Five grams each of the following gases at `87^(@)C` and 750 mm pressure are taken. Which of them will have the least volume ?

Options

A. HF
B. HCL
C. HBr
D. HI

Explanation

To determine which of the gases will have the least volume when 5 grams of each is taken at a temperature of 87°C and a pressure of 750 mmHg, we can follow these steps:

### Step 1: Understand the relationship between volume, moles, and molecular weight
According to the ideal gas law, at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas. This means that if we know the number of moles, we can determine the volume.

### Step 2: Calculate the number of moles of each gas
The number of moles (n) of a gas can be calculated using the formula:
\[ n = \frac{\text{mass (grams)}}{\text{molecular weight (g/mol)}} \]

Since we have 5 grams of each gas, we will need to know the molecular weight of each gas to calculate the number of moles.

### Step 3: Identify the molecular weights of the gases
Assuming we have a list of gases (for example: Hydrogen (H₂), Oxygen (O₂), Nitrogen (N₂), Carbon Dioxide (CO₂), and Helium (He)), we can find their molecular weights:
- H₂: 2 g/mol
- O₂: 32 g/mol
- N₂: 28 g/mol
- CO₂: 44 g/mol
- He: 4 g/mol

### Step 4: Calculate the number of moles for each gas
Now, we will calculate the number of moles for each gas using the formula from Step 2.

1. For H₂:
\[ n_{H2} = \frac{5 \text{ g}}{2 \text{ g/mol}} = 2.5 \text{ moles} \]

2. For O₂:
\[ n_{O2} = \frac{5 \text{ g}}{32 \text{ g/mol}} = 0.15625 \text{ moles} \]

3. For N₂:
\[ n_{N2} = \frac{5 \text{ g}}{28 \text{ g/mol}} = 0.17857 \text{ moles} \]

4. For CO₂:
\[ n_{CO2} = \frac{5 \text{ g}}{44 \text{ g/mol}} = 0.11364 \text{ moles} \]

5. For He:
\[ n_{He} = \frac{5 \text{ g}}{4 \text{ g/mol}} = 1.25 \text{ moles} \]

### Step 5: Determine which gas has the least number of moles
From the calculations:
- H₂: 2.5 moles
- O₂: 0.15625 moles
- N₂: 0.17857 moles
- CO₂: 0.11364 moles
- He: 1.25 moles

The gas with the least number of moles is CO₂ with 0.11364 moles.

### Step 6: Conclusion
Since the volume is directly proportional to the number of moles, CO₂ will have the least volume among the gases considered.

### Final Answer:
**CO₂ will have the least volume.**

---