# Determining Activation Energy Using Rate Constants and Temperatures

## Calculating Activation Energy

**The rate constant at 701 K is measured as 2.57 m**

^{-1}and that at 895 K is measured as 567 m^{-1}. Find the activation energy for the reaction in kJ/mol.The activation energy for the reaction is 171.4 kJ/mol. To find the activation energy for the reaction in kJ/mol, we can use the Arrhenius equation:

k = A * exp(-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 the temperature in Kelvin. We have two sets of data, one at 701 K and another at 895 K. We can use both of these to solve for the activation energy.

## Solving for Activation Energy

Taking the natural logarithm of both sides of the Arrhenius equation, we get:ln(k) = ln(A) - Ea/RT

We can now use the two sets of data to solve for the activation energy.

ln(k

_{1}/k

_{2}) = Ea/R * (1/T

_{2}- 1/T

_{1})

Substituting the values given in the problem, we get:

ln(2.57/567) = Ea/8.314 * (1/895 - 1/701)

Simplifying, we get:

-6.280 = Ea/8.314 * (-0.001302)

Solving for Ea, we get:

Ea = 171.4 kJ/mol

Therefore, the activation energy for the reaction is 171.4 kJ/mol.

What is the activation energy for the reaction based on the given rate constants and temperatures?

The activation energy can be determined using the Arrhenius equation. Substituting the given rate constants and temperatures allows us to solve for the activation energy. The activation energy is calculated to be 226.26 kJ/mol.

Explanation:

The activation energy can be determined using the Arrhenius equation:

k_{1}/k_{2} = e^{-Ea/R}(1/T_{2} - 1/T_{1})

Using the given values, we can substitute the rate constants (k) and temperatures (T) to solve for the activation energy (Ea).

Assuming both rate constants are measured in m^{-1}s^{-1}, we have:

2.57/567 = e^{-Ea/R}(1/701 - 1/895)

Simplifying this equation gives the activation energy (Ea) as 226.26 kJ/mol.