Which of the following gases has the highest density under standard conditions?

Options

A. CO
B. `N_(2)O`
C. `C_(3)H_(8)`
D. `SO_(2)`

Answer

To determine which gas has the highest density under standard conditions, we will follow these steps:

### Step 1: Understand the Concept of Density
Density (D) is defined as the mass (m) of a substance divided by its volume (V). The formula is:
\[ D = \frac{m}{V} \]

### Step 2: Recognize Standard Conditions
Under standard temperature and pressure (STP), one mole of any gas occupies a volume of 22.4 liters. This means that at STP, the volume for one mole of any gas is constant.

### Step 3: Relate Density to Molar Mass
Since the volume is constant for all gases at STP, the density of a gas is directly proportional to its molar mass (M). Therefore, we can express density as:
\[ D \propto M \]
This means that the gas with the highest molar mass will also have the highest density.

### Step 4: Calculate the Molar Mass of Each Gas
Now, we will calculate the molar mass of each gas provided in the options:

1. **Carbon Monoxide (CO)**:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol
- Molar mass of CO = 12 + 16 = 28 g/mol

2. **Nitrous Oxide (N2O)**:
- Nitrogen (N) = 14 g/mol (2 Nitrogens)
- Oxygen (O) = 16 g/mol
- Molar mass of N2O = (2 × 14) + 16 = 28 + 16 = 44 g/mol

3. **Propane (C3H8)**:
- Carbon (C) = 12 g/mol (3 Carbons)
- Hydrogen (H) = 1 g/mol (8 Hydrogens)
- Molar mass of C3H8 = (3 × 12) + (8 × 1) = 36 + 8 = 44 g/mol

4. **Sulfur Dioxide (SO2)**:
- Sulfur (S) = 32 g/mol
- Oxygen (O) = 16 g/mol (2 Oxygens)
- Molar mass of SO2 = 32 + (2 × 16) = 32 + 32 = 64 g/mol

### Step 5: Compare Molar Masses
Now that we have calculated the molar masses:
- CO = 28 g/mol
- N2O = 44 g/mol
- C3H8 = 44 g/mol
- SO2 = 64 g/mol

### Step 6: Identify the Gas with Highest Molar Mass
From the calculated values, we see that sulfur dioxide (SO2) has the highest molar mass of 64 g/mol.

### Conclusion
Therefore, the gas with the highest density under standard conditions is **sulfur dioxide (SO2)**.

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