To find the mass in grams of [tex]\(4.8 \times 10^{24}\)[/tex] atoms of sodium, we need to use the concepts of moles and Avogadro's number. Follow these steps:
1. Find the number of moles of sodium:
- We use Avogadro's number, which tells us the number of atoms in one mole of a substance. Avogadro's number is [tex]\(6.022 \times 10^{23}\)[/tex] atoms/mole.
- Divide the number of atoms ([tex]\(4.8 \times 10^{24}\)[/tex]) by Avogadro's number to find the number of moles.
[tex]\[
\text{Number of moles} = \frac{4.8 \times 10^{24} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mole}} \approx 7.971 \text{ moles}
\][/tex]
2. Calculate the mass in grams:
- Now, we use the atomic mass of sodium. The atomic mass of sodium (Na) is 23 grams/mole.
- Multiply the number of moles by the atomic mass to find the mass in grams.
[tex]\[
\text{Mass in grams} = 7.971 \text{ moles} \times 23 \text{ grams/mole} \approx 183.33 \text{ grams}
\][/tex]
Thus, the mass of [tex]\(4.8 \times 10^{24}\)[/tex] atoms of sodium is approximately 183.33 grams.
