Understanding Atomic Mass
To solve for the weight of a specific number of atoms, we need to bridge the gap between the microscopic world (individual atoms) and the macroscopic world (grams).
We use two key concepts:
- Atomic Mass of Oxygen: The atomic mass of a single oxygen atom is approximately 16.00 atomic mass units (u). In molar terms, one mole of oxygen atoms has a mass of 16.00 grams.
- Avogadro’s Number ($N_A$): One mole of any substance contains exactly $6.022 \times 10^{23}$ particles (atoms, in this case). Therefore, $6.022 \times 10^{23}$ atoms of oxygen weigh 16.00 grams.
Step-by-Step Calculation
We are asked to find the weight of 0.5 atoms of oxygen. While it is physically impossible to have half an atom in a stable, isolated state, we can compute the value mathematically using the proportionality of mass.
1. Identify the mass of one atom
The mass of a single oxygen atom is given by: $$\text{Mass of 1 atom} = \frac{\text{Molar Mass}}{N_A}$$ $$\text{Mass of 1 atom} = \frac{16.00 \text{ g/mol}}{6.022 \times 10^{23} \text{ atoms/mol}} \approx 2.657 \times 10^{-23} \text{ g}$$
2. Calculate the mass of 0.5 atoms
To find the mass of 0.5 atoms, we simply multiply the mass of one atom by 0.5: $$\text{Weight} = 0.5 \times (2.657 \times 10^{-23} \text{ g})$$ $$\text{Weight} \approx 1.3285 \times 10^{-23} \text{ g}$$
Conclusion
The weight of 0.5 atoms of oxygen is approximately $1.3285 \times 10^{-23}$ grams.
This exercise illustrates how incredibly small individual atoms are. Even a tiny fraction of an atom represents a mass on the scale of $10^{-23}$ grams, reinforcing why we use units like atomic mass units (u) or moles for chemical calculations rather than standard grams.