Which of the following gases will have least volume if 10g of each gas is taken at same temperature and pressure?

Options

A. `CO_2`
B. `N_2`
C. `CH_4`
D. HCl

Explanation

To determine which gas will have the least volume when 10 grams of each gas is taken at the same temperature and pressure, we can follow these steps:

### Step 1: Identify the Molecular Masses
First, we need to identify the molecular masses of the gases in question. Let's assume the gases are:
- Carbon Dioxide (CO₂) - Molecular mass = 44 g/mol
- Nitrogen (N₂) - Molecular mass = 28 g/mol
- Oxygen (O₂) - Molecular mass = 32 g/mol
- Chlorine (Cl₂) - Molecular mass = 70.9 g/mol

### Step 2: Calculate the Number of Moles
Next, we calculate the number of moles for each gas using the formula:
\[ \text{Number of moles} (n) = \frac{\text{mass (g)}}{\text{molecular mass (g/mol)}} \]

For each gas:
- For CO₂:
\[ n = \frac{10 \text{ g}}{44 \text{ g/mol}} \approx 0.227 \text{ moles} \]

- For N₂:
\[ n = \frac{10 \text{ g}}{28 \text{ g/mol}} \approx 0.357 \text{ moles} \]

- For O₂:
\[ n = \frac{10 \text{ g}}{32 \text{ g/mol}} \approx 0.3125 \text{ moles} \]

- For Cl₂:
\[ n = \frac{10 \text{ g}}{70.9 \text{ g/mol}} \approx 0.141 \text{ moles} \]

### Step 3: Determine the Volume
Using the Ideal Gas Law \( PV = nRT \), we can express volume (V) as:
\[ V = \frac{nRT}{P} \]
At constant temperature (T) and pressure (P), the volume is directly proportional to the number of moles (n). Therefore, the gas with the least number of moles will occupy the least volume.

### Step 4: Compare the Number of Moles
Now, we compare the number of moles calculated:
- CO₂: 0.227 moles
- N₂: 0.357 moles
- O₂: 0.3125 moles
- Cl₂: 0.141 moles

### Step 5: Identify the Gas with Least Volume
The gas with the least number of moles is Cl₂ (0.141 moles), which means it will have the least volume when 10 grams of each gas is taken at the same temperature and pressure.

### Final Answer
Thus, the gas that will have the least volume is **Chlorine (Cl₂)**.

---