How many grams of $Mg(OH)_2$ are in $7.5 \times 10^{23}$ formula units (f.un.) of $Mg(OH)_2$?
Answer (2)
Convert formula units to moles: 7.5 × 1 0 23 f.un. × 6.02 × 1 0 23 f.un. 1 mole
Convert moles to grams: moles × 1 mole 58.32 g
Calculate the mass: 6.02 × 1 0 23 7.5 × 1 0 23 × 58.32 ≈ 72.66 g
Round to the nearest whole number: 73 g
Explanation
Problem Analysis We are asked to find the mass in grams of 7.5 × 1 0 23 formula units of M g ( O H ) 2 . We will use the given conversion factors to convert from formula units to moles and then from moles to grams.
Solution Plan First, we convert formula units to moles using the conversion factor 1 mole = 6.02 × 1 0 23 formula units .
Then, we convert moles to grams using the molar mass of M g ( O H ) 2 , which is 58.32 g/mol.
We multiply the given number of formula units by the two conversion factors to obtain the mass in grams:
mass (g) = 7.5 × 1 0 23 f.un. × 6.02 × 1 0 23 f.un. 1 mole × 1 mole 58.32 g
Calculations Now, we perform the calculation:
mass (g) = 6.02 × 1 0 23 7.5 × 1 0 23 × 58.32 g
mass (g) = 6.02 7.5 × 58.32 g
mass (g) = 6.02 437.4 g
mass (g) ≈ 72.66 g
Rounding to the nearest whole number, we get 73 g.
Final Answer Therefore, there are approximately 73 grams of M g ( O H ) 2 in 7.5 × 1 0 23 formula units of M g ( O H ) 2 .
Examples
This calculation is essential in chemistry for converting between the number of individual molecules or formula units and the mass of a substance. For instance, if you're conducting an experiment that requires a specific number of magnesium hydroxide formula units, you need to convert that number into a mass that you can measure using a balance. This is crucial in preparing solutions of specific concentrations or in stoichiometric calculations for chemical reactions. Knowing how to perform these conversions allows for accurate and reproducible experimental results.
The mass of M g ( O H ) 2 in 7.5 × 1 0 23 formula units is approximately 74 grams. This is calculated by converting formula units to moles using Avogadro's number and then converting moles to grams using the molar mass of M g ( O H ) 2 .
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