To find the mass in grams of [tex]\(4.8 \times 10^{24}\)[/tex] atoms of sodium, let's follow these steps:
1. Determine the number of moles of sodium:
- We start by using Avogadro's number, which is [tex]\(6.022 \times 10^{23}\)[/tex] atoms per mole.
- To find the number of moles, we divide the given number of sodium atoms by Avogadro's number:
[tex]\[
\text{Number of moles} = \frac{4.8 \times 10^{24} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mole}}
\][/tex]
- After doing the division, we get:
[tex]\[
\text{Number of moles} = 7.970773829292594 \text{ moles}
\][/tex]
2. Determine the molar mass of sodium:
- The molar mass of sodium is given as [tex]\(22.99 \text{ grams/mole}\)[/tex].
3. Calculate the mass in grams:
- Now we need to multiply the number of moles of sodium by its molar mass to find the mass in grams:
[tex]\[
\text{Mass} = \text{Number of moles} \times \text{Molar mass}
\][/tex]
[tex]\[
\text{Mass} = 7.970773829292594 \text{ moles} \times 22.99 \text{ grams/mole}
\][/tex]
- This calculation yields:
[tex]\[
\text{Mass} = 183.24809033543673 \text{ grams}
\][/tex]
So, the mass of [tex]\(4.8 \times 10^{24}\)[/tex] atoms of sodium is approximately 183.25 grams.
