Calculation of Activation Energy:

The Arrhenius equation is used to calculate activation energy (Ea) of a chemical reaction. The equation is as follows:

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 gas constant, and T is temperature in Kelvin.

Given Information:

- The rate constant doubles when the temperature increases from 27°C to 37°C.
- We need to calculate the activation energy (Ea) in kJ.

Solution:

Step 1: Convert the temperatures from Celsius to Kelvin.

27°C + 273 = 300 K

37°C + 273 = 310 K

Step 2: Use the Arrhenius equation to calculate the activation energy.

Let's assume that the pre-exponential factor (A) does not change. We can write two equations using the given information:

k1 = A * e^(-Ea/RT1)

k2 = A * e^(-Ea/RT2)

Divide the second equation by the first equation:

k2/k1 = e^(-Ea/R * (1/T2 - 1/T1))

2 = e^(-Ea/R * (1/310 - 1/300))

Take the natural logarithm of both sides:

ln(2) = -Ea/R * (1/310 - 1/300)

Ea = -ln(2) * R * (1/310 - 1/300)

Ea = 62.3 kJ/mol

Therefore, the activation energy of the chemical reaction is 62.3 kJ/mol.

Explanation:

The rate constant of a chemical reaction is directly proportional to the activation energy and inversely proportional to the temperature. As the temperature increases, more reactant molecules have sufficient energy to overcome the activation energy barrier and react. This leads to an increase in the rate constant. The Arrhenius equation relates the rate constant to the temperature and activation energy of the reaction. By using the equation and the given information, we can calculate the activation energy of the reaction.