If three gases X, Y and Z are arranged in increasing order of their relative molecular mass and the mass of each gas is 10 g at S.T.P state, which gas will contain the least number of molecules and which will contain the most?

Options

A. X least and Y maximum
B. X maximum and Z least
C. Y maximum and Z least
D. Y least and Z maximum

Explanation

To solve the problem, we need to determine the number of moles of each gas (X, Y, and Z) based on their relative molecular masses and the mass of each gas at STP (Standard Temperature and Pressure). Here’s a step-by-step solution:

### Step 1: Understand the Relationship Between Mass, Molar Mass, and Moles
The number of moles of a substance can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]

### Step 2: Assign Molar Masses to the Gases
Since the gases are arranged in increasing order of their relative molecular mass, we can assign:
- Molar mass of gas X = \( m \)
- Molar mass of gas Y = \( m + 1 \)
- Molar mass of gas Z = \( m + 2 \)

### Step 3: Calculate the Number of Moles for Each Gas
Given that the mass of each gas is 10 g, we can calculate the number of moles for each gas:
- For gas X:
\[ \text{Moles of X} = \frac{10 \, \text{g}}{m} \]
- For gas Y:
\[ \text{Moles of Y} = \frac{10 \, \text{g}}{m + 1} \]
- For gas Z:
\[ \text{Moles of Z} = \frac{10 \, \text{g}}{m + 2} \]

### Step 4: Compare the Number of Moles
To determine which gas has the least and most number of moles, we compare:
\[ \frac{10}{m} > \frac{10}{m + 1} > \frac{10}{m + 2} \]
This implies:
- Moles of X > Moles of Y > Moles of Z

### Step 5: Determine the Number of Molecules
The number of molecules can be calculated by multiplying the number of moles by Avogadro's number (\( N_A \)). Since the number of moles is directly proportional to the number of molecules:
- Number of molecules of X is maximum.
- Number of molecules of Y is intermediate.
- Number of molecules of Z is minimum.

### Conclusion
- **Gas with the least number of molecules**: Gas Z
- **Gas with the most number of molecules**: Gas X