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

Options

A. 669 kJ `mol^(-1)`
B. 232. 79 kJ `mol^(-1)`
C. `4.5 xx 10^(11) kJ mol^(-1)`
D. 28000 kJ `mol^(-1)`

Explanation

To solve the problem of calculating the activation energy \( E_a \) from the given equation for the decomposition of hydrocarbon, we can follow these steps:

### Step 1: Understand the given equation
The equation provided is:
\[ k = (4.5 \times 10^{11} \, s^{-1}) e^{-\frac{28000 \, K}{T}} \]
This equation resembles the Arrhenius equation:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) is the rate constant,
- \( A \) is the pre-exponential factor,
- \( E_a \) is the activation energy,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin.

### Step 2: Compare the two equations
From the given equation, we can see that:
\[ \frac{E_a}{R} = 28000 \, K \]
This means that:
\[ E_a = 28000 \, K \times R \]

### Step 3: Substitute the value of \( R \)
The universal gas constant \( R \) is approximately \( 8.314 \, \text{J/mol·K} \). Now we can substitute this value into the equation:
\[ E_a = 28000 \, K \times 8.314 \, \text{J/mol·K} \]

### Step 4: Calculate \( E_a \)
Now we perform the multiplication:
\[ E_a = 28000 \times 8.314 \]
Calculating this gives:
\[ E_a = 232792 \, \text{J/mol} \]

### Step 5: Convert to kilojoules per mole
To convert joules to kilojoules, we divide by 1000:
\[ E_a = \frac{232792}{1000} = 232.792 \, \text{kJ/mol} \]

### Step 6: Round off the answer
Rounding off to two decimal places, we get:
\[ E_a \approx 232.79 \, \text{kJ/mol} \]

### Final Answer
Thus, the activation energy \( E_a \) is:
\[ \boxed{232.79 \, \text{kJ/mol}} \]

---