Assuming that the activation energy is about 111kjmol-1, calculate the fractional variation in the rate constant that would result from a temparature of 323.15 K

I just would liek to know how to go about calculating it fromt eh equation

k= Ae-Ea/RT..

To calculate the fractional variation in the rate constant, we need to use the Arrhenius equation. The Arrhenius equation relates the rate constant (k) of a chemical reaction to the activation energy (Ea) and the temperature (T):

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 (8.314 J/(mol*K))
- T is the temperature in Kelvin

To calculate the fractional variation in the rate constant, we need to calculate the rate constant (k) at two different temperatures and then compare them. Let's assume the first temperature is T1 = 298.15 K and the second temperature is T2 = 323.15 K.

To calculate the rate constant at T1, we'll substitute the values into the Arrhenius equation:

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

To calculate the rate constant at T2, we'll substitute the values into the Arrhenius equation again:

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

Now, we can calculate the fractional variation:

Fractional Variation = (k2 - k1) / k1

Let's calculate it step by step:

Step 1: Convert the activation energy to Joules:

Ea = 111 kJ/mol * (1000 J/kJ) = 111,000 J/mol

Step 2: Plug in the values of R, T1, and T2:

R = 8.314 J/(mol*K)
T1 = 298.15 K
T2 = 323.15 K

Step 3: Calculate the rate constant at T1:

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

Step 4: Calculate the rate constant at T2:

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

Step 5: Calculate the fractional variation:

Fractional Variation = (k2 - k1) / k1

By following these steps, you can calculate the fractional variation in the rate constant resulting from a temperature of 323.15 K.