Question

A certain reaction has an activation energy of 70.0 kj mol−1 and a frequency factor of a1 = 3.30×1012 l mol−1 s−1 . what is the rate constant, k , of this reaction at 25.0 ∘c ?

Answer 1

To calculate the rate constant (k) at 25.0 °C for a reaction with a given activation energy and frequency factor, you use the Arrhenius equation, converting the energy to joules, the temperature to Kelvin, and then plugging these values along with the ideal gas constant into the equation before computing the result.

Step-by-step explanation:

You're asking how to calculate the rate constant (k) of a reaction at a specific temperature given the activation energy and the frequency factor (A). To find k at 25.0 °C for the reaction with an activation energy (Ea) of 70.0 kJ mol−1 and a frequency factor of 3.30×10¹² L mol−1 s−1, we'll use the Arrhenius equation:

k = Ae−Ea/RT

First, convert the activation energy from kJ to J (1 kJ = 1000 J), so Ea = 70.0 kJ mol−1 = 70000 J mol−1. Next, since the temperature must be in Kelvin, convert 25.0 °C to Kelvin (T = 25.0 + 273.15 = 298.15 K). Now we can plug in all the values into the Arrhenius equation, using R = 8.314 J/mol/K and the base of the natural logarithm e = 2.7183.

k = (3.30×10¹² L mol−1 s−1) × e−(70000 J mol−1)/(8.314 J/mol/K × 298.15 K)

Calculate the exponent first, then multiply it by the frequency factor to find the rate constant at 25.0 °C.