Question

Calculate the molar mass for each of the following compounds: a. \(\mathrm{FeSO}_{4}\) (iron supplement) b. \(\mathrm{Al}_{2} \mathrm{O}_{3}\) (absorbent and abrasive) c. \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{NO}_{3} \mathrm{~S}\) (saccharin) d. \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}\) (rubbing alcohol) e. \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}\) (baking powder) f. \(\mathrm{Zn}\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)_{2}\) (zinc dietary supplement)

Short answer

a. 151.92 g/mol, b. 101.96 g/mol, c. 183.19 g/mol, d. 60.09 g/mol, e. 96.09 g/mol, f. 183.48 g/mol.

Step-by-step solution

- Write down the atomic masses of the elements

Identify the atomic masses of each element present in the compounds from the periodic table. For example: Fe = 55.85, S = 32.07, O = 16.00, Al = 26.98, C = 12.01, H = 1.01, N = 14.01, Zn = 65.38.

- Calculate the molar mass for \( \text{FeSO}_{4} \)

Use the formula: \( \text{Molar mass of FeSO}_4 = \text{mass of Fe} + \text{mass of S} + 4 \times \text{mass of O} = 55.85 + 32.07 + 4 \times 16.00 = 151.92 \text{ g/mol} \)

- Calculate the molar mass for \( \text{Al}_2{\text{O}}_3 \)

Use the formula: \( \text{Molar mass of Al}_2{\text{O}}_3 = 2 \times \text{mass of Al} + 3 \times \text{mass of O} = 2 \times 26.98 + 3 \times 16.00 = 101.96 \text{ g/mol} \)

- Calculate the molar mass for \( \text{C}_7{\text{H}}_5{\text{NO}}_3{\text{S}} \)

Use the formula: \( {\text{Molar mass of C}}_7{\text{H}}_5{\text{NO}}_3{\text{S}} = 7 \times \text{mass of C} + 5 \times \text{mass of H} + \text{mass of N} + 3 \times \text{mass of O} + \text{mass of S} = 7 \times 12.01 + 5 \times 1.01 + 14.01 + 3 \times 16.00 + 32.07 = 183.19 \text{ g/mol} \)

- Calculate the molar mass for \( \text{C}_3{\text{H}}_8{\text{O}} \)

Use the formula: \( \text{Molar mass of C}_3{\text{H}}_8{\text{O}} = 3 \times \text{mass of C} + 8 \times \text{mass of H} + \text{mass of O} = 3 \times 12.01 + 8 \times 1.01 + 16.00 = 60.09 \text{ g/mol} \)

- Calculate the molar mass for \( \text{(NH}_4)_2{\text{CO}}_3 \)

Use the formula: \( \text{Molar mass of (NH}_4)_2{\text{CO}}_3 = 2 \times (\text{mass of N} + 4 \times \text{mass of H}) + \text{mass of C} + 3 \times \text{mass of O} = 2 \times (14.01 + 4 \times 1.01) + 12.01 + 3 \times 16.00 = 96.09 \text{ g/mol} \)

- Calculate the molar mass for \( \text{Zn}\text{(C}_2{\text{H}}_3{\text{O}}_2)_2 \)

Use the formula: \( \text{Molar mass of Zn(C}_2{\text{H}}_3{\text{O}}_2)_2 = \text{mass of Zn} + 2 \times (2 \times \text{mass of C} + 3 \times \text{mass of H} + 2 \times \text{mass of O}) = 65.38 + 2 \times (2 \times 12.01 + 3 \times 1.01 + 2 \times 16.00) = 183.48 \text{ g/mol} \)

Key concepts

Atomic Mass

Understanding atomic mass is crucial in chemistry. Atomic mass refers to the mass of a single atom, usually measured in atomic mass units (amu). Each element's atomic mass can be found on the periodic table and represents the average mass of the atoms, taking into account isotopes and their relative abundance. For example, you can find that:

• Iron (Fe) has an atomic mass of 55.85 amu.
• Sulfur (S) has an atomic mass of 32.07 amu.
• Oxygen (O) has an atomic mass of 16.00 amu.

Knowing these atomic masses allows you to calculate the molar mass of compounds by summing the atomic masses of all constituent atoms.

Molecular Formula

A molecular formula provides the number and type of atoms in a molecule. This information is vital when calculating molar mass. For instance, the molecular formula of saccharin is \(\mathrm{C}_7\mathrm{H}_5\mathrm{NO}_3\mathrm{S}\), indicating it contains:

• 7 Carbon (C) atoms
• 5 Hydrogen (H) atoms
• 1 Nitrogen (N) atom
• 3 Oxygen (O) atoms
• 1 Sulfur (S) atom

Each atom type's number is then multiplied by its atomic mass to derive the molar mass. For saccharin: \ M = 7(12.01) + 5(1.01) + 14.01 + 3(16.00) + 32.07 = 183.19 \text{ g/mol} \

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It uses the balanced chemical equation to relate quantities. For molar mass calculations, stoichiometry ensures that each element's atomic mass is multiplied by the correct number of atoms in the molecular formula. Consider aluminum oxide \(\mathrm{Al}_2\mathrm{O}_3\) for example. Here, we see it has:

• 2 Aluminum (Al) atoms
• 3 Oxygen (O) atoms

To calculate its molar mass:
\ M = 2(26.98) + 3(16.00) = 101.96 \text{ g/mol} \ Correct stoichiometric coefficients ensure accurate molar mass.

Periodic Table

The periodic table is a fundamental tool in chemistry, organizing elements by increasing atomic number and similar chemical properties. Atomic masses and other vital information are provided for each element. When calculating molar mass, the periodic table helps you quickly locate atomic masses. For instance,
if given the task to find the molar mass of iron sulfate \(\mathrm{FeSO}_4\):

• Iron (Fe): Atomic mass = 55.85
• Sulfur (S): Atomic mass = 32.07
• Oxygen (O): Atomic mass = 16.00

Summing these gives: \ M = 55.85 + 32.07 + 4(16.00) = 151.92 \text{ g/mol} \ The periodic table ensures this process is clear and accurate.