Answer:3480s⁻¹
Explanation:We can solve the following problem using the Arrhenius equation.
Arrhenius equation is given by:
[tex]K=Aexp[-Ea/RT][/tex]
A=Pre-exponential factor or frequency factor
Ea=Activation energy
R=Ideal gas constant
T=Temperature
K=Rate constant
From the Arrhenius equation we can see that the rate constant K is related with the activation energy and frequency factor.
In the question we are given with the following data:
Ea=42KJ/mol=42x 1000 J/mol
A=8.0×10¹ per second
T=298K
R=8.314J/K mol
when we substitute these given values in Arrhenius equation
[tex]K=A{exp[-Ea \div RT]}\\K=8\ \times10^{10} s^{-1}{exp[-42000\div 8.314\times298]}\\K=8\ \times10^{10} s^{-1}{exp[-16.95]}\\K=4.35\times10^{^{-8}}\times8.0\times10^{^{10}}s^{-1}\\K=34.8\times10^{2}s^{-1}\\[/tex]
K=3480s⁻¹
The value of rate constant obtained is 3480s⁻¹.
