Rate constant at different temperatures

The rate constant (k) of a reaction is a measure of how fast the reaction proceeds. It is dependent on the temperature at which the reaction occurs. The rate constant can be determined experimentally by measuring the rate of the reaction at different temperatures.

Arrhenius equation

The Arrhenius equation relates the rate constant of a reaction to the temperature and the activation energy (Ea) of the reaction. It is given by the equation:

k = Ae^(-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.

Determination of activation energy

To determine the activation energy of a reaction, we can use the Arrhenius equation and the rate constants at two different temperatures. By taking the natural logarithm of both sides of the equation, we can linearize the equation and solve for Ea.

ln(k1/k2) = (Ea/R)(1/T2 - 1/T1)

where k1 and k2 are the rate constants at temperatures T1 and T2, respectively.

Calculation

Given: k1 = 8 L mol-1s-1 at 300 K, k2 = 160 L mol-1s-1 at 350 K

Using the Arrhenius equation, we can calculate the activation energy as follows:

ln(8/160) = (Ea/R)(1/350 - 1/300)

ln(1/20) = (Ea/R)(1/350 - 1/300)

-3.912 = (Ea/R)(0.002857 - 0.003333)

-3.912 = (Ea/R)(-0.000476)

Solving for Ea/R:

(Ea/R) = -3.912 / -0.000476

(Ea/R) ≈ 8203.36

Conversion to KJ/mol

Since the gas constant R is given in units of J/(mol K), we need to convert the activation energy to KJ/mol by dividing by 1000:

Ea ≈ 8203.36 / 1000

Ea ≈ 8.203 KJ/mol

Therefore, the activation energy of the reaction is approximately 8.203 KJ/mol.