To determine how many grams of magnesium hydroxide (Mg(OH)₂) are present in [tex]\(7.5 \times 10^{23}\)[/tex] formula units, we will proceed with the following steps:
1. Find the molar mass of Mg(OH)₂:
- Magnesium (Mg) has a molar mass of 24.305 g/mol.
- Oxygen (O) has a molar mass of 16.00 g/mol, but there are 2 oxygen atoms, so: [tex]\(16.00 \times 2\)[/tex]
- Hydrogen (H) has a molar mass of 1.008 g/mol, but there are 2 hydrogen atoms, so: [tex]\(1.008 \times 2\)[/tex]
Hence, the molar mass of Mg(OH)₂ is:
[tex]\[
24.305 + (2 \times 16.00) + (2 \times 1.008) = 58.321 \, \text{g/mol}
\][/tex]
2. Convert formula units to moles:
The conversion factor needed to convert formula units to moles involves Avogadro's number, which is [tex]\(6.02 \times 10^{23}\)[/tex] formula units/mole.
[tex]\[
\frac{7.5 \times 10^{23} \, \text{formula units}}{6.02 \times 10^{23} \, \text{formula units/mole}} = 1.2458471760797343 \, \text{moles}
\][/tex]
3. Convert moles to grams:
Once we have the number of moles, we multiply it by the molar mass to get the mass in grams.
[tex]\[
1.2458471760797343 \, \text{moles} \times 58.321 \, \text{g/mol} = 72.65905315614619 \, \text{grams}
\][/tex]
So, the mass of magnesium hydroxide in [tex]\(7.5 \times 10^{23}\)[/tex] formula units is approximately 72.659 g.
Regarding the conversion factor in the box:
To convert from formula units to moles, the denominator of the conversion factor should match with formula units and the numerator should be moles. As such, the correct conversion factor to use is [tex]\( \frac{1 \, \text{mole}}{6.02 \times 10^{23} \, \text{fun}} \)[/tex].
Thus, the correct answer choice that represents the denominator in the green box is:
2) [tex]\(6.02 \times 10^{23}\)[/tex] fun
So, enter the answer choice number:
2
