Values of E_a = 6.3 kJ/mol and A = 6.0⨉10⁸/(M s) have been measured for the bimolecular reaction: NO(g) + F₂(g) → NOF(g) + F(g) (a) Calculate the rate constant at 25 °C.

검증된 단계별 안내

Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature in Celsius: \( T = 25 + 273.15 \).

Use the Arrhenius equation to relate the rate constant \( k \) to the activation energy \( E_a \), the frequency factor \( A \), and the temperature \( T \): \( k = A \cdot e^{-E_a/(RT)} \).

Substitute the given values into the Arrhenius equation: \( A = 6.0 \times 10^8 \text{ M}^{-1}\text{s}^{-1} \), \( E_a = 6.3 \text{ kJ/mol} \) (convert to J/mol by multiplying by 1000), and \( R = 8.314 \text{ J/mol K} \).

Calculate the exponent in the Arrhenius equation: \( -E_a/(RT) \).

Substitute the calculated exponent back into the Arrhenius equation to find the rate constant \( k \).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 pre-exponential factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. This equation helps predict how changes in temperature affect 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 form products. In the context of the Arrhenius equation, a lower Ea results in a higher rate constant, indicating that the reaction can proceed more quickly at a given temperature.

Rate Constant (k)

The rate constant is a proportionality factor in the rate law of a chemical reaction, indicating the speed of the reaction. It varies with temperature and is influenced by factors such as activation energy and molecular collisions. For bimolecular reactions, the rate constant can be calculated using the Arrhenius equation, which incorporates temperature and activation energy.

Values of Ea = 6.3 kJ/mol and A = 6.0⨉108/(M s) have been measured for the bimolecular reaction: NO(g) + F2(g) → NOF(g) + F(g) (a) Calculate the rate constant at 25 °C.