The flashing of fireflies is the result of a chemical reaction, and the rate of flashing can be described by the Arrhenius equation. A certain batch of fireflies were observed to flash at a rate of 17.0 times per minute at 25°C and at a rate of 5.0 times per minute at 15°C. Use these data to find the apparent activation energy for the reaction that causes the flies to flash.

-87.4 kJ/mol

Explanation:

We can rewrite Arrhenius' equation as:

ln (k₂/k₁) = - Ea/R * (1/T₂ - 1/T₁)

Where k₂ and k₁ are the rates of the reaction at temperatures T₂ and T₁, Ea is the activation energy and R is the universal gas constant.

For this problem:

k₂ = 5

k₁ = 17

T₂ = 15°C = 288.16 K

T₁ = 25°C = 298.16 K

R = 8.314 J/mol·K

We put the data in the equation and solve for Ea:

ln (5/17) = - Ea/8.314 J/mol·K * (1/288.16K - 1/298.16K)

-1.224 = - Ea/8.314 J/mol·K * 1.1639x10⁻⁴K⁻¹

Ea = - 87416.78 J/mol ≅ - 87.4 kJ/mol