As K=Ae−EaRTK=Ae^{-\frac{E_a}{RT}}K=Ae−RTEa
So, at T=27°C=300KT=27°C=300KT=27°C=300K
K=Ae−Ea300RK=Ae^{-\frac{E_a}{300R}}K=Ae−300REa
At T=37°C=310KT=37°C=310KT=37°C=310K
2K=Ae−Ea310R2K=Ae^{-\frac{E_a}{310R}}2K=Ae−310REa
Dividing the two equations, we get
2=eEa300R−Ea310R2=e^{\frac{E_a}{300R}-\frac{E_a}{310R}}2=e300REa−310REa
log2=Ea300R−Ea310Rlog2=\frac{E_a}{300R}-\frac{E_a}{310R}log2=300REa−310REa
Ea=53582.8986JE_a=53582.8986JEa=53582.8986J
Now, K=Ae−Ea300R=4.6779×10−10AK=Ae^{-\frac{E_a}{300R}}=4.6779\times10^{-10}AK=Ae−300REa=4.6779×10−10A
Hence, Arrhenius factor A=0.2137×1010KA=0.2137\times10^{10}KA=0.2137×1010K
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