Answered

Use the periodic table to calculate the molar mass of each of the following compounds. Each answer must have 2 decimal places.


  1. Ammonia (NH₃)
  2. Magnesium hydroxide (Mg(OH)₂)
  3. Iron(III) oxide (Fe₂O₃)

Verified Answer :

  • Identify the atomic masses for each element (N: 14.01, H: 1.01, Mg: 24.31, O: 16.00, Fe: 55.85 g/mol).
  • Calculate molar mass of \(\text{NH}_3 = 14.01 + 3(1.01) = 17.04 \text{ g/mol}\).
  • Calculate molar mass of \(\text{Mg(OH)}_2 = 24.31 + 2(16.00) + 2(1.01) = 58.33 \text{ g/mol}\).
  • Calculate molar mass of \(\text{Fe}_2\text{O}_3 = 2(55.85) + 3(16.00) = 159.70 \text{ g/mol}\).
  • Final answers: \(\text{NH}_3: \boxed{17.04 \text{ g/mol}}\), \(\text{Mg(OH)}_2: \boxed{58.33 \text{ g/mol}}\), \(\text{Fe}_2\text{O}_3: \boxed{159.70 \text{ g/mol}}\).

Explanation

  1. Analysis of the Problem and Data

To determine the molar mass of a chemical compound, we sum the atomic masses of all the atoms present in its chemical formula. We use the standard atomic masses (in g/mol) for each element:

  • Nitrogen (N): 14.01 g/mol
  • Hydrogen (H): 1.01 g/mol
  • Magnesium (Mg): 24.31 g/mol
  • Oxygen (O): 16.00 g/mol
  • Iron (Fe): 55.85 g/mol

The goal is to calculate the molar masses for Ammonia (\(\text{NH}_3\)), Magnesium hydroxide (\(\text{Mg(OH)}_2\)), and Iron(III) oxide (\(\text{Fe}_2\text{O}_3\)) using these atomic values and providing the results rounded to two decimal places.

  1. Calculating the Molar Mass of Ammonia (\(\text{NH}_3\))

For ammonia, the chemical formula is \(\text{NH}_3\), which consists of one nitrogen atom and three hydrogen atoms.
The molar mass is calculated as:
\[M(\text{NH}_3) = 1 \times M(\text{N}) + 3 \times M(\text{H})\]
\[M(\text{NH}_3) = 1 \times 14.01 + 3 \times 1.01 = 14.01 + 3.03 = 17.04 \text{ g/mol}\]
Thus, the molar mass of ammonia is 17.04 g/mol.

  1. Calculating the Molar Mass of Magnesium Hydroxide (\(\text{Mg(OH)}_2\))

For magnesium hydroxide, the chemical formula is \(\text{Mg(OH)}_2\), which consists of one magnesium atom, two oxygen atoms, and two hydrogen atoms.
The molar mass is calculated as:
\[M(\text{Mg(OH)}_2) = 1 \times M(\text{Mg}) + 2 \times M(\text{O}) + 2 \times M(\text{H})\]
\[M(\text{Mg(OH)}_2) = 1 \times 24.31 + 2 \times 16.00 + 2 \times 1.01\]
\[M(\text{Mg(OH)}_2) = 24.31 + 32.00 + 2.02 = 58.33 \text{ g/mol}\]
Thus, the molar mass of magnesium hydroxide is 58.33 g/mol.

  1. Calculating the Molar Mass of Iron(III) Oxide (\(\text{Fe}_2\text{O}_3\))

For iron(III) oxide, the chemical formula is \(\text{Fe}_2\text{O}_3\), which consists of two iron atoms and three oxygen atoms.
The molar mass is calculated as:
\[M(\text{Fe}_2\text{O}_3) = 2 \times M(\text{Fe}) + 3 \times M(\text{O})\]
\[M(\text{Fe}_2\text{O}_3) = 2 \times 55.85 + 3 \times 16.00\]
\[M(\text{Fe}_2\text{O}_3) = 111.70 + 48.00 = 159.70 \text{ g/mol}\]
Thus, the molar mass of iron(III) oxide is 159.70 g/mol.

  1. Conclusion

The calculated molar masses for the requested compounds are:

  • Ammonia (\(\text{NH}_3\)): \(\boxed{17.04 \text{ g/mol}}\)
  • Magnesium hydroxide (\(\text{Mg(OH)}_2\)): \(\boxed{58.33 \text{ g/mol}}\)
  • Iron(III) oxide (\(\text{Fe}_2\text{O}_3\)): \(\boxed{159.70 \text{ g/mol}}\)

Examples

Calculating molar masses is fundamental in chemistry for determining stoichiometric ratios in chemical reactions. For instance, if you were preparing a laboratory solution of magnesium hydroxide to neutralize an acid, you would need its molar mass to calculate exactly how many grams are required to react with a specific number of moles of acid. This ensures that the chemical reaction proceeds efficiently and without excess reagents, a vital practice in pharmaceutical and industrial chemical processes.