The chirping of tree crickets has sometimes been used to predict temperatures. at 25.0 °c, the rate was 179 chirps/min. at 21.7 °c, it was 142 chirps/min. what is the ea of the process?

The relation of the rate, K, the activation energy, Ea, and the absolute temperature, T, is given by Arrhenius equation.

Arrhenius equation is:

K(T) = A* e^( -Ea / RT)

Then A is a constant for the specific reaction and R is the universal constant of gases.

Then you can use two set of values, at different T, to find Ea

1) K = 179 chirp/min; T = 25 + 273 = 298 K

2) K = 142 chirp/min; T = 21.7 + 273 = 294.7 K

=>

179 = A* [ e ^(-Ea / R*298) ]

142 = A* [e^(-Ea / R* 294.7) ]

Divide thw two equations:

[179 / 142 ] = e ^ [-(Ea/ R) * ( 1 /298 - 1 / 294.7) ]

=> -Ea / R = Ln [179/142] / (1 / 298 - 1/294.7)

=> - Ea / R = -6162.31 K

The value of the Universal Constant of gases is R = 8.31 J/K*mol

=> Ea = (6162.31 K )* (8.31 J/K*mol) = 51208.81 J/mol

Answer: 51209 J/mol