Answer to Question #108839 in Physical Chemistry for Mitul

Question #108839
The rate constant of a certain first order reaction is doubled when the temperature is increased from
27 °C to 37 °C. Calculate the energy of activation and Arrhenius factor for the reaction.
1
Expert's answer
2020-04-10T13:36:37-0400

As K=AeEaRTK=Ae^{-\frac{E_a}{RT}}

So, at T=27°C=300KT=27°C=300K

K=AeEa300RK=Ae^{-\frac{E_a}{300R}}

At T=37°C=310KT=37°C=310K

2K=AeEa310R2K=Ae^{-\frac{E_a}{310R}}

Dividing the two equations, we get

2=eEa300REa310R2=e^{\frac{E_a}{300R}-\frac{E_a}{310R}}

log2=Ea300REa310Rlog2=\frac{E_a}{300R}-\frac{E_a}{310R}

Ea=53582.8986JE_a=53582.8986J

Now, K=AeEa300R=4.6779×1010AK=Ae^{-\frac{E_a}{300R}}=4.6779\times10^{-10}A

Hence, Arrhenius factor A=0.2137×1010KA=0.2137\times10^{10}K


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