Which one of the following is the lighest?

Options

A. 0.2 mole of hydrogen gas
B. `6.023xx10^(22)` molecules of nitrogen
C. 0.1 g of silver
D. 0.1 mole of oxygen gas

Explanation

To determine which of the given options is the lightest, we will calculate the weight of each substance based on the information provided. We will analyze each option step by step.

### Step 1: Calculate the weight of 0.2 moles of Hydrogen (H2)
- The molecular mass of hydrogen (H2) is 2 grams per mole.
- For 0.2 moles:
\[ \text{Weight} = \text{Number of moles} \times \text{Molecular mass} = 0.2 \, \text{moles} \times 2 \, \text{g/mol} = 0.4 \, \text{grams} \]

### Step 2: Calculate the weight of 6.023 x 10^22 molecules of Nitrogen (N2)
- First, we need to convert the number of molecules to moles. We know that 1 mole contains approximately 6.022 x 10^23 molecules.
- Therefore, the number of moles of nitrogen is:
\[ \text{Number of moles} = \frac{6.023 \times 10^{22}}{6.022 \times 10^{23}} \approx 0.1 \, \text{moles} \]
- The molecular mass of nitrogen (N2) is 28 grams per mole (14 grams per atom × 2).
- Now, calculate the weight:
\[ \text{Weight} = 0.1 \, \text{moles} \times 28 \, \text{g/mol} = 2.8 \, \text{grams} \]

### Step 3: Weight of 0.1 grams of Silver (Ag)
- The weight is already given as:
\[ \text{Weight} = 0.1 \, \text{grams} \]

### Step 4: Calculate the weight of 0.1 moles of Oxygen (O2)
- The molecular mass of oxygen (O2) is 32 grams per mole.
- For 0.1 moles:
\[ \text{Weight} = 0.1 \, \text{moles} \times 32 \, \text{g/mol} = 3.2 \, \text{grams} \]

### Step 5: Compare the weights calculated
- Hydrogen (H2): 0.4 grams
- Nitrogen (N2): 2.8 grams
- Silver (Ag): 0.1 grams
- Oxygen (O2): 3.2 grams

### Conclusion
The lightest substance among the given options is **0.1 grams of Silver (Ag)**.