How many grams of $Mg(OH)_2$ are in $7.5 \times 10^{23}$ formula units (f.un.) of $Mg(OH)_2$? Which part of the conversion factor goes in the green box?
$6.02 \times 10^{23}$ f.un.
58.32 g
1 mole
Answer (2)
Convert formula units to moles using Avogadro's number: 6.02 × 1 0 23 7.5 × 1 0 23 = 1.2458 moles.
Convert moles to grams using the molar mass of M g ( O H ) 2 : 1.2458 mol × 58.32 g/mol = 72.6578 g.
The missing part of the conversion factor is the molar mass of M g ( O H ) 2 , which is 58.32 g.
The mass of 7.5 × 1 0 23 formula units of M g ( O H ) 2 is approximately 72.66 g .
Explanation
Problem Setup and Strategy We are given 7.5 × 1 0 23 formula units of M g ( O H ) 2 and asked to find the corresponding mass in grams. We will use the molar mass of M g ( O H ) 2 and Avogadro's number to convert from formula units to grams.
Converting Formula Units to Moles First, we need to convert the number of formula units to moles. We know that 1 mole of any substance contains Avogadro's number of formula units ( 6.02 × 1 0 23 f.un./mol). Therefore, we can set up the conversion as follows:
moles of M g ( O H ) 2 = 6.02 × 1 0 23 f.un./mol 7.5 × 1 0 23 f.un.
moles of M g ( O H ) 2 = 1.2458 mol
Converting Moles to Grams Next, we convert moles of M g ( O H ) 2 to grams using the molar mass of M g ( O H ) 2 , which is 58.32 g/mol:
grams of M g ( O H ) 2 = 1.2458 mol × 58.32 g/mol
grams of M g ( O H ) 2 = 72.6578 g
Identifying the Missing Conversion Factor Finally, we need to identify the missing part of the conversion factor in the table. The table shows the conversion from formula units to moles, and then from moles to grams. The missing part is the conversion from moles to grams, which is the molar mass of M g ( O H ) 2 . Therefore, the missing part is 58.32 g.
Final Answer and Conclusion Therefore, 7.5 × 1 0 23 formula units of M g ( O H ) 2 is equal to approximately 72.66 grams. The missing part of the conversion factor is 58.32 g.
Examples
Magnesium hydroxide, M g ( O H ) 2 , is often used in antacids to neutralize stomach acid. If a tablet contains 7.5 × 1 0 23 formula units of M g ( O H ) 2 , we can calculate the mass of M g ( O H ) 2 in the tablet to ensure the correct dosage. This calculation helps in determining the effectiveness and safety of the antacid tablet. Knowing the mass allows for proper formulation and quality control in pharmaceutical applications.
The mass of 7.5 × 1 0 23 formula units of M g ( O H ) 2 is approximately 72.66 grams. The missing conversion factor for the mass is the molar mass of M g ( O H ) 2 , which is 58.32 g. Therefore, to convert to grams, the value needed in the green box is 58.32 g.
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