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11 November, 22:57

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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  1. 12 November, 02:42
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    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
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