Which of the following does have minimum mass in grams ?
(i) 1 gram atom of oxygen
(ii) 4.2 gram molecules of `H_2`
(iii) 2 gram molecules of helium
(iv) 1.6 gram atoms of chlorine

Answer

To determine which of the given options has the minimum mass in grams, we will calculate the mass for each option step by step.

### Step 1: Calculate the mass of 1 gram atom of oxygen
- **Definition**: 1 gram atom of oxygen means we are considering the molar mass of oxygen.
- **Molar mass of oxygen (O)**: Approximately 16 grams.
- **Calculation**:
\[ \text{Mass} = 16 \text{ grams} \]

### Step 2: Calculate the mass of 4.2 gram molecules of \( H_2 \)
- **Definition**: \( H_2 \) is a diatomic molecule, meaning it consists of 2 hydrogen atoms.
- **Molar mass of \( H_2 \)**: The molar mass of hydrogen (H) is approximately 1 gram, so for \( H_2 \):
\[ \text{Molar mass of } H_2 = 2 \times 1 = 2 \text{ grams} \]
- **Calculation**: For 4.2 gram molecules of \( H_2 \):
\[ \text{Mass} = 4.2 \text{ molecules} \times 2 \text{ grams/molecule} = 8.4 \text{ grams} \]

### Step 3: Calculate the mass of 2 gram molecules of helium
- **Definition**: Helium is a monatomic gas, meaning it consists of single atoms.
- **Molar mass of helium (He)**: Approximately 4 grams.
- **Calculation**: For 2 gram molecules of helium:
\[ \text{Mass} = 2 \text{ molecules} \times 4 \text{ grams/molecule} = 8 \text{ grams} \]

### Step 4: Calculate the mass of 1.6 gram atoms of chlorine
- **Definition**: 1 gram atom of chlorine means we are considering the molar mass of chlorine.
- **Molar mass of chlorine (Cl)**: Approximately 35.5 grams.
- **Calculation**: For 1.6 gram atoms of chlorine:
\[ \text{Mass} = 1.6 \text{ atoms} \times 35.5 \text{ grams/atom} = 56.8 \text{ grams} \]

### Summary of Calculated Masses
1. Mass of 1 gram atom of oxygen: **16 grams**
2. Mass of 4.2 gram molecules of \( H_2 \): **8.4 grams**
3. Mass of 2 gram molecules of helium: **8 grams**
4. Mass of 1.6 gram atoms of chlorine: **56.8 grams**

### Conclusion
Now, we compare the calculated masses:
- 16 grams (O)
- 8.4 grams (\( H_2 \))
- 8 grams (He)
- 56.8 grams (Cl)

The minimum mass is **8 grams**, which corresponds to **2 gram molecules of helium**.

### Final Answer
The option with the minimum mass is **(iii) 2 gram molecules of helium**.

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