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

Molar masses in g/mol are: (a) 119.00, (f) 231.55, (b) 142.04, (g) 342.29, (c) 331.22, (h) 342.14, (d) 46.07, (i) 131.05, (e) 60.05.

Step-by-step solution

Determine Atomic Mass Units (amu)

List the periodic table atomic masses of each element appearing in the compounds. For accuracy, use the following values: - K: 39.10 - Br: 79.90 - Na: 22.99 - S: 32.06 - O: 16.00 - Fe: 55.85 - C: 12.01 - H: 1.008 - Pb: 207.2 - N: 14.01 - Al: 26.98 - P: 30.97

Molar Mass of KBr

Calculate molar mass of \(\text{KBr}\): \( K: 39.10 \text{ g/mol} \) and \( Br: 79.90 \text{ g/mol} \)\[ \text{Molar Mass of KBr} = 39.10 + 79.90 = 119.00 \text{ g/mol} \]

Molar Mass of Fe_{3}O_{4}

Calculate molar mass of \(\text{Fe}_{3}\text{O}_{4}\): \( 3 \times \text{Fe: 55.85 g/mol} \) and \( 4 \times \text{O: 16.00 g/mol} \)\[ \text{Molar Mass of } \text{Fe}_{3}\text{O}_{4} = 3 \times 55.85 + 4 \times 16.00 = 167.55 + 64.00 = 231.55 \text{ g/mol} \]

Molar Mass of Na_{2}SO_{4}

Calculate molar mass of \(\text{Na}_{2}\text{SO}_{4}\): \( 2 \times \text{Na: 22.99 g/mol} \), \( \text{S: 32.06 g/mol} \), and \( 4 \times \text{O: 16.00 g/mol} \)\[ \text{Molar Mass of } \text{Na}_{2}\text{SO}_{4} = 2 \times 22.99 + 32.06 + 4 \times 16.00 = 45.98 + 32.06 + 64.00 = 142.04 \text{ g/mol} \]

Molar Mass of C_{12}H_{22}O_{11}

Calculate molar mass of \(\text{C}_{12}\text{H}_{22}\text{O}_{11}\): \( 12 \times \text{C: 12.01 g/mol} \), \( 22 \times \text{H: 1.008 g/mol} \), and \( 11 \times \text{O: 16.00 g/mol} \)\[ \text{Molar Mass of } \text{C}_{12}\text{H}_{22}\text{O}_{11} = 12 \times 12.01 + 22 \times 1.008 + 11 \times 16.00 = 144.12 + 22.176 + 176.00 = 342.29 \text{ g/mol} \]

Molar Mass of Pb(NO_{3})_{2}

Calculate molar mass of \(\text{Pb(NO}_{3})_{2}\): \( \text{Pb: 207.2 g/mol} \), \( 2 \times \text{N: 14.01 g/mol} \), and \( 6 \times \text{O: 16.00 g/mol} \)\[ \text{Molar Mass of Pb(NO}_{3})_{2} = 207.2 + 2 \times 14.01 + 6 \times 16.00 = 207.2 + 28.02 + 96.00 = 331.22 \text{ g/mol} \]

Molar Mass of Al_{2}(SO_{4})_{3}

Calculate molar mass of \(\text{Al}_{2}(\text{SO}_{4})_{3}\): \( 2 \times \text{Al: 26.98 g/mol} \), \( 3 \times \text{S: 32.06 g/mol} \), and \( 12 \times \text{O: 16.00 g/mol} \)\[ \text{Molar Mass of } \text{Al}_{2}(\text{SO}_{4})_{3} = 2 \times 26.98 + 3 \times 32.06 + 12 \times 16.00 = 53.96 + 96.18 + 192.00 = 342.14 \text{ g/mol} \]

Molar Mass of C_{2}H_{5}OH

Calculate molar mass of \(\text{C}_{2}\text{H}_{5}\text{OH}\): \( 2 \times \text{C: 12.01 g/mol} \), \( 6 \times \text{H: 1.008 g/mol} \) (including H in OH), and \( \text{O: 16.00 g/mol} \)\[ \text{Molar Mass of } \text{C}_{2}\text{H}_{5}\text{OH} = 2 \times 12.01 + 6 \times 1.008 + 16.00 = 24.02 + 6.048 + 16.00 = 46.07 \text{ g/mol} \]

Molar Mass of HC_{2}H_{3}O_{2}

Calculate molar mass of \(\text{HC}_{2}\text{H}_{3}\text{O}_{2}\): \( 2 \times \text{C: 12.01 g/mol} \), \( 4 \times \text{H: 1.008 g/mol} \) (including H in OH), and \( 2 \times \text{O: 16.00 g/mol} \)\[ \text{Molar Mass of } \text{HC}_{2}\text{H}_{3}\text{O}_{2} = 2 \times 12.01 + 4 \times 1.008 + 2 \times 16.00 = 24.02 + 4.032 + 32.00 = 60.05 \text{ g/mol} \]

Molar Mass of (NH_{4})_{2}HPO_{4}

Calculate molar mass of \(\text{(NH}_{4})_{2}\text{HPO}_{4}\): \( 2 \times \text{N: 14.01 g/mol} \), \( 8 \times \text{H: 1.008 g/mol} \), \( \text{P: 30.97 g/mol} \), and \( 4 \times \text{O: 16.00 g/mol} \)\[ \text{Molar Mass of (NH}_{4)}_{2}\text{HPO}_{4} = 2 \times 14.01 + 8 \times 1.008 + 30.97 + 4 \times 16.00 = 28.02 + 8.064 + 30.97 + 64.00 = 131.05 \text{ g/mol} \]

Key concepts

Atomic Masses

When we talk about calculating molar masses, understanding atomic masses is crucial. Atomic mass is the weighted average mass of an element's atoms, expressed in atomic mass units (amu). Each element has a unique atomic mass found on the periodic table.
For example, the atomic mass of Potassium (K) is 39.10 amu, while that of Bromine (Br) is 79.90 amu. These atomic masses are essential because they are the building blocks for calculating the molar mass of compounds.
To calculate the molar mass, you'll need to know the atomic mass of each element in the compound. Once you have those values, you can sum up the masses based on the number of each type of atom in the molecule. This gives you the molar mass in grams per mole (g/mol).

• Potassium (K): 39.10 g/mol
• Bromine (Br): 79.90 g/mol
• Sodium (Na): 22.99 g/mol
• Sulfur (S): 32.06 g/mol
• Oxygen (O): 16.00 g/mol
• Iron (Fe): 55.85 g/mol
• Carbon (C): 12.01 g/mol
• Hydrogen (H): 1.008 g/mol
• Lead (Pb): 207.2 g/mol
• Nitrogen (N): 14.01 g/mol
• Aluminum (Al): 26.98 g/mol
• Phosphorus (P): 30.97 g/mol

Stoichiometry

Stoichiometry is a key concept in chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It helps us understand the proportions in which elements combine and the quantities of compounds formed.
When calculating molar masses of compounds, stoichiometry comes into play. You need to multiply the atomic masses of each element by the number of atoms of that element in the molecule.
Consider the compound \(\text{Na}_{2}\text{SO}_{4}\). The stoichiometry tells us that the compound consists of two Sodium (Na) atoms, one Sulfur (S) atom, and four Oxygen (O) atoms.
To find the molar mass:

• Sodium (Na): 2 atoms \( \times 22.99 \text{ g/mol} \) = 45.98 g/mol
• Sulfur (S): 1 atom \( \times 32.06 \text{ g/mol} \) = 32.06 g/mol
• Oxygen (O): 4 atoms \( \times 16.00 \text{ g/mol} \) = 64.00 g/mol

Adding these together: \(\text{Molar Mass of Na}_{2}\text{SO}_{4} = 45.98 + 32.06 + 64.00 = 142.04 \text{ g/mol} \)
This breakdown demonstrates the importance of stoichiometry in calculating the molar masses of compounds accurately.

Compound Molar Mass

The molar mass of a compound is the sum of the atomic masses of all the atoms in its chemical formula. This is usually expressed in grams per mole (g/mol). Knowing the molar mass is critical for converting between grams and moles, which is an essential part of many chemical calculations.
Let’s take a look at a more complex example, \(\text{Pb(NO}_{3})_{2}\):

• Lead (Pb): 1 atom \( \times 207.2 \text{ g/mol} \) = 207.2 g/mol
• Nitrogen (N): 2 atoms \( \times 14.01 \text{ g/mol} \) = 28.02 g/mol
• Oxygen (O): 6 atoms \( \times 16.00 \text{ g/mol} \) = 96.00 g/mol

Adding these together: \(\text{Molar Mass of Pb(NO}_{3})_{2} = 207.2 + 28.02 + 96.00 = 331.22 \text{ g/mol} \)
This total gives us the molar mass of the compound, which we can now use in various stoichiometric calculations.
Whether the compound is simple like KBr or complex like \(\text{Al}_{2}(\text{SO}_{4})_{3}\), the process remains the same. Sum up the products of the atomic masses and the stoichiometric coefficients of each element to find the compound's molar mass.