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Rate constant:
The rate constant at 65°C is [tex]k_{2} = 3.069 x 10^{-6}[/tex]
What is the Arrhenius equation?
Sometimes the Arrhenius equation is written as [tex]k = Ae^{-E/RT}[/tex], where k is the rate of the chemical reaction, A is a constant that varies depending on the chemicals involved, E is the activation energy, and R is the universal gas constant, and T is the temperature.
According to the exponential part in the Arrhenius equation, a reaction's rate constant rises exponentially as the activation energy falls. The rate also grows exponentially because the rate of a reaction is precisely proportional to its rate constant.
Calculation:
According to the Arrhenius equation for variable temperature:
[tex]ln(\frac{k2}{k1}) = - \frac{Ea}{R} (\frac{1}{T2} - \frac{1}{T1})[/tex]
The temperatures are given to be computed in kelvins and then both temperature and activation energy will be put in the above equation, we get,
[tex]ln ( \frac{k_{2}}{3.54 x 10^{-5}} ) = -\frac{89000J/mol}{8.314J (mol* K)} ( \frac{1}{338.15K} - \frac{1}{318.15K} \\ln ( \frac{k_{2}}{3.54 x 10^{-5}} ) = 2.1602\\k_{2} = 3.54 x 10^{-5} *exp(2.1602)\\k_{2} = 3.54 x 10^{-5} *8.67\\ k_{2} = 30.69 x 10^{-5}\\k_{2} = 3.069 x 10^{-6}[/tex]
Learn more about rate constant here,
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