   # The dimerization of butadiene 2C 4 H 6 ( g ) → C 8 H 12 ( g ) was studied at 500. K, and the following data were obtained: Time(s) [C 4 H 6 ](mol/L) 195 1.6 × 10 −2 604 1.5 × 10 −2 1246 1.3 × 10 −2 2180 1.1 × 10 −2 6210 0.68 × 10 −2 Assuming that Rate = - Δ [ C 4 H 6 ] Δ t determine the form of the rate law, the integrated rate law, and the value of the rate constant for this reaction. ### 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 43E
Textbook Problem
94 views

## The dimerization of butadiene 2C 4 H 6 ( g ) → C 8 H 12 ( g ) was studied at 500. K, and the following data were obtained: Time(s) [C4H6](mol/L) 195 1.6 × 10−2 604 1.5 × 10−2 1246 1.3 × 10−2 2180 1.1 × 10−2 6210 0.68 × 10−2 Assuming that Rate = - Δ [ C 4 H 6 ] Δ t determine the form of the rate law, the integrated rate law, and the value of the rate constant for this reaction.

Interpretation Introduction

Interpretation: The reaction of dimerization of butadiene is given. The table of concentration of butadiene (C4H6) as a function of time is given. The rate law, the integrated rate law and the value of rate constant is to be calculated based on these data.

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.

### Explanation of Solution

The given reaction is,

2C4H6(g)C8H12(g)

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

Rate=k[C4H6]a (1)

Where,

• k is rate constant.
• [C4H6] is concentration of reactant.
• a is reaction order.

The table of concentration of butadiene as a function of time is,

 Time (s) [C4H6] (mol/L) 195 1.6×10−2 604 1.5×10−2 1246 1.3×10−2 2180 1.1×10−2 6210 0.68×10−2

The order of the given reaction can be determined by using following parameters,

• For first order reaction, ln[C4H6]vstime graph is straight line.
• For second order reaction, 1[C4H6]vstime graph is straight line.
• For zero order reaction, [C4H6]vstime graph is straight line.

The value of ln[C4H6] and 1[C4H6] for different values of time is shown in table,

 Time (s) ln[C4H6] 1[C4H6] (L/mol) 195 −4.14 62.5 604 −4.20 66.6 1246 −4.34 76.9 2180 −4.51 90.90 6210 −4.99 147.05

The graph is drawn for ln[C4H6]vstime is,

Figure 1

The above plot shows curved region. Hence, the given reaction is not first order.

The graph is drawn for 1[C4H6]vstime is,

Figure 2

Theabove plotis straight line with positiveslope

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