If the value of Avogadro's number is changed to `1.0 xx 10^20`, what would be the molecular mass of nitrogen gas ?

Answer

To find the molecular mass of nitrogen gas (N₂) when Avogadro's number is changed to \(1.0 \times 10^{20}\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Current Molecular Mass of Nitrogen Gas**:
- The molecular mass of nitrogen gas (N₂) is known to be 28 g/mol. This means that 1 mole of nitrogen gas weighs 28 grams and contains \(6.022 \times 10^{23}\) molecules.

2. **Identify the New Avogadro's Number**:
- The problem states that Avogadro's number is changed to \(1.0 \times 10^{20}\).

3. **Calculate the Mass of One Molecule of Nitrogen Gas**:
- The mass of one molecule of nitrogen gas can be calculated using the formula:
\[ \text{Mass of one molecule} = \frac{\text{Molecular mass}}{\text{Avogadro's number}} \]
- Substituting the values:
\[ \text{Mass of one molecule} = \frac{28 \text{ g/mol}}{6.022 \times 10^{23} \text{ molecules/mol}} \approx 4.65 \times 10^{-23} \text{ g/molecule} \]

4. **Calculate the Mass of \(1.0 \times 10^{20}\) Molecules of Nitrogen Gas**:
- Now, we need to find the mass of \(1.0 \times 10^{20}\) molecules of nitrogen gas:
\[ \text{Mass of } 1.0 \times 10^{20} \text{ molecules} = \text{Mass of one molecule} \times 1.0 \times 10^{20} \]
- Substituting the mass of one molecule:
\[ \text{Mass of } 1.0 \times 10^{20} \text{ molecules} = 4.65 \times 10^{-23} \text{ g/molecule} \times 1.0 \times 10^{20} \approx 4.65 \times 10^{-3} \text{ g} \]

5. **Convert the Mass to Atomic Mass Units (amu)**:
- Since \(1 \text{ g} = 6.022 \times 10^{23} \text{ amu}\), we can convert grams to amu:
\[ \text{Mass in amu} = 4.65 \times 10^{-3} \text{ g} \times 6.022 \times 10^{23} \text{ amu/g} \approx 4.6 \text{ amu} \]

### Final Answer:
The molecular mass of nitrogen gas (N₂) when Avogadro's number is \(1.0 \times 10^{20}\) is approximately **4.6 amu**.