A heterogeneous chemical reaction decomposes following the Arrhenius Rate Law. T

Question

A heterogeneous chemical reaction decomposes following the Arrhenius Rate Law. The reaction rate constants are as follows. Calculate the activation energy of the reaction. Since this reaction is heterogeneous, based on the activation what is the likely rate controlling step? On typical summer days, crickets nibble, jump, and chirp now and then. But at night, when great numbers of crickets congregate, chirping seems to become a very serious business. The chirping rate becomes quite rythmic and regular. In 1897 Dolbear reported that not only was it regular cricket chirping but that the chirping rate was readily determined by the ambient temperature given as; (number of chirps in 15 seconds) + 40 = (temperature, degree F) If we assume that the chirping of crickets is a direct measure of their metabolic rate, find the activation energy, in calories, of the crickets in the temperature range of 60 to 80 degree F.

Explanation / Answer

Solution :-

Temperature T1 = 60 F = 288.7 K

Temperature T2 = 80 F = 299.8 K

Number of chirps in 15 sec + 40 = temperature in F

Therefore

At the 60 F number of chirps = 60-40 = 20

At 80 F number of chirps = 80 – 40 = 40

Now lets use this to calculate the activation energy

ln [K2/K1] = Ea/R [(1/T1) – (1/T2)]

lets put the values in the formula

ln[40/20] = Ea/8.314 J per mol K [(1/288.7)-(1/299.8)]

0.693 = Ea/ 8.314 J per mol K * 0.0001282 K

0.693 *8.314 J per mol K / 0.0001282 K = Ea

44942 J = Ea

Lets convert it to cal

44942 J * 1 cal / 4.0184 J = 11236 cal

So the activation energy for the metabolism is 11236 cal

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