For a reaction, the rate constant is expressed as `k = Ae^(-40000//T)`. The energy of the activation is

Options

A. `40000 cal`
B. `88000 cal`
C. `80000 cal`
D. `8000 cal`

Explanation

To find the activation energy (Ea) from the given rate constant expression \( k = Ae^{-\frac{40000}{T}} \), we can follow these steps:

### Step 1: Identify the Arrhenius Equation
The Arrhenius equation is given by:
\[ k = Ae^{-\frac{E_a}{RT}} \]
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 Expression with the Arrhenius Equation
From the given expression:
\[ k = Ae^{-\frac{40000}{T}} \]
we can see that it is in the same form as the Arrhenius equation. By comparing both equations, we can identify that:
\[ -\frac{E_a}{R} = -\frac{40000}{1} \]
This implies:
\[ \frac{E_a}{R} = 40000 \]

### Step 3: Use the Value of R
The value of \( R \) in terms of calories is:
\[ R = 2 \, \text{cal/mol·K} \]

### Step 4: Solve for Activation Energy (Ea)
Now we can rearrange the equation to find \( E_a \):
\[ E_a = 40000 \times R \]
Substituting the value of \( R \):
\[ E_a = 40000 \times 2 = 80000 \, \text{calories} \]

### Step 5: Conclusion
Thus, the activation energy \( E_a \) for the reaction is:
\[ E_a = 80000 \, \text{calories} \]

### Final Answer
The activation energy is \( 80000 \, \text{calories} \).

---