   # Experiments have shown that the average frequency of chirping by a snowy tree cricket (Oecanthus fultoni) depends on temperature as shown in the table. Chirping Rate (per min) Temperature (°C) 178 25.0 126 20.3 100. 17.3 What is the apparent activation energy of the process that controls the chirping? What is the rate of chirping expected at a temperature of 7.5°C? ### 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 101CWP
Textbook Problem
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## Experiments have shown that the average frequency of chirping by a snowy tree cricket (Oecanthus fultoni) depends on temperature as shown in the table. Chirping Rate (per min) Temperature (°C) 178 25.0 126 20.3 100. 17.3 What is the apparent activation energy of the process that controls the chirping? What is the rate of chirping expected at a temperature of 7.5°C?

Interpretation Introduction

Interpretation: For the givenexperiment the apparent activation energy of the process that controls the chirping is to be calculated. The expected rate of the chirping at a temperature 7.5°C is to be calculated.

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

Activation energy is the minimum amount of energy required to activate the reaction.

Rate of a reaction tells the speed of the reaction per unit time.

To determine: The amount of time required for the reaction to reach 22.9% completion.

### Explanation of Solution

Explanation

Given

The chirping rate given in table is as,

Chirpingrate(m-1)Temperature(°C)17825.012620.310017.3

In the given experiment the average frequency of chirping by snowy tree cricket is given which concludes as rate constant with respect to the given temperatures.

The activation energy of the process that controls chirping is given by the Arrhenius equation,

k=AeEaRT

Where,

• k is the rate of chirping or chirping constant.
• A is the pre-exponential function.
• Ea is the activation energy.
• R is the universal gas constant.
• T is the temperature in Kelvin.

The above given Arrhenius equation is written as,

k=AeEaRTlnk=lnA+(EaRT)lnk=lnA+(EaR)(1T)lnk=(EaR)(1T)+lnA

The above expression resembles with the straight line equation that is,

y=mx+c

Where,

• m is the slope.
• y is the vertical axis.
• x is the horizontal axis.
• c is the intercept on the y -axis.

Compare the straight line equation with Arrhenius equation it is clear that the Arrhenius reaction is a straight line plot of lnk Vs 1T . Therefore the slope of the line is calculated as,

Slope=ΔlnkΔ(1/T) (1)

Slope is also represented as,

Slope=(EaR) (2)

To calculate the slope the given table is extended as,

Chirpingratek(m-1)lnkTemperature(°C)tempuratureinKelvin1/T1785.1825.02980.003351264.8320.3293.30.003401004.6017.3290.30.00344

Substitute the values in equation (1).

Slope=ΔlnkΔ(1/T)=4.835.180.003400.00335=(0.35)0.00005=7.0×103K

Substitute this value in equation (2)

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