The rate constant for a second order reaction is given by `k=(5 times 10^11)e^(-29000k//T)`. The value of `E_a` will be:

Options

A. `275 kJ//mol e`
B. `250 kJ// mol e`
C. `241 kJ//mol e`
D. `225KJ//mol e`

Answer

To find the activation energy \(E_a\) for the given second-order reaction, we can follow these steps:

### Step 1: Write down the Arrhenius equation
The Arrhenius equation relates the rate constant \(k\) to the activation energy \(E_a\):
\[ k = A e^{-\frac{E_a}{RT}} \]
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 given equation with the Arrhenius equation
The given rate constant for the reaction is:
\[ k = (5 \times 10^{11}) e^{-\frac{29000}{T}} \]
From this, we can identify:
- \(A = 5 \times 10^{11}\)
- \(-\frac{E_a}{R} = -29000\)

### Step 3: Rearrange to find \(E_a\)
From the comparison, we can express \(E_a\) as:
\[ \frac{E_a}{R} = 29000 \]
Thus,
\[ E_a = 29000 \times R \]

### Step 4: Substitute the value of \(R\)
The universal gas constant \(R\) is \(8.314 \, \text{J/(mol K)}\). Substituting this value in:
\[ E_a = 29000 \times 8.314 \, \text{J/(mol K)} \]

### Step 5: Calculate \(E_a\)
Now we perform the multiplication:
\[ E_a = 29000 \times 8.314 = 241106 \, \text{J/mol} \]

### Step 6: Convert \(E_a\) to kilojoules per mole
Since the options are given in kilojoules per mole, we convert joules to kilojoules:
\[ E_a = 241106 \, \text{J/mol} \times 10^{-3} \, \text{kJ/J} = 241.106 \, \text{kJ/mol} \]

### Step 7: Round the answer
Rounding \(241.106 \, \text{kJ/mol}\) gives us:
\[ E_a \approx 241 \, \text{kJ/mol} \]

### Final Answer
The value of \(E_a\) is approximately \(241 \, \text{kJ/mol}\).

---