calculate the activation energy, ea, for a reaction with a frequency factor, a, of 6.10 Ã 1014 s-1 and a rate constant of 13.0 s-1 at 320 k. express your answer in kj/mol and to three significant figures.
Calculate the activation energy, Ea, for a reaction:
Answer:
To calculate the activation energy (Ea) for a reaction, we can use the Arrhenius equation:
k = a \times e^{-\frac{Ea}{RT}}
Given data:
- Frequency factor (a): 6.10 × 10^14 s^-1
- Rate constant (k): 13.0 s^-1
- Temperature (T): 320 K
Let’s convert the temperature to Kelvin and plug the values into the equation to solve for activation energy:
13.0 = 6.10 \times 10^{14} \times e^{-\frac{Ea}{8.314 \times 320}}
13.0 = 6.10 \times 10^{14} \times e^{-\frac{Ea}{2651.2}}
e^{-\frac{Ea}{2651.2}} = \frac{13.0}{6.10 \times 10^{14}}
e^{-\frac{Ea}{2651.2}} = 2.1311 \times 10^{-14}
-\frac{Ea}{2651.2} = ln(2.1311 \times 10^{-14})
Ea = -2651.2 \times ln(2.1311 \times 10^{-14})
Ea = -2651.2 \times (-32.4808)
Ea = 86242.9365
Therefore, the activation energy (Ea) for the reaction is approximately 86.243 kJ/mol to three significant figures.