To determine the mass of 2.80 x 10^23 atoms of zinc, we need to follow a series of logical steps involving the principles of chemistry and mathematics.
1. Find Avogadro's Number: Avogadro's number (6.02214076 × 10^23 mol^-1) is used to calculate the number of particles (atoms, molecules, etc.) in one mole of a substance. This provides a bridge between the microscopic scale (atoms) and the macroscopic scale (moles).
2. Determine the Atomic Mass of Zinc: The atomic mass of zinc is 65.38 grams per mole. This value tells us how many grams one mole of zinc weighs.
3. Calculate the Number of Moles of Zinc:
- Given number of atoms: [tex]\( 2.80 \times 10^{23} \)[/tex]
- Avogadro's number: [tex]\( 6.02214076 \times 10^{23} \text{ atoms/mol} \)[/tex]
- Number of moles ([tex]\( n \)[/tex]) = [tex]\(\frac{\text{Number of atoms}}{\text{Avogadro's number}} \)[/tex]
[tex]\[
n = \frac{2.80 \times 10^{23}}{6.02214076 \times 10^{23}}
\][/tex]
4. Convert the Number of Moles to Mass:
- Number of moles of zinc was calculated previously.
- Molar mass of zinc: 65.38 g/mol
- Mass ([tex]\( m \)[/tex]) = Number of moles ([tex]\( n \)[/tex]) [tex]\(\times \)[/tex] Molar mass
[tex]\[
m = n \times 65.38 \text{ g/mol}
\][/tex]
After carrying out these steps, we find that:
1. The number of moles of zinc is approximately 0.464950938808677 mol.
2. The mass of these moles of zinc is approximately 30.3984923793113 grams.
Therefore, the mass of 2.80 x 10^23 atoms of zinc is approximately 30.40 grams.
