Answer :
Final answer:
The activation energy of a reaction, whose rate constant doubles when the temperature increases from 27°C to 37°C, can be estimated using the Arrhenius equation. Approximation and prior knowledge suggest that the activation energy should be around 53.6 kJ/mol, which aligns with the general Q10 rule that the reaction rate doubles with a 10°C temperature increase.
Hence, the correct answer is option 4.
Explanation:
Determining Activation Energy
The question involves finding the activation energy given that the rate constant of a chemical reaction doubles when the temperature is increased from 27°C to 37°C. Based on the Arrhenius equation, the activation energy can be calculated using the initial and final temperatures along with the knowledge that the rate constant has doubled. To calculate the activation energy, we use the Arrhenius equation in the following form:
k = Ae^(-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. We would set up two equations, one for each temperature, to solve for Ea since the rate constants are given as having a ratio of 2:1 at these temperatures.
Using the information that a reaction's rate constant doubles with a 10°C increase in temperature, we can infer an approximate activation energy. Exemplary data suggests for a known activation energy of about 54 kJ/mol, this doubling effect occurs. However, the exact activation energy can be calculated using the rate constants and temperatures by incorporating the Arrhenius equation and taking the natural logarithm of both sides, leading to a linear relationship.
Comparing the available options for activation energy, we find that the value is approximately 53.6 kJ/mol. This calculation takes into consideration the general rule of the temperature dependence of reaction rates and the concept of Q10, which describes the rate of increase of a reaction over a 10°C interval. Although Q10 can vary, it frequently approximates to 2, representing a doubling of the reaction rate.
