Which mixture is lighter than humid air ?

Options

A. `N_2+O_2+SO_2`
B. `N_2+O_2+CO_2`
C. `N_2+O_2+C_2H_6`
D. `N_2+O_2+He`

Answer

To determine which mixture is lighter than humid air, we need to analyze the components of humid air and compare the molecular weights of the given options.

### Step-by-Step Solution:

1. **Understand Humid Air Composition**:
- Humid air is primarily composed of nitrogen (N2), oxygen (O2), and water vapor (H2O).
- The molecular formula for humid air can be represented as:
\[ \text{Humid Air} = \text{N}_2 + \text{O}_2 + \text{H}_2\text{O} \]

2. **Calculate the Molecular Weight of Humid Air**:
- The molecular weight of water (H2O) is calculated as follows:
- Atomic weight of hydrogen (H) = 1
- Atomic weight of oxygen (O) = 16
- Therefore, molecular weight of H2O = \(2 \times 1 + 16 = 18\)

3. **List the Options**:
- We need to compare the molecular weights of the following options:
1. SO2
2. CO2
3. C2H6
4. He (Helium)

4. **Calculate Molecular Weights of Each Option**:
- **Option 1: SO2**:
- Atomic weight of sulfur (S) = 32
- Molecular weight of SO2 = \(32 + 2 \times 16 = 32 + 32 = 64\)
- **Option 2: CO2**:
- Atomic weight of carbon (C) = 12
- Molecular weight of CO2 = \(12 + 2 \times 16 = 12 + 32 = 44\)
- **Option 3: C2H6**:
- Molecular weight of C2H6 = \(2 \times 12 + 6 \times 1 = 24 + 6 = 30\)
- **Option 4: He**:
- Atomic weight of helium (He) = 4

5. **Comparison with Humid Air**:
- Now we compare the calculated molecular weights with that of water (18):
- SO2: 64 (greater than 18)
- CO2: 44 (greater than 18)
- C2H6: 30 (greater than 18)
- He: 4 (less than 18)

6. **Conclusion**:
- The only option that is lighter than humid air (which has a molecular weight of 18) is **Helium (He)**.

### Final Answer:
- The mixture that is lighter than humid air is **Option 4: Helium (He)**.