The decomposition of hydrocarbon follows the equation `k=(4.5xx10^(11)s^(-1))e^(-28000K//T)`
Calculate `E_(a)`.

Explanation

To calculate the activation energy \( E_a \) from the given equation, we will use the Arrhenius equation, which is expressed as:

\[ k = A e^{-\frac{E_a}{RT}} \]

Where:
- \( k \) is the rate constant,
- \( A \) is the pre-exponential factor,
- \( E_a \) is the activation energy,
- \( R \) is the universal gas constant (\( 8.314 \, \text{J/mol·K} \)),
- \( T \) is the temperature in Kelvin.

Given the equation:

\[ k = (4.5 \times 10^{11} \, s^{-1}) e^{-\frac{28000 \, K}{T}} \]

We can identify that:

\[ -\frac{E_a}{R} = -\frac{28000 \, K}{T} \]

This implies:

\[ E_a = 28000 \, K \cdot R \]

Now, substituting the value of \( R \):

\[ E_a = 28000 \, K \cdot 8.314 \, \text{J/mol·K} \]

Calculating this:

\[ E_a = 28000 \times 8.314 = 232792 \, \text{J/mol} \]

To convert this to kilojoules per mole, we divide by 1000:

\[ E_a = \frac{232792 \, \text{J/mol}}{1000} = 232.79 \, \text{kJ/mol} \]

Thus, the activation energy \( E_a \) is:

\[ \boxed{232.79 \, \text{kJ/mol}} \]