To find the mass of [tex]$5.30 \times 10^{22}$[/tex] formula units of barium nitrate [tex]$\left( Ba \left( NO_3\right)_2 \right)$[/tex], we can follow a series of steps systematically. Here's the detailed solution:
1. Given Information:
- Molar mass of [tex]$\left( Ba \left( NO_3 \right)_2 \right)$[/tex]: [tex]\( 261.35 \, \text{g/mol} \)[/tex]
- Number of formula units: [tex]\( 5.30 \times 10^{22} \)[/tex]
2. Avogadro's Number:
- Avogadro's number defines the number of formula units in one mole of a substance, which is [tex]\( 6.022 \times 10^{23} \)[/tex] formula units/mol.
3. Calculate the Moles:
- The number of moles of [tex]$\left( Ba \left( NO_3 \right)_2 \right)$[/tex] can be found using the formula:
[tex]\[
\text{Moles} = \frac{\text{Number of Formula Units}}{\text{Avogadro's Number}}
\][/tex]
- Plugging in the values:
[tex]\[
\text{Moles} = \frac{5.30 \times 10^{22}}{6.022 \times 10^{23}} \approx 0.08801062769843906 \, \text{moles}
\][/tex]
4. Calculate the Mass:
- The mass can then be found using the formula:
[tex]\[
\text{Mass} = \text{Moles} \times \text{Molar Mass}
\][/tex]
- Using the given molar mass:
[tex]\[
\text{Mass} \approx 0.08801062769843906 \, \text{moles} \times 261.35 \, \text{g/mol} \approx 23.00157754898705 \, \text{g}
\][/tex]
5. Select the Closest Answer:
- Among the options given:
\begin{itemize}
\item [tex]$0.0900 \, \text{g}$[/tex]
\item [tex]$12.0 \, \text{g}$[/tex]
\item [tex]$23.0 \, \text{g}$[/tex]
\item [tex]$3,130 \, \text{g}$[/tex]
\end{itemize}
- The calculated mass rounds to [tex]$23.0 \, \text{g}$[/tex], which matches the given option.
Therefore, the mass of [tex]$5.30 \times 10^{22}$[/tex] formula units of [tex]$\left( Ba \left( NO_3 \right)_2 \right)$[/tex] is approximately [tex]\(23.0 \, \text{g}\)[/tex].
The correct answer is:
[tex]\[
\boxed{23.0 \, \text{g}}
\][/tex]
