If the activation energy of a reaction is 80.9 kJ `mol^(-1)`, the fraction of molecules at 700 K, having enough energy to react to form products is `e^(-x)`. The value of x is ______
((Rounded off to the nearest integer) [Use `R=8.31JK^(-1)mol^(-1)`]

Answer

To solve the problem, we need to determine the value of \( x \) in the expression \( e^{-x} \), which represents the fraction of molecules that have enough energy to overcome the activation energy barrier at a given temperature. We will use the Arrhenius equation to find \( x \).

### Step-by-Step Solution:

1. **Understanding the Arrhenius Equation**:
The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
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.

2. **Relating the Fraction of Molecules to Activation Energy**:
The fraction of molecules that have enough energy to react is given by:
\[ e^{-x} \]
From the Arrhenius equation, we can equate:
\[ -x = -\frac{E_a}{RT} \]
This simplifies to:
\[ x = \frac{E_a}{RT} \]

3. **Substituting the Values**:
We are given:
- \( E_a = 80.9 \, \text{kJ mol}^{-1} \)
- \( R = 8.31 \, \text{J K}^{-1} \text{mol}^{-1} \)
- \( T = 700 \, \text{K} \)

First, convert the activation energy from kJ to J:
\[ E_a = 80.9 \, \text{kJ mol}^{-1} \times 1000 \, \text{J kJ}^{-1} = 80900 \, \text{J mol}^{-1} \]

4. **Calculating \( x \)**:
Now we can substitute the values into the equation for \( x \):
\[ x = \frac{E_a}{RT} = \frac{80900 \, \text{J mol}^{-1}}{(8.31 \, \text{J K}^{-1} \text{mol}^{-1})(700 \, \text{K})} \]

Calculate the denominator:
\[ RT = 8.31 \times 700 = 5817 \, \text{J mol}^{-1} \]

Now, calculate \( x \):
\[ x = \frac{80900}{5817} \approx 13.9 \]

5. **Rounding to the Nearest Integer**:
The problem asks for the value of \( x \) rounded to the nearest integer:
\[ x \approx 14 \]

### Final Answer:
The value of \( x \) is **14**.