Final answer:
The activation energy of a reaction can be determined using the Arrhenius equation. Given the activation energy of 50.2 kJ/mol at 25°C, we can use the equation k₂ = 2k₁ to find the temperature at which the rate constant doubles. The temperature at which the rate constant doubles is approximately 345°C.
Step-by-step explanation:
The activation energy of a reaction can be determined using the Arrhenius equation, which relates the rate constant of a reaction to its temperature. The equation is k = Ae^(-Ea/RT), where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. In this case, we are given the activation energy of 50.2 kJ/mol at 25°C. To find the temperature at which the rate constant doubles, we can use the equation k₂ = 2k₁, where k₂ is the rate constant at the new temperature and k₁ is the rate constant at 25°C.
First, we need to convert the given activation energy from kJ/mol to J/mol, so Ea = 50.2 x 1000 = 50200 J/mol. Next, we can rearrange the Arrhenius equation in terms of temperature: T₂ = (Ea/R)((1/T₁) - (1/T₂)). Substituting the given values, T₁ = 25°C = 298 K and k₂ = 2k₁, we can solve for T₂. Plugging the values into the equation, we get 2 = e^-(50200/RT₂), which simplifies to ln(2) = -(50200/RT₂). Solving for T₂, we find that the temperature at which the rate constant doubles is approximately 345°C.