The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy of 24 kj/mol . If the rate constant of this reaction is 1.3 x 10^5 M^-1s^-1 at 163 degrees celsius, what will the rate constant be at 83.0 degrees celsius?
Round your answer to 2 significant digits.
To find the rate constant at 83.0 degrees Celsius, we can use the Arrhenius equation:
k2 = Ae^(-Ea/RT2)
where:
k2 is the rate constant at temperature T2
A is the pre-exponential factor
Ea is the activation energy
R is the gas constant (8.314 J/(mol K))
T2 is the new temperature in Kelvin
First, let's convert the activation energy from kJ/mol to J/mol:
Ea = 24 kJ/mol * (1000 J/1 kJ) = 24000 J/mol
Next, let's convert the given temperatures to Kelvin:
T1 = 163 degrees Celsius + 273.15 = 436.15 K
T2 = 83.0 degrees Celsius + 273.15 = 356.15 K
Now we can calculate the new rate constant, k2:
k2 = (1.3 x 10^5 M^-1s^-1) * e^(-24000 J/mol / (8.314 J/(mol K) * 356.15 K))
k2 ≈ (1.3 x 10^5) * e^(-7.168)
k2 ≈ (1.3 x 10^5) * 0.000852
k2 ≈ 110.76 M^-1s^-1 ≈ 1.1 x 10^2 M^-1s^-1
Therefore, the rate constant at 83.0 degrees Celsius is approximately 1.1 x 10^2 M^-1s^-1.