Respuesta :
Answer: 365 K
Explanation:
According to the Arrhenius equation,
[tex]K=A\times e^{\frac{-Ea}{RT}}[/tex]
or,
[tex]\log (\frac{K_2}{K_1})=\frac{Ea}{2.303\times R}[\frac{1}{T_1}-\frac{1}{T_2}][/tex]
where,
[tex]K_1[/tex] = rate constant at [tex]T_1[/tex] = 1.00
[tex]K_2[/tex] = rate constant at [tex]T_2[/tex] = 5.00
[tex]Ea[/tex] = activation energy for the reaction = 28.90 kJ/mol= 28900 j/mol
R = gas constant = 8.314 J/mole.K
[tex]T_1[/tex] = initial temperature = 313 K
[tex]T_2[/tex] = final temperature = ?
Now put all the given values in this formula, we get
[tex]\log (\frac{5.00}{1.00})=\frac{28900}{2.303\times 8.314J/mole.K}[\frac{1}{313K}-\frac{1}{T_2K}][/tex]
[tex]0.69=\frac{28900}{2.303\times 8.314J/mole.K}[\frac{1}{313K}-\frac{1}{T_2K}][/tex]
[tex]T_2=365K[/tex]
Therefore, 365 K is required to increase the reaction rate by 5.00 times.
