   # The decomposition of ethanol (C 2 H 5 OH) on an alumina (Al 2 O 3 ) surface C 2 H 5 OH ( g ) → C 2 H 4 ( g ) + H 2 O ( g ) was studied at 600 K. Concentration versus time data were collected for this reaction, and a plot of [A] versus time resulted in a straight line with a slope of −4.00 × 10 −5 mol/L · s. a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. If the initial concentration of C 2 H 5 OH was 1.25 × 10 −2 M , calculate the half-life for this reaction. c. How much time is required for all the 1.25 × 10 −2 M C 2 H 5 OH to decompose? ### 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 41E
Textbook Problem
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## The decomposition of ethanol (C2H5OH) on an alumina (Al2O3) surface C 2 H 5 OH ( g ) → C 2 H 4 ( g ) + H 2 O ( g ) was studied at 600 K. Concentration versus time data were collected for this reaction, and a plot of [A] versus time resulted in a straight line with a slope of −4.00 × 10−5 mol/L · s.a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction.b. If the initial concentration of C2H5OH was 1.25 × 10−2 M, calculate the half-life for this reaction.c. How much time is required for all the 1.25 × 10−2 M C2H5OH to decompose?

(a)

Interpretation Introduction

Interpretation: The general reaction is given. The temperature and slope value of [A] versus time is given. Based on these data answers are to be given.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

To determine: The rate law, the integrated rate law and the value of rate constant for the given reaction.

### Explanation of Solution

Given

The value of slope is 4.00×105 .

The given reaction for the decomposition of ethanol (C2H5OH) on alumina surface is,

C2H5OH(g)C2H4(g)+H2O(g)

The rate law gives the relation between reaction rate and concentration of reactants. The reactant is C2H5OH . Hence, the rate law is represented as,

Rate=k[C2H5OH]

Where,

• k is rate constant.
• [C2H5OH] is concentration of reactant.

Given

The given reaction for the decomposition of ethanol (C2H5OH) on alumina surface is,

C2H5OH(g)C2H4(g)+H2O(g)

The rate law in integral form is known as integrated rate law

(b)

Interpretation Introduction

Interpretation: The general reaction is given. The temperature and slope value of [A] versus time is given. Based on these data answers are to be given.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

(c)

Interpretation Introduction

Interpretation: The general reaction is given. The temperature and slope value of [A] versus time is given. Based on these data answers are to be given.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

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