Ratio of `C_(p)` and `C_(v)` of a gas X is 1.4, the number of atom of the gas 'X' present in 11.2 litres of it at NTP will be

Options

A. (a) `6.02xx10^(23)`
B. (b) `1.2xx10^(23)`
C. (c) `3.01xx10^(23)`
D. (d) `2.01xx10^(23)`

Explanation

To find the number of atoms of gas X present in 11.2 liters at NTP, we can follow these steps:

### Step 1: Understand the relationship between Cp and Cv
The ratio of heat capacities at constant pressure (Cp) and constant volume (Cv) is given as 1.4. This ratio is known as gamma (γ).

**Hint:** Recall that for ideal gases, γ = Cp/Cv, and it can help identify the type of gas (monoatomic, diatomic, etc.).

### Step 2: Identify the type of gas
Since γ = 1.4, we can conclude that gas X is diatomic. Diatomic gases have a γ value of approximately 1.4.

**Hint:** Remember that diatomic gases consist of two atoms per molecule.

### Step 3: Use the volume of gas at NTP
At Normal Temperature and Pressure (NTP), 22.4 liters of any ideal gas contains 1 mole of gas, which is equivalent to 6.02 x 10²³ molecules (Avogadro's number).

**Hint:** Familiarize yourself with the concept of molar volume at NTP, which is 22.4 liters for 1 mole of gas.

### Step 4: Calculate the number of molecules in 11.2 liters
Since 11.2 liters is half of 22.4 liters, it will contain half a mole of gas X. Therefore, the number of molecules in 11.2 liters is:

\[ \text{Number of molecules} = \frac{1}{2} \times 6.02 \times 10^{23} = 3.01 \times 10^{23} \text{ molecules} \]

**Hint:** Use the proportional relationship between volume and the number of moles to find the number of molecules.

### Step 5: Calculate the number of atoms
Since gas X is diatomic, each molecule contains 2 atoms. Therefore, the total number of atoms in 11.2 liters is:

\[ \text{Number of atoms} = 2 \times \text{Number of molecules} = 2 \times 3.01 \times 10^{23} = 6.02 \times 10^{23} \text{ atoms} \]

**Hint:** Remember to multiply the number of molecules by 2 to account for the two atoms in each diatomic molecule.

### Conclusion
The number of atoms of gas X present in 11.2 liters at NTP is \(6.02 \times 10^{23}\).

**Final Answer:** Option A: \(6.02 \times 10^{23}\) atoms.