We had a homework problem in which the Arrhenius equation was applied to the blinking of fireflies. Several other natural phenomena also obey that equation, including the temperature dependent chirping of crickets. A particular species, the snowy tree cricket, has been widely studied. These crickets chirp at a rate of 178 times per minute at 25.0°C, and the activation energy for the chirping process is 53.9 kJ/mol. What is the temperature if the crickets chirp at a rate of 126 times per minute?

Question

Physics

Francisco Horton

29 March, 07:54

We had a homework problem in which the Arrhenius equation was applied to the blinking of fireflies. Several other natural phenomena also obey that equation, including the temperature dependent chirping of crickets. A particular species, the snowy tree cricket, has been widely studied. These crickets chirp at a rate of 178 times per minute at 25.0°C, and the activation energy for the chirping process is 53.9 kJ/mol. What is the temperature if the crickets chirp at a rate of 126 times per minute?

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Answers (1)

Know the Answer?

Mckayla Tate · Answer 1

Temperature = 20.35 °C

Explanation:

Arrhenius equation is as follows:

k = A*exp (-Ea / (R*T)), where

k = rate of chirps

Ea = Activation Energy

R = Universal Gas Constant

T = Temperature (in Kelvin)

A = Constant

Given Data

Ea = 53.9*10^3 J/mol

R = 8.3145 J / (mol. K)

T = 273.15 + 25 K

k = 178 chirps per minutes

Calculation

Using the Arrhenius equation, we can find A,

A = 4.935x10^11

Now we can apply the same equation with the data below to find T at k=126,

k = A*exp (-Ea / (R*T))

Ea = 53.9*10^3

R = 8.3145

k = 126

T = 20.35 °C