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?

Verified step by step guidance

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 $E_a$.

Key Concepts

Arrhenius Equation

The Arrhenius equation relates the rate constant of a reaction to the temperature and activation energy. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. This equation helps in understanding how temperature influences reaction rates.

Activation Energy (Ea)

Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to transform into products. A higher activation energy indicates a slower reaction rate, while a lower activation energy suggests a faster reaction, making it a crucial factor in reaction kinetics.

Frequency Factor (A)

The frequency factor, also known as the pre-exponential factor, is a constant that reflects the frequency of collisions and the orientation of reactants in a chemical reaction. It is a component of the Arrhenius equation and indicates how often reactants collide with sufficient energy to react. A higher frequency factor typically correlates with a faster reaction rate.