The rate constant of a reaction at 32 °C is 0.055 s⁻¹. If the frequency factor is 1.2 × 10¹³ s⁻¹, what is the activation barrier?

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1. Identify the Arrhenius equation: $k = A e^{-\frac{E_a}{RT}}$, where $k$ is the rate constant, $A$ is the frequency factor, $E_a$ is the activation energy, $R$ is the gas constant, and $T$ is the temperature in Kelvin.
2. Convert the temperature from Celsius to Kelvin: $T = 32 + 273.15$.
3. Rearrange the Arrhenius equation to solve for the activation energy $E_a$: $E_a = -RT \ln\left(\frac{k}{A}\right)$.
4. Substitute the known values into the equation: $R = 8.314 \text{ J/mol·K}$, $k = 0.055 \text{ s}^{-1}$, $A = 1.2 \times 10^{13} \text{ s}^{-1}$, and the calculated $T$ in Kelvin.
5. Calculate the natural logarithm and multiply by $-RT$ to find the activation energy $E_a$.