Answer: 365 K
Explanation:
According to the Arrhenius equation,
![K=A\times e^{\frac{-Ea}{RT}}](https://tex.z-dn.net/?f=K%3DA%5Ctimes%20e%5E%7B%5Cfrac%7B-Ea%7D%7BRT%7D%7D)
or,
![\log (\frac{K_2}{K_1})=\frac{Ea}{2.303\times R}[\frac{1}{T_1}-\frac{1}{T_2}]](https://tex.z-dn.net/?f=%5Clog%20%28%5Cfrac%7BK_2%7D%7BK_1%7D%29%3D%5Cfrac%7BEa%7D%7B2.303%5Ctimes%20R%7D%5B%5Cfrac%7B1%7D%7BT_1%7D-%5Cfrac%7B1%7D%7BT_2%7D%5D)
where,
= rate constant at
= 1.00
= rate constant at
= 5.00
= activation energy for the reaction = 28.90 kJ/mol= 28900 j/mol
R = gas constant = 8.314 J/mole.K
= initial temperature = 313 K
= final temperature = ?
Now put all the given values in this formula, we get
![\log (\frac{5.00}{1.00})=\frac{28900}{2.303\times 8.314J/mole.K}[\frac{1}{313K}-\frac{1}{T_2K}]](https://tex.z-dn.net/?f=%5Clog%20%28%5Cfrac%7B5.00%7D%7B1.00%7D%29%3D%5Cfrac%7B28900%7D%7B2.303%5Ctimes%208.314J%2Fmole.K%7D%5B%5Cfrac%7B1%7D%7B313K%7D-%5Cfrac%7B1%7D%7BT_2K%7D%5D)
![0.69=\frac{28900}{2.303\times 8.314J/mole.K}[\frac{1}{313K}-\frac{1}{T_2K}]](https://tex.z-dn.net/?f=0.69%3D%5Cfrac%7B28900%7D%7B2.303%5Ctimes%208.314J%2Fmole.K%7D%5B%5Cfrac%7B1%7D%7B313K%7D-%5Cfrac%7B1%7D%7BT_2K%7D%5D)
![T_2=365K](https://tex.z-dn.net/?f=T_2%3D365K)
Therefore, 365 K is required to increase the reaction rate by 5.00 times.
Answer:
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