   # The decomposition of iodoethane in the gas phase proceeds according to the following equation: C 2 H 5 I ( g ) → C 2 H 4 ( g ) + HI ( g ) At 660. K, k = 7.2 ×10 −4 s −l ; at 720. K, k = 1.7 × 10 −2 s −l . What is the value of the rate constant for this first-order decomposition at 325°C? If the initial pressure of iodoethane is 894 torr at 245°C, what is the pressure of iodoethane after three half-lives? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 11, Problem 115IP
Textbook Problem
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## The decomposition of iodoethane in the gas phase proceeds according to the following equation: C 2 H 5 I ( g ) → C 2 H 4 ( g ) + HI ( g ) At 660. K, k = 7.2 ×10−4 s−l; at 720. K, k = 1.7 × 10−2 s−l. What is the value of the rate constant for this first-order decomposition at 325°C? If the initial pressure of iodoethane is 894 torr at 245°C, what is the pressure of iodoethane after three half-lives?

Interpretation Introduction

Interpretation: The value of the rate constant for the given first order decomposition of iodoethane in the gas phase reaction at 325°C is to be stated. The value of the pressure of iodoethane after three half-lives is to be calculated corresponds to the fact that if the initial pressure of iodoethane is 894torr at 245°C.

Concept introduction: Rate constant is a proportionalitycoefficient that relates the rate of any chemical reaction at a specific temperature to the concentration of the reactant or the concentration of the product.

Order of the reaction is an experimental value which is expressed by some power of concentration terms in the chemical equation.

To determine: The value of rate constant for the given first order decomposition reaction of iodoethane; the pressure of the iodoethane correspond to the fact that if the initial pressure of iodoethane is 894torr at 245°C.

### Explanation of Solution

Explanation

The value of the rate constant for the first order decomposition of iodoethaneis 1.38×10-5s-1_.

(Given)

The value of the rate constant for the first order decomposition of iodoethane is 1.38×10-5s-1_.

(Given)

Equation for the decomposition of iodoethane is,

C2H5I(g)C2H4(g)+HI(g)

The value of rate constants at two different temperatures is given as,

At 660K, the value of k=7.2×104s1.

At 720K, the value of k=1.7×102s1.

The value of rate constant is determined with the help of activation energy.

The value of activation energy at 325°C is determined by the formula,

lnk2k1=EaR(1T11T2)

Where,

• The constants k1,k2 are the rate constants and T1,T2 are the temperatures.
• The term Ea is known as activation energy.
• The term R is known as gas constant with the universal value of 8.314J/mol.
• The temperature 660K is considered as T1 so, its rate constant is termed as k1.
• The temperature 720K is considered as T2 so, its rate constant is termed as k2.

Substitute the values of k1,k2,T1,T2 to calculate the activation energy.

lnk2k1=EaR(1T11T2)ln(1.7×102s-17.2×104s1)=Ea8.314J/mol(1660K1720K)ln(.236×10+2)=Ea×1.51mol/JEa=2.09×105J/mol

The calculated value of activation energy Ea=2.09×105J/mol.

The value of temperature in degree Celsius is supposed to be x.

The relationship between the degree Celsius and the Kelvin is given by the formula,

x°C=(x+273)K.

Where,

• x is a temperature in degree Celsius.

Substitute the value of x to calculate the temperature in Kelvin.

x°C=(x+273)K325°C=(325+273)K=598K

Now the value of rate constant at temperature 598K is calculated by the formula,

lnk2k1=EaR(1T11T2)

The value of rate constant at temperature 598K is supposed to be k,

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