A stationary vessel contains a mixture of equal moles of Nitrogen and Helium gas. The percentage of the total kinetic energy of the mixture that is possessed by the molecules of Nitrogen is ___________

Explanation

To solve the problem, we need to find the percentage of the total kinetic energy of a mixture of nitrogen (N₂) and helium (He) gas that is possessed by the nitrogen molecules.

### Step-by-Step Solution:

1. **Understand the Kinetic Energy Formula**:
The kinetic energy (KE) of an ideal gas can be expressed as:
\[ KE = \frac{f}{2} nRT \]
where:
- \( f \) = degrees of freedom of the gas molecules,
- \( n \) = number of moles,
- \( R \) = universal gas constant,
- \( T \) = temperature.

2. **Identify Degrees of Freedom**:
- For nitrogen (N₂), which is a diatomic molecule, the degrees of freedom \( f \) is 5 (3 translational + 2 rotational).
- For helium (He), which is a monatomic gas, the degrees of freedom \( f \) is 3 (3 translational).

3. **Calculate Kinetic Energy for Each Gas**:
- For nitrogen (N₂):
\[ KE_{N_2} = \frac{5}{2} nRT \]
- For helium (He):
\[ KE_{He} = \frac{3}{2} nRT \]

4. **Total Kinetic Energy of the Mixture**:
The total kinetic energy of the mixture is the sum of the kinetic energies of nitrogen and helium:
\[ KE_{total} = KE_{N_2} + KE_{He} = \frac{5}{2} nRT + \frac{3}{2} nRT = \frac{8}{2} nRT = 4nRT \]

5. **Calculate the Percentage of Kinetic Energy from Nitrogen**:
To find the percentage of the total kinetic energy that is possessed by nitrogen:
\[ \text{Percentage of } KE_{N_2} = \left(\frac{KE_{N_2}}{KE_{total}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage of } KE_{N_2} = \left(\frac{\frac{5}{2} nRT}{4nRT}\right) \times 100 \]

6. **Simplify the Expression**:
The \( nRT \) cancels out:
\[ \text{Percentage of } KE_{N_2} = \left(\frac{5/2}{4}\right) \times 100 = \left(\frac{5}{8}\right) \times 100 \]

7. **Final Calculation**:
\[ \text{Percentage of } KE_{N_2} = 62.5\% \]

Thus, the percentage of the total kinetic energy of the mixture that is possessed by the molecules of nitrogen is **62.5%**.