To determine how many grams of magnesium hydroxide (Mg(OH)_2) are present in [tex]\(7.5 \times 10^{23}\)[/tex] formula units, we can follow these steps:
1. Understand the given values:
- Number of formula units: [tex]\(7.5 \times 10^{23}\)[/tex]
- Avogadro's number: [tex]\(6.02 \times 10^{23}\)[/tex] formula units per mole
- Molar mass of Mg(OH)_2: 58.32 grams per mole
2. Convert formula units to moles:
- We know that one mole of any substance contains [tex]\(6.02 \times 10^{23}\)[/tex] formula units.
- Therefore, to find the number of moles, we divide the number of formula units by Avogadro's number.
[tex]\[
\text{moles} = \frac{7.5 \times 10^{23}\ \text{formula units}}{6.02 \times 10^{23}\ \text{formula units/mole}}
\][/tex]
- Calculating this, we get approximately 1.2458471760797343 moles of Mg(OH)_2.
3. Convert moles to grams:
- We know the molar mass of Mg(OH)_2 is 58.32 grams per mole.
- To find the mass in grams, multiply the number of moles by the molar mass.
[tex]\[
\text{grams} = \text{moles} \times \text{molar mass}
\][/tex]
[tex]\[
\text{grams} = 1.2458471760797343\ \text{moles} \times 58.32\ \text{g/mole}
\][/tex]
- Calculating this, we get approximately 72.6578073089701 grams of Mg(OH)_2.
4. Determine which part of the conversion factor goes in the green box:
- The formula units to mole conversion uses Avogadro’s number, [tex]\(6.02 \times 10^{23}\)[/tex], as the conversion factor.
- The conversion of moles to grams involves the molar mass, which is 58.32 grams per mole.
Given the choices:
1) 1 mole
2) [tex]\(6.02 \times 10^{23}\)[/tex] formula units
3) 58.32 grams
The conversion factor to go in the green box is [tex]\(6.02 \times 10^{23}\)[/tex] formula units per mole.
Therefore, 2) [tex]\(6.02 \times 10^{23}\)[/tex] formula units is the correct answer.
To summarize:
[tex]\[
7.5 \times 10^{23}\ \text{formula units} = 1.2458471760797343\ \text{moles} \Rightarrow 72.6578073089701\ \text{grams}
\][/tex]
Answer choice: 2
