   # Experiments during a recent summer on a number of fireflies (small beetles, Lampyridaes photinus) showed that the average interval between flashes of individual insects was 16.3 s at 21.0°C and 13.0 sat 27.8°C. a. What is the apparent activation energy of the reaction that controls the flashing? b. What would be the average interval between flashes of an individual firefly at 30.0°C? c. Compare the observed intervals and the one you calculated in part b to the rule of thumb that the Celsius temperature is 54 minus twice the interval between flashes. ### 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 91AE
Textbook Problem
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## Experiments during a recent summer on a number of fireflies (small beetles, Lampyridaes photinus) showed that the average interval between flashes of individual insects was 16.3 s at 21.0°C and 13.0 sat 27.8°C.a. What is the apparent activation energy of the reaction that controls the flashing?b. What would be the average interval between flashes of an individual firefly at 30.0°C?c. Compare the observed intervals and the one you calculated in part b to the rule of thumb that the Celsius temperature is 54 minus twice the interval between flashes.

(a)

Interpretation Introduction

Interpretation: The average interval between flashes of individual insects at two different temperatures is given in an experiment. By using these values, the apparent activation energy of the reaction, average interval between flashes of a firefly at a given temperature is to be calculated and compare to the rule of thumb.

Concept introduction: A chemical reaction occurs inside the bodies of fireflies, which results in the flashing.  This reaction is called bioluminescence and follows first order kinetics.

The threshold energy needed to overcome to produce a chemical reaction is called activation energy.

The activation energy for bioluminescence reaction can be calculated by the following formula:

ln(k2k1)=EaR(1T11T2)

To determine: The activation energy of a chemical reaction that results in the flashing.

### Explanation of Solution

Given

The average interval between the flashes of individual insects at 21°C is 16.3 s .

The average interval between the flashing of individual insects at 27.8°C is 13.0 s .

Rate constant at temperature 21°C is,

k1=1  flash16.3 s=6.13×102 s1

Rate constant at temperature 27.8°C is,

k2=1  flash13.0 s=7.69×102 s1

The activation energy is calculated using the formula,

ln(k2k1)=EaR(1T11T2)

Where,

• k1 is rate constant at temperature T1 .
• k2 is rate constant at temperature T2 .
• R is universal gas constant (8.314J/Kmol) .
• Ea is the activation energy.

Substitute the values of k1,k2,T1,T2 , and R in the above equation.

ln(7.69×102 s16.13×10=2 s1)=Ea8.314J/Kmol(1(21+273)K1(27

(b)

Interpretation Introduction

Interpretation: The average interval between flashes of individual insects at two different temperatures is given in an experiment. By using these values, the apparent activation energy of the reaction, average interval between flashes of a firefly at a given temperature is to be calculated and compare to the rule of thumb.

Concept introduction: A chemical reaction occurs inside the bodies of fireflies, which results in the flashing.  This reaction is called bioluminescence and follows first order kinetics.

The threshold energy needed to overcome to produce a chemical reaction is called activation energy.

The activation energy for bioluminescence reaction can be calculated by the following formula:

ln(k2k1)=EaR(1T11T2)

To determine: The average time interval between flashes of an individual firefly at 30°C .

(c)

Interpretation Introduction

Interpretation: The average interval between flashes of individual insects at two different temperatures is given in an experiment. By using these values, the apparent activation energy of the reaction, average interval between flashes of a firefly at a given temperature is to be calculated and compare to the rule of thumb.

Concept introduction: A chemical reaction occurs inside the bodies of fireflies, which results in the flashing.  This reaction is called bioluminescence and follows first order kinetics.

The threshold energy needed to overcome to produce a chemical reaction is called activation energy.

The activation energy for bioluminescence reaction can be calculated by the following formula:

ln(k2k1)=EaR(1T11T2)

To determine: Comparison of observed and calculated interval and verify the value of temperature for each interval by using the rule of thumb.

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