To find the mass in grams of a sample of bismuth (Bi) containing [tex]\( 7.35 \times 10^{23} \)[/tex] atoms, follow these steps:
1. Identify the given values:
- Molar mass of bismuth ([tex]\( M \)[/tex]) = [tex]\( 208.98 \, \text{g/mol} \)[/tex]
- Number of atoms ([tex]\( N \)[/tex]) = [tex]\( 7.35 \times 10^{23} \)[/tex] atoms
- Avogadro's number ([tex]\( N_A \)[/tex]) = [tex]\( 6.022 \times 10^{23} \)[/tex] atoms/mol
2. Calculate the number of moles:
The number of moles ([tex]\( n \)[/tex]) can be found using the formula:
[tex]\[
n = \frac{N}{N_A}
\][/tex]
Plugging in the values:
[tex]\[
n = \frac{7.35 \times 10^{23} \, \text{atoms}}{6.022 \times 10^{23} \, \text{atoms/mol}} = 1.2205247426104284 \, \text{mol}
\][/tex]
3. Calculate the mass in grams:
The mass ([tex]\( m \)[/tex]) of the bismuth sample can be calculated using the formula:
[tex]\[
m = n \times M
\][/tex]
Substituting the values:
[tex]\[
m = 1.2205247426104284 \, \text{mol} \times 208.98 \, \text{g/mol} = 255.06526071072733 \, \text{g}
\][/tex]
4. Round the mass to three significant figures:
The final mass should be rounded to three significant figures to match the precision of the given data:
[tex]\[
255.065 \, \text{g}
\][/tex]
Therefore, the mass of the bismuth sample containing [tex]\( 7.35 \times 10^{23} \)[/tex] atoms is [tex]\( \boxed{255.065} \, \text{g} \)[/tex].
