Understanding Atomic Mass and Avogadro's Number
In chemistry, the atomic mass of an element is defined as the mass of one mole of its atoms. A mole is a fundamental unit, represented by Avogadro's constant ($N_A$), which is approximately $6.022 \times 10^{23}$ particles (atoms, in this case).
To find the mass of a specific number of atoms, we use the relationship between the molar mass and the number of atoms present.
The Concept
- Atomic Mass of Nitrogen ($N$): The relative atomic mass of Nitrogen is approximately $14$ atomic mass units (u), or $14$ grams per mole (g/mol).
- Avogadro's Law: We know that $1 \text{ mole of Nitrogen} = 14 \text{ grams} = 6.022 \times 10^{23} \text{ atoms}$.
- Unitary Method: Since we know the mass of a massive collection of atoms ($6.022 \times 10^{23}$ atoms), we can find the mass of a single atom by dividing by this constant, then multiply by the requested amount.
Step-by-Step Calculation
Step 1: Identify the values
- Atomic mass of Nitrogen = $14 \text{ g/mol}$
- Avogadro's number ($N_A$) = $6.022 \times 10^{23} \text{ atoms/mol}$
- Number of atoms ($n$) = $2$
Step 2: Set up the formula
The mass of a single atom is given by: $$\text{Mass of 1 atom} = \frac{\text{Molar Mass}}{N_A} = \frac{14}{6.022 \times 10^{23}} \text{ grams}$$
Step 3: Calculate for two atoms
$$\text{Mass of 2 atoms} = 2 \times \left( \frac{14}{6.022 \times 10^{23}} \right)$$ $$\text{Mass of 2 atoms} = \frac{28}{6.022 \times 10^{23}}$$
Step 4: Final calculation
$$\text{Mass} \approx 4.65 \times 10^{-23} \text{ grams}$$
Conclusion
The mass of two nitrogen atoms is incredibly small, approximately $4.65 \times 10^{-23}$ grams. This highlights the extreme scale of atoms; even two atoms are virtually weightless by macroscopic standards, which is why chemists prefer to work in units of 'moles' rather than individual atoms.