Question

Calculate the molecular mass or formula mass (in amu) of each of the following substances: (a) \(\mathrm{CH}_{4},\) (b) \(\mathrm{NO}_{2}\), (c) \(\mathrm{SO}_{3}\) (d) \(\mathrm{C}_{6} \mathrm{H}_{6}\) (e) NaI, (f) \(\mathrm{K}_{2} \mathrm{SO}_{4},(\mathrm{~g}) \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

Short answer

(a) 16.05 amu, (b) 46.01 amu, (c) 80.07 amu, (d) 78.12 amu, (e) 149.89 amu, (f) 174.27 amu, (g) 310.18 amu.

Step-by-step solution

Determining Atomic Masses

To calculate the molecular mass of the substances, we first need to know the atomic masses of each element: - C (Carbon) = 12.01 amu - H (Hydrogen) = 1.01 amu - N (Nitrogen) = 14.01 amu - O (Oxygen) = 16.00 amu - S (Sulfur) = 32.07 amu - Na (Sodium) = 22.99 amu - I (Iodine) = 126.90 amu - K (Potassium) = 39.10 amu - Ca (Calcium) = 40.08 amu - P (Phosphorus) = 30.97 amu

Calculate Molecular Mass of CH4

For \(\mathrm{CH}_{4}\): - 1 Carbon atom = 12.01 amu- 4 Hydrogen atoms = 4 \times 1.01 = 4.04 amu- Total = 12.01 + 4.04 = 16.05 amu

Calculate Molecular Mass of NO2

For \(\mathrm{NO}_{2}\): - 1 Nitrogen atom = 14.01 amu- 2 Oxygen atoms = 2 \times 16.00 = 32.00 amu- Total = 14.01 + 32.00 = 46.01 amu

Calculate Molecular Mass of SO3

For \(\mathrm{SO}_{3}\): - 1 Sulfur atom = 32.07 amu- 3 Oxygen atoms = 3 \times 16.00 = 48.00 amu- Total = 32.07 + 48.00 = 80.07 amu

Calculate Molecular Mass of C6H6

For \(\mathrm{C}_{6} \mathrm{H}_{6}\): - 6 Carbon atoms = 6 \times 12.01 = 72.06 amu- 6 Hydrogen atoms = 6 \times 1.01 = 6.06 amu- Total = 72.06 + 6.06 = 78.12 amu

Calculate Molecular Mass of NaI

For NaI: - 1 Sodium atom = 22.99 amu - 1 Iodine atom = 126.90 amu - Total = 22.99 + 126.90 = 149.89 amu

Calculate Molecular Mass of K2SO4

For \(\mathrm{K}_{2} \mathrm{SO}_{4}\):- 2 Potassium atoms = 2 \times 39.10 = 78.20 amu- 1 Sulfur atom = 32.07 amu- 4 Oxygen atoms = 4 \times 16.00 = 64.00 amu- Total = 78.20 + 32.07 + 64.00 = 174.27 amu

Calculate Molecular Mass of Ca3(PO4)2

For \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\):- 3 Calcium atoms = 3 \times 40.08 = 120.24 amu- 2 Phosphorus atoms = 2 \times 30.97 = 61.94 amu- 8 Oxygen atoms = 8 \times 16.00 = 128.00 amu- Total = 120.24 + 61.94 + 128.00 = 310.18 amu

Key concepts

Atomic Mass

To begin any molecular mass calculation, it's essential to understand the concept of atomic mass. Atomic mass refers to the mass of a single atom of a chemical element. It is usually expressed in atomic mass units (amu). This unit provides a convenient way to express the large numbers associated with the mass of individual atoms.
Each element has a specific atomic mass based on the weighted average of all its isotopes. For example, carbon ( C) has an atomic mass of 12.01 amu, while hydrogen ( H) has an atomic mass of 1.01 amu.
The atomic masses are vital as they are used in calculating the molecular or formula mass of compounds. By adding up the atomic masses of each constituent atom in the chemical formula, you can determine the overall mass of a molecule.

Chemical Formula

A chemical formula provides a simple notation to represent the elements in a compound and the number of each type of atom present. It serves as a map that shows how atoms combine and in what proportions. For example, the chemical formula CH₄ tells us that one molecule contains one carbon atom and four hydrogen atoms.
When using a chemical formula, it's important to accurately note the numbers of each type of atom, as this directly influences the molecular mass calculation. Even a small change in a compound's chemical formula can result in a different substance. For instance, H₂O (water) and H₂O₂ (hydrogen peroxide) are completely different, even though they share similar elements. Thus, a chemical formula is crucial for stoichiometry, as it provides the basis for calculating reactant and product quantities.

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). The concept is an extension of molecular mass, which is measured in amu. To find the molar mass, you add together the atomic masses of the individual atoms that make up a molecule, just like in molecular mass calculations.
For example, the molar mass of methane ( CH₄) can be calculated by summing the atomic masses: one carbon atom (12.01 amu) plus four hydrogen atoms (4 × 1.01 amu = 4.04 amu), resulting in a molecular mass of 16.05 amu.
Although molar mass and molecular mass are numerically identical for a molecule (since they sum to 16.05), molar mass is typically expressed in g/mol to reflect its relevance in laboratory measurements and stoichiometry.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It is essential for understanding how much of each reactant is needed to produce a desired amount of product. This concept uses a balanced chemical equation along with the molar masses of the substances involved.
When dealing with stoichiometry, you'll convert between moles and masses to ensure you have the correct proportions for a reaction to occur efficiently. This calculation helps chemists understand how much of each chemical is required or produced in a reaction. For instance, if you were to use the molar masses calculated, you could determine how many grams of a reactant are necessary to produce a specific amount of product.
Understanding stoichiometry allows students and chemists to predict yields, optimize reactions, and reduce waste, making it a fundamental aspect of chemistry education.