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19 February, 22:13

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.

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  1. 20 February, 02:07
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    -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
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