25 g of each of the following gases are taken at `27^@C`and 600 mm pressure. Which of these will have the least volume?

Options

A. `HBr`
B. `HCl`
C. `HF `
D. `HI`

Explanation

To determine which of the given gases (HBr, HCl, HF, and HI) will have the least volume when 25 g of each is taken at 27°C and 600 mm pressure, we can follow these steps:

### Step 1: Understand the relationship between volume, moles, and molecular weight
According to Avogadro's 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 want to find the gas with the least volume, we need to find the gas with the least number of moles.

### Step 2: Calculate the number of moles for each gas
The number of moles (n) of a gas can be calculated using the formula:
\[ n = \frac{\text{mass (g)}}{\text{molecular weight (g/mol)}} \]
Since the mass is constant (25 g) for all gases, we need to find the molecular weights of HBr, HCl, HF, and HI.

### Step 3: Determine the molecular weights
- **HF (Hydrogen Fluoride)**:
- H = 1 g/mol
- F = 19 g/mol
- Molecular weight of HF = 1 + 19 = 20 g/mol

- **HCl (Hydrogen Chloride)**:
- H = 1 g/mol
- Cl = 35.5 g/mol
- Molecular weight of HCl = 1 + 35.5 = 36.5 g/mol

- **HBr (Hydrogen Bromide)**:
- H = 1 g/mol
- Br = 80 g/mol
- Molecular weight of HBr = 1 + 80 = 81 g/mol

- **HI (Hydrogen Iodide)**:
- H = 1 g/mol
- I = 127 g/mol
- Molecular weight of HI = 1 + 127 = 128 g/mol

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

- For HF:
\[ n_{HF} = \frac{25 \text{ g}}{20 \text{ g/mol}} = 1.25 \text{ moles} \]

- For HCl:
\[ n_{HCl} = \frac{25 \text{ g}}{36.5 \text{ g/mol}} \approx 0.685 \text{ moles} \]

- For HBr:
\[ n_{HBr} = \frac{25 \text{ g}}{81 \text{ g/mol}} \approx 0.308 \text{ moles} \]

- For HI:
\[ n_{HI} = \frac{25 \text{ g}}{128 \text{ g/mol}} \approx 0.195 \text{ moles} \]

### Step 5: Identify the gas with the least number of moles
From the calculations:
- HF: 1.25 moles
- HCl: 0.685 moles
- HBr: 0.308 moles
- HI: 0.195 moles

The gas with the least number of moles is HI.

### Step 6: Conclusion
Since HI has the least number of moles, it will also have the least volume at the given conditions of temperature and pressure.

**Final Answer:** HI will have the least volume.

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