To determine the number of atoms of germanium present in a sample containing 4.20 moles of germanium (Ge), we need to use Avogadro's number. Avogadro's number is [tex]\( 6.022 \times 10^{23} \)[/tex] atoms per mole, which is a fundamental constant used to convert between moles and number of atoms.
Here are the step-by-step calculations:
1. We start with the given quantity of germanium in moles:
[tex]\[ \text{Moles of Ge} = 4.20 \, \text{moles} \][/tex]
2. To find the number of atoms, we multiply the number of moles by Avogadro's number:
[tex]\[ \text{Number of atoms} = \text{Moles of Ge} \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of atoms} = 4.20 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole} \][/tex]
3. Performing the multiplication:
[tex]\[ \text{Number of atoms} = 4.20 \times 6.022 \times 10^{23} \][/tex]
[tex]\[ \text{Number of atoms} = 2.529 \times 10^{24} \, \text{atoms} \][/tex]
Therefore, the number of atoms of germanium in a sample containing 4.20 moles of Ge is [tex]\( 2.529 \times 10^{24} \)[/tex] atoms.
