Question

Determine the molar masses of these compounds: (a) \(\mathrm{KBr}\) (f) \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) (b) \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) (g) \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) (c) \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) (h) \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) (d) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) (i) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\) (e) \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\)

Short answer

KBr: 119.00 g/mol, \text{Na}_{2} \text{SO}_{4}: 142.04 g/mol, \text{Pb}(\text{NO}_{3})_{2}: 331.22 g/mol, \text{C}_{2} \text{H}_{5} \text{OH}: 46.08 g/mol, \text{HC}_{2} \text{H}_{3} \text{O}_{2}: 60.06 g/mol, \text{Fe}_{3} \text{O}_{4}: 231.55 g/mol, \text{C}_{12} \text{H}_{22} \text{O}_{11}: 342.34 g/mol, \text{Al}_{2} (\text{SO}_{4})_{3}: 342.14 g/mol, (\text{NH}_{4})_{2} \text{HPO}_{4}: 131.07 g/mol

Step-by-step solution

- Calculate Molar Mass of \(\text{KBr}\)

Determine the atomic masses: K (\text{39.10 g/mol}), Br (\text{79.90 g/mol}). Sum these values to find the molar mass of \(\text{KBr}\). \[39.10 + 79.90 = 119.00 \text{ g/mol}\]

- Calculate Molar Mass of \(\text{Na}_{2} \text{SO}_{4}\)

Determine the atomic masses: Na (\text{22.99 g/mol}), S (\text{32.06 g/mol}), O (\text{16.00 g/mol}). Sum accordingly: \[2(22.99) + 32.06 + 4(16.00) = 45.98 + 32.06 + 64.00 = 142.04 \text{ g/mol}\]

- Calculate Molar Mass of \(\text{Pb}(\text{NO}_{3})_{2}\)

Determine the atomic masses: Pb (\text{207.20 g/mol}), N (\text{14.01 g/mol}), O (\text{16.00 g/mol}). Sum accordingly: \[207.20 + 2(14.01 + 3(16.00)) = 207.20 + 2(14.01 + 48.00) = 207.20 + 2(62.01) = 207.20 + 124.02 = 331.22 \text{ g/mol}\]

- Calculate Molar Mass of \(\text{C}_{2} \text{H}_{5} \text{OH}\)

Determine the atomic masses: C (\text{12.01 g/mol}), H (\text{1.01 g/mol}), O (\text{16.00 g/mol}). Sum accordingly: \[2(12.01) + 6(1.01) + 16.00 = 24.02 + 6.06 + 16.00 = 46.08 \text{ g/mol}\]

- Calculate Molar Mass of \(\text{HC}_{2} \text{H}_{3} \text{O}_{2}\)

Determine the atomic masses: H (\text{1.01 g/mol}), C (\text{12.01 g/mol}), O (\text{16.00 g/mol}). Sum accordingly: \[1.01 + 2(12.01) + 3(1.01) + 2(16.00) = 1.01 + 24.02 + 3.03 + 32.00 = 60.06 \text{ g/mol}\]

- Calculate Molar Mass of \(\text{Fe}_{3} \text{O}_{4}\)

Determine the atomic masses: Fe (\text{55.85 g/mol}), O (\text{16.00 g/mol}). Sum accordingly: \[3(55.85) + 4(16.00) = 167.55 + 64.00 = 231.55 \text{ g/mol}\]

- Calculate Molar Mass of \(\text{C}_{12} \text{H}_{22} \text{O}_{11}\)

Determine the atomic masses: C (\text{12.01 g/mol}), H (\text{1.01 g/mol}), O (\text{16.00 g/mol}). Sum accordingly: \[12(12.01) + 22(1.01) + 11(16.00) = 144.12 + 22.22 + 176.00 = 342.34 \text{ g/mol}\]

- Calculate Molar Mass of \(\text{Al}_{2} (\text{SO}_{4})_{3}\)

Determine the atomic masses: Al (\text{26.98 g/mol}), S (\text{32.06 g/mol}), O (\text{16.00 g/mol}). Sum accordingly: \[2(26.98) + 3(32.06 + 4(16.00)) = 53.96 + 3(32.06 + 64.00) = 53.96 + 3(96.06) = 53.96 + 288.18 = 342.14 \text{ g/mol}\]

- Calculate Molar Mass of \((\text{NH}_{4})_{2} \text{HPO}_{4}\)

Determine the atomic masses: N (\text{14.01 g/mol}), H (\text{1.01 g/mol}), P (\text{30.97 g/mol}), O (\text{16.00 g/mol}). Sum accordingly: \[2(14.01 + 4(1.01)) + 30.97 + 4(16.00) = 2(14.01 + 4.04) + 30.97 + 64.00 = 2(18.05) + 30.97 + 64.00 = 36.10 + 30.97 + 64.00 = 131.07 \text{ g/mol}\]

Key concepts

Chemical Compounds

Chemical compounds are substances formed when two or more elements chemically bond together in fixed proportions. These compounds are represented by chemical formulas which denote the types and numbers of atoms included. For instance, in the chemical compound \(\text{KBr}\), one potassium (K) atom is bonded with one bromine (Br) atom. This understanding is crucial when calculating molar masses since it informs us of the number of each type of atom present.

Atomic Mass

Atomic mass is a measure of the mass of an individual atom, typically given in atomic mass units (amu). It represents the mass of protons and neutrons in the atom's nucleus, as electrons have negligible mass. For example, the atomic mass of potassium (K) is approximately 39.10 g/mol, which means one mole of potassium atoms weighs 39.10 grams. Understanding atomic masses is crucial for calculating the molar masses of chemical compounds, which involves summing the atomic masses of all atoms in the compound.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It relies heavily on the concept of the mole and molar mass, enabling chemists to predict yields and reactant usage. For example, to find the molar mass of \(\text{Na}_{2} \text{SO}_{4}\), the stoichiometric ratios of sodium (Na), sulfur (S), and oxygen (O) atoms need to be identified and multiplied by their respective atomic masses. After finding these amounts, you sum them to get the total molar mass. Mastery of stoichiometry is key to solving many chemistry problems, as it connects the macroscopic and atomic scales.