Respuesta :
Answer: The rate constant for the reaction at 65°C is [tex]0.350s^{-1}[/tex]
Explanation:
To calculate rate constant at 65°C of the reaction, we use Arrhenius equation, which is:
[tex]\ln(\frac{K_{65^oC}}{K_{40^oC}})=\frac{E_a}{R}[\frac{1}{T_1}-\frac{1}{T_2}][/tex]
where,
[tex]K_{65^oC}[/tex] = equilibrium constant at 65°C = ?
[tex]K_{40^oC}[/tex] = equilibrium constant at 40°C = [tex]5.45\times 10^{-2}s^{-1}[/tex]
[tex]E_a[/tex] = Activation energy of the reaction = 65.5 kJ/mol = 65500 J/mol (Conversion factor: 1 kJ = 1000 J)
R = Gas constant = 8.314 J/mol K
[tex]T_1[/tex] = initial temperature = [tex]40^oC=[40+273]K=313K[/tex]
[tex]T_2[/tex] = final temperature = [tex]65^oC=[65+273]K=338K[/tex]
Putting values in above equation, we get:
[tex]\ln(\frac{K_{65^oC}}{5.45\times 10^{-2}})=\frac{65500J/mol}{8.314J/mol.K}[\frac{1}{313}-\frac{1}{338}]\\\\K_{65^oC}=0.350s^{-1}[/tex]
Hence, the rate constant for the reaction at 65°C is [tex]0.350s^{-1}[/tex]
