Decomposition of a hydrocarbon follows the equation $$k = (5.5 \times 10^{11} s^{-1}) e^{\frac{-28000K}{T}}$$. The activation energy of reaction is __________ kJ mol$$^{-1}$$. (Nearest Integer) Given : R = 8.3 J K$$^{-1}$$ mol$$^{-1}$$

The Arrhenius equation for a reaction is given by

$$k=Ae^{-\frac{E_a}{RT}}$$

where (k) is the rate constant, (A) is the Arrhenius pre-exponential factor, (E_a) is the activation energy, (R) is the universal gas constant, and (T) is the absolute temperature.

The given rate equation is

$$k=(5.5\times10^{11},s^{-1})e^{-\frac{28000}{T}}.$$

Comparing this expression with the standard Arrhenius equation,

$$e^{-\frac{E_a}{RT}}=e^{-\frac{28000}{T}},$$

we obtain

$$\frac{E_a}{R}=28000.$$

Using the value of the gas constant,

$$R=8.3\ \text{J K}^{-1}\text{mol}^{-1},$$

the activation energy is

$$E_a=28000\times8.3=232400\ \text{J mol}^{-1}.$$

Converting this into (\text{kJ mol}^{-1}),

$$E_a=\frac{232400}{1000}=232.4\ \text{kJ mol}^{-1}.$$

Rounding to the nearest integer,

$$E_a\approx232\ \text{kJ mol}^{-1}.$$

Hence, the activation energy of the reaction is (232\ \text{kJ mol}^{-1}).