8(g) → 2 C2H4(g)The activation energy, Ea, for this reaction is 260 kJ/mol. At 800 K, the rate constant k = 0.0315 s−1. Determine the value of k at 850 K.

Interpretation Introduction

Interpretation:

For the given reaction under given conditions, activation energy and the rate constants at particular temperature, the rate constant for temperature of 850K should be determined.

Concept introduction:

In order to establish the plausibility of a mechanism, one must compare the rate law of the rate determining step to the experimentally determined rate law.

Rate determining step: In a chemical reaction the rate determining step is the slowest step in which the rate of the reaction depends on the rate of that slowest step.

Rate law: It is generally the rate equation that consists of the reaction rate with the concentration or the pressures of the reactants and constant parameters.

Activation energy: It is defined as the minimum energy required by the reacting species in order to undergo chemical reaction.

Intermediate species: It is the species formed during the middle of the chemical reaction between the reactant and the desired product.

Arrhenius equation:

• Arrhenius equation is a formula that represents the temperature dependence of reaction rates
• The Arrhenius equation has to be represented as follows

k=AeEa/RTlnk=lnAeEa/RTlnk=(EaR)(1T)+lnA

• Ea represents the activation energy and it’s unit is kJ/mol
• R represents the universal gas constant and it has the value of 8.314 J/K.mol
• T represents the absolute temperature
• A represents the frequency factor or collision frequency
• e represents the base of natural logarithm
•  Arrhenius equation equation was proposed by Svante Arrhenius in 1889.

### Explanation of Solution

In order to find the rate constant at given temperature we need to use the following expression which relates the rate constant, activation energy and the temperature.

ln(K1K2)=EaR(1T2-1T1)T1=850T2=800K1=KK2=0.0315s-1 Ea=260kJ/mol

With known rate constant, temperature and the activation energy the rate constant for the other given temperature is calculated as follows,

ln(K0.0315s-1)=260×103J/mol8

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