개똥벌레. Lampyridaes photinus 21.0℃ 16.3 s 27.8℃ 13.0 s

개똥벌레. Lampyridaes photinus 21.0℃ 16.3 s 27.8℃ 13.0 s

 

 

Experiments during a recent summer on a number of fireflies (small beetles, Lampyridaes photinus) showed that the average interval between flashes of individual insects was 16.3 s at 21.0°C and 13.0 s at 27.8°C.

 

a. What is the apparent activation energy of the reaction that controls the flashing?

b. What would be the average interval between flashes of an individual firefly at 30.0°C?

c. Compare the observed intervals and the one you calculated in part b to the rule of thumb that the Celsius temperature is 54 minus twice the interval between flashes.

 

섭씨 온도 = 54 – 2(발광 간격)

 

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“속도 = 변위 / 시간” 이고,

발광 간격을 변위라 보면,

 

속도 = 발광 간격 / 시간

( 간단히, 속도 = 발광 / 시간 )

 

속도와 속도상수는 비례 관계이므로,

k = 발광 / 시간

 

 

 

 

a.

 

T_1 = 21.0℃ + 273.15 = 294.15 K 에서,

1 발광 / 16.3 s = k_1

---> k_1 = 0.0613 /s

 

 

 

T_2 = 27.8℃ + 273.15 = 300.95 K 에서,

1 발광 / 13.0 s = k_2

---> k_2 = 0.0769 /s

 

 

 

아레니우스 식

ln(k_2 / k_1) = Ea/R (1/T_1 – 1/T_2)

( R = 8.314 J/K•mol )

( 참고 https://ywpop.tistory.com/7288 )

 

Ea = [ln((k_2) / (k_1)) × 8.314] / [(1/T_1) - (1/T_2)]

= [ln((0.0769) / (0.0613)) × 8.314] / [(1/294.15) - (1/300.95)]

= 24539 J/mol

= 24.5 kJ/mol

 

 

 

 

b.

 

T_3 = 30.0℃ + 273.15 = 303.15 K

 

 

 

ln(k_3 / k_1) = Ea/R (1/T_1 – 1/T_3)

 

ln(k_3 / 0.0613) = (24539/8.314) [(1/294.15) - (1/303.15)]

 

k_3 = e^0.2978948 × 0.0613

= 0.0826 /s

 

 

 

1 / 0.0826 = 12.1 s

 

 

 

 

c.

 

섭씨 온도 = 54 – 2(발광 간격)

 

발광 간격 = (54 – 섭씨 온도) / 2

= (54 – 30.0) / 2

= 12.0 s

---> 0.1 s 차이남.

 

 

 

 

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