The activation energy of a reaction is 56.8 kJ/mol and the frequency factor is 1.5⨉10¹¹/ s. Calculate the rate constant of the reaction at 25 °C.

Verified step by step guidance

1. Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature in Celsius: \( T = 25 + 273.15 \).
2. Use the Arrhenius equation to relate the rate constant \( k \) to the activation energy \( E_a \), frequency factor \( A \), and temperature \( T \): \( k = A \cdot e^{-E_a/(RT)} \).
3. Convert the activation energy from kJ/mol to J/mol by multiplying by 1000: \( E_a = 56.8 \times 1000 \).
4. Use the gas constant \( R = 8.314 \) J/(mol·K) in the Arrhenius equation.
5. Substitute the values for \( A \), \( E_a \), \( R \), and \( T \) into the Arrhenius equation and solve for \( k \).

Key Concepts

Activation Energy

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. In the context of the Arrhenius equation, a higher activation energy typically results in a slower reaction rate, as fewer molecules have sufficient energy to react at a given temperature.

Arrhenius Equation

The Arrhenius equation relates the rate constant of a reaction to its activation energy and temperature. 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 highlights how temperature and energy barriers influence reaction rates.

Rate Constant

The rate constant (k) is a proportionality factor in the rate law of a chemical reaction, indicating the speed at which the reaction occurs. It is influenced by factors such as temperature and activation energy. A higher rate constant signifies a faster reaction, while a lower rate constant indicates a slower reaction, making it a crucial parameter in chemical kinetics.