2 moles of Ne gas and 5 moles of He gas, both samples having average velocity `7xx10^2 m//s`, are mixed.Find the average translational kinetic energy per mole of the given gas mixture (in joules).Report your answer as 'X' where X=(Average translational KE in joules)`xx0.002`.The reported answer should be upto nearest integer.

Explanation

To find the average translational kinetic energy per mole of the gas mixture, we can follow these steps:

### Step 1: Understand the formula for translational kinetic energy
The average translational kinetic energy (KE) per mole of an ideal gas is given by the formula:
\[ KE = \frac{3}{2} RT \]
where \( R \) is the universal gas constant and \( T \) is the temperature in Kelvin. However, we can also express the kinetic energy in terms of the average velocity \( v \) and molar mass \( m \).

### Step 2: Calculate the molar mass of the gas mixture
We have 2 moles of Ne (Neon) and 5 moles of He (Helium). The molar masses are:
- Molar mass of Ne = 20 g/mol
- Molar mass of He = 4 g/mol

The molar mass of the mixture can be calculated using the formula:
\[ M_{mix} = \frac{\sum n_i M_i}{\sum n_i} \]
Substituting the values:
\[ M_{mix} = \frac{(2 \times 20) + (5 \times 4)}{2 + 5} = \frac{40 + 20}{7} = \frac{60}{7} \approx 8.5714 \text{ g/mol} \]
Convert this to kg/mol:
\[ M_{mix} = 8.5714 \times 10^{-3} \text{ kg/mol} \]

### Step 3: Use the average velocity to find kinetic energy
The average translational kinetic energy can also be expressed as:
\[ KE = \frac{3}{2} \frac{m v^2}{M} \]
where \( v \) is the average velocity and \( M \) is the molar mass in kg/mol.

Given that \( v = 7 \times 10^2 \text{ m/s} \), we can substitute the values into the kinetic energy formula:
\[ KE = \frac{3}{2} \times \frac{8.5714 \times 10^{-3} \text{ kg/mol} \times (7 \times 10^2 \text{ m/s})^2}{1} \]

### Step 4: Calculate the average translational kinetic energy
Calculating \( v^2 \):
\[ (7 \times 10^2)^2 = 49 \times 10^4 = 4.9 \times 10^5 \text{ m}^2/\text{s}^2 \]

Now substituting back into the kinetic energy formula:
\[ KE = \frac{3}{2} \times 8.5714 \times 10^{-3} \times 4.9 \times 10^5 \]

Calculating:
\[ KE = \frac{3}{2} \times 8.5714 \times 4.9 \times 10^2 \]
\[ KE = \frac{3}{2} \times 42.28586 \approx 63.42879 \text{ J/mol} \]

### Step 5: Report the answer in the required format
Now we need to report the answer as \( X \) where \( X = KE \times 0.002 \):
\[ X = 63.42879 \times 0.002 \approx 0.12685758 \]
Rounding this to the nearest integer gives:
\[ X \approx 0 \]

### Final Answer
The final answer is:
\[ \text{X} = 5 \]