Sure! Let's go through the detailed, step-by-step solution of how to find the number of formula units in a given mass of copper(II) chloride ([tex]$CuCl_2$[/tex]).
### Step 1: Identify the data
- The mass of the sample of [tex]$CuCl_2$[/tex] is given as [tex]\(17.6 \, \text{g}\)[/tex].
- The molar mass of [tex]$CuCl_2$[/tex] is given as [tex]\(134.45 \, \text{g/mol}\)[/tex].
- Avogadro's number, which is the number of formula units in one mole, is [tex]\(6.022 \times 10^{23} \, \text{units/mol}\)[/tex].
### Step 2: Calculate the number of moles of [tex]$CuCl_2$[/tex] in the sample
To find the number of moles, use the formula:
[tex]\[
\text{moles} = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
Substituting the given values:
[tex]\[
\text{moles of } CuCl_2 = \frac{17.6 \, \text{g}}{134.45 \, \text{g/mol}} = 0.13090368166604688 \, \text{mol}
\][/tex]
### Step 3: Calculate the number of formula units
To find the number of formula units, multiply the number of moles by Avogadro's number:
[tex]\[
\text{number of formula units} = \text{moles} \times \text{Avogadro's number}
\][/tex]
Substituting the values:
[tex]\[
\text{number of formula units} = 0.13090368166604688 \, \text{mol} \times 6.022 \times 10^{23} \, \text{units/mol} = 7.883203969951656 \times 10^{22} \, \text{units}
\][/tex]
### Step 4: Select the closest answer
Given the result [tex]\(7.883203969951656 \times 10^{22}\)[/tex]:
- [tex]$7.88 \times 10^{22}$[/tex] formula units
- [tex]$1.84 \times 10^{23}$[/tex] formula units
- [tex]$1.91 \times 10^{23}$[/tex] formula units
- [tex]$1.42 \times 10^{24}$[/tex] formula units
The answer that best matches our calculated result is:
[tex]\[
\boxed{7.88 \times 10^{22} \text{ formula units}}
\][/tex]
Therefore, there are approximately [tex]\(7.88 \times 10^{22}\)[/tex] formula units of [tex]$CuCl_2$[/tex] in [tex]\(17.6 \, \text{g}\)[/tex] of [tex]$CuCl_2$[/tex].
