Consider the two reactions:
O + N₂ → NO + N E_a = 315 kJ/mol
Cl + H₂ → HCl + H E_a = 23 kJ/mol
b. The frequency factors for these two reactions are very close to each other in value. Assuming that they are the same, calculate the ratio of the reaction rate constants for these two reactions at 25 °C.

검증된 단계별 안내

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 (8.314 J/mol·K), and \( T \) is the temperature in Kelvin.

Convert the temperature from Celsius to Kelvin: \( T = 25 + 273.15 = 298.15 \text{ K} \).

Since the frequency factors \( A \) are assumed to be the same for both reactions, the ratio of the rate constants \( \frac{k_1}{k_2} \) can be expressed as \( \frac{e^{-\frac{E_{a1}}{RT}}}{e^{-\frac{E_{a2}}{RT}}} = e^{-\frac{E_{a1} - E_{a2}}{RT}} \).

Substitute the given activation energies into the equation: \( E_{a1} = 315 \text{ kJ/mol} = 315,000 \text{ J/mol} \) and \( E_{a2} = 23 \text{ kJ/mol} = 23,000 \text{ J/mol} \).

Calculate the exponent: \( -\frac{(315,000 - 23,000)}{8.314 \times 298.15} \) and use this to find the ratio \( \frac{k_1}{k_2} = e^{\text{calculated exponent}} \).

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주요 개념

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

Arrhenius Equation

The Arrhenius equation describes how the rate constant of a chemical reaction depends on 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 highlights the exponential relationship between temperature and reaction rates, indicating that higher temperatures generally lead to faster reactions.

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. In the context of the given reactions, the activation energies of 315 kJ/mol and 23 kJ/mol indicate that the first reaction is significantly more energy-intensive than the second, which affects their respective reaction rates at a given temperature.

Reaction Rate Constant (k)

The reaction rate constant (k) is a proportionality factor that relates the rate of a reaction to the concentrations of the reactants. It is influenced by factors such as temperature and activation energy. In the context of the question, calculating the ratio of the rate constants for the two reactions involves using the Arrhenius equation, allowing for a comparison of how the different activation energies impact the overall reaction rates at 25 °C.