To determine the mass of [tex]\( 5.30 \times 10^{22} \)[/tex] formula units of barium nitrate [tex]\((Ba(NO_3)_2)\)[/tex], we can follow these steps:
1. Understand what is given:
- Molar mass of barium nitrate [tex]\((Ba(NO_3)_2)\)[/tex] is [tex]\( 261.35 \, \text{g/mol} \)[/tex].
- Number of formula units, [tex]\( 5.30 \times 10^{22} \)[/tex].
2. Use Avogadro's number:
- Avogadro's number [tex]\( 6.022 \times 10^{23} \, \text{units/mol} \)[/tex] tells us how many formula units are in one mole.
3. Calculate the number of moles:
To find the number of moles corresponding to [tex]\( 5.30 \times 10^{22} \)[/tex] formula units, divide the number of formula units by Avogadro's number:
[tex]\[
\text{Number of moles} = \frac{5.30 \times 10^{22}}{6.022 \times 10^{23}}
\][/tex]
Through calculation, we find:
[tex]\[
\text{Number of moles} \approx 0.0880 \, \text{moles}
\][/tex]
4. Calculate the mass:
Multiply the number of moles by the molar mass to get the mass:
[tex]\[
\text{Mass} = \text{Number of moles} \times \text{Molar mass}
\][/tex]
Substituting the values:
[tex]\[
\text{Mass} = 0.0880 \, \text{moles} \times 261.35 \, \text{g/mol}
\][/tex]
This gives:
[tex]\[
\text{Mass} \approx 23.0 \, \text{grams}
\][/tex]
Thus, the mass of [tex]\( 5.30 \times 10^{22} \)[/tex] formula units of [tex]\( Ba(NO_3)_2 \)[/tex] is approximately [tex]\(23.0 \, \text{g}\)[/tex]. Therefore, the correct choice is:
[tex]\[ 23.0 \, \text{g} \][/tex]
