The rate constant for the rxn of hydrogen reacting with iodine to form hydrogen iodide is 2.7 X 10^-4 L/mol*s at 600. K and 3.5 X 10^-3 L/mol*s at 650. K.
a) determine the activation energy for this reaction.
b) determine the rate constant at 700. K
a. ln(k2/k1) = Ea(1/T1 - 1/T2)/RT
b. After you have Ea, then use the same formula to determine the new k.
To determine the activation energy for this reaction, we can use the Arrhenius equation:
k = Ae^(-Ea/RT)
Where:
- k is the rate constant
- A is the pre-exponential factor (a constant)
- Ea is the activation energy
- R is the gas constant (8.314 J/mol*K)
- T is the temperature in Kelvin
We have two sets of conditions (600 K and 650 K) with their respective rate constants. By rearranging the equation, we can calculate the activation energy:
For 600 K:
k1 = 2.7 x 10^(-4) L/mol*s
T1 = 600 K
For 650 K:
k2 = 3.5 x 10^(-3) L/mol*s
T2 = 650 K
Taking the ratio of the rate constants:
k2/k1 = e^(-Ea/R) * (1/T2 - 1/T1)
Substituting the known values:
(3.5 x 10^(-3))/(2.7 x 10^(-4)) = e^(-Ea/(8.314)) * (1/650 - 1/600)
Now we can solve for Ea:
Ea = -8.314 * ln((3.5 x 10^(-3))/(2.7 x 10^(-4))) / (1/650 - 1/600)
Calculating this gives us the activation energy.
To determine the rate constant at 700 K, we can again use the Arrhenius equation:
k = Ae^(-Ea/RT)
Given the activation energy (Ea) obtained from the previous calculation and the new temperature of 700 K, we can substitute these values into the equation to find the rate constant (k) at 700 K.