Question

Calculate the molar mass for each of the following substances. a. adipic acid, \(\mathrm{C}_{6} \mathrm{H}_{10} \mathrm{O}_{4}\) b. caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2}\) c. eicosane, \(\mathrm{C}_{20} \mathrm{H}_{42}\) d. cyclohexanol, \(\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{OH}\) e. vinyl acetate, \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2}\) f. dextrose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\)

Short answer

The molar masses for the given substances are as follows: a. Adipic acid: 146.14 g/mol b. Caffeine: 194.20 g/mol c. Eicosane: 282.54 g/mol d. Cyclohexanol: 99.15 g/mol e. Vinyl acetate: 86.09 g/mol f. Dextrose: 180.16 g/mol

Step-by-step solution

Recall the atomic masses for each element

To calculate the molar masses, we should know the atomic masses of each element involved. Carbon (C) = 12.01 g/mol Hydrogen (H) = 1.008 g/mol Nitrogen (N) = 14.01 g/mol Oxygen (O) = 16.00 g/mol

Calculate the molar mass for adipic acid

Adipic acid has the chemical formula \(\mathrm{C}_{6} \mathrm{H}_{10} \mathrm{O}_{4}\). Calculate the molar mass by adding the atomic masses of each atom. Molar mass of adipic acid = (6 × 12.01) + (10 × 1.008) + (4 × 16.00) = 72.06 + 10.08 + 64.00 = 146.14 g/mol

Calculate the molar mass for caffeine

Caffeine has the chemical formula \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\). Calculate the molar mass by adding the atomic masses of each atom. Molar mass of caffeine = (8 × 12.01) + (10 × 1.008) + (4 × 14.01) + (2 × 16.00) = 96.08 + 10.08 + 56.04 + 32.00 = 194.20 g/mol

Calculate the molar mass for eicosane

Eicosane has the chemical formula \(\mathrm{C}_{20} \mathrm{H}_{42}\). Calculate the molar mass by adding the atomic masses of each atom. Molar mass of eicosane = (20 × 12.01) + (42 × 1.008) = 240.20 + 42.34 = 282.54 g/mol

Calculate the molar mass for cyclohexanol

Cyclohexanol has the chemical formula \(\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{OH}\). Calculate the molar mass by adding the atomic masses of each atom. Molar mass of cyclohexanol = (6 × 12.01) + (11 × 1.008) + 16.00 = 72.06 + 11.09 + 16.00 = 99.15 g/mol

Calculate the molar mass for vinyl acetate

Vinyl acetate has the chemical formula \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2}\). Calculate the molar mass by adding the atomic masses of each atom. Molar mass of vinyl acetate = (4 × 12.01) + (6 × 1.008) + (2 × 16.00) = 48.04 + 6.05 + 32.00 = 86.09 g/mol

Calculate the molar mass for dextrose

Dextrose has the chemical formula \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\). Calculate the molar mass by adding the atomic masses of each atom. Molar mass of dextrose = (6 × 12.01) + (12 × 1.008) + (6 × 16.00) = 72.06 + 12.10 + 96.00 = 180.16 g/mol By following these steps, the molar masses for all the substances have been calculated.

Key concepts

Atomic Mass

The concept of atomic mass is a fundamental building block in chemistry that helps us understand the mass of an individual atom. It is measured in atomic mass units (amu), with one amu defined as one-twelfth the mass of a carbon-12 atom. In the context of our exercise, atomic mass is essential for calculating the molar mass of a compound.

For example, the atomic masses of common elements like carbon (C), hydrogen (H), nitrogen (N), and oxygen (O) were used: Carbon has an atomic mass of approximately 12.01 g/mol, hydrogen has a lighter mass at about 1.008 g/mol, nitrogen stands at 14.01 g/mol, and oxygen, a bit heavier, is around 16.00 g/mol. These values are averages that account for the presence of various isotopes of each element in nature.

Chemical Formula

The chemical formula of a substance provides a lot of information in a very compact form. It tells us the types of atoms present and the exact number of each type of atom in a molecule of the substance. For instance, the chemical formula for caffeine is \(\mathrm{C}_{8}\mathrm{H}_{10}\mathrm{N}_{4}\mathrm{O}_{2}\), which indicates that each caffeine molecule consists of 8 carbon atoms, 10 hydrogen atoms, 4 nitrogen atoms, and 2 oxygen atoms.

This notation is crucial for stoichiometry calculations because it allows us to understand the proportions in which elements combine. With the chemical formula known, calculating the molar mass becomes a straightforward task of multiplying the number of atoms of each element by their respective atomic mass and summing these values.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships of elements and compounds as they undergo chemical reactions. It is rooted in the law of conservation of mass, which states that mass is neither created nor destroyed in chemical reactions. Thus, the mass of the reactants equals the mass of the products.

When we talk about stoichiometry in the context of molar mass calculation, we are looking at the mass relationship between atoms in a molecule and the overall mass of that molecule. By knowing the stoichiometry of a compound, we can precisely calculate how much of each element is present in a given quantity of that compound. This is essential for scaling reactions, calculating yields, and conducting various quantitative analyses in chemistry.

Mole Concept

The mole concept is a bridge between the atomic world and the macroscopic world that we can manipulate in the laboratory. One mole of any substance contains Avogadro's number (approximately \(6.022 \times 10^{23}\)) of particles (whether they're atoms, molecules or ions). This number is analogous to a 'dozen' but on a much larger scale.

With the molar mass, we can convert between the mass of a substance and the number of moles. The molar mass, essentially, tells us how many grams one mole of a substance weighs. For instance, adipic acid has a molar mass of 146.14 g/mol. This informs us that if you have 146.14 grams of adipic acid, you have exactly one mole, which is \(6.022 \times 10^{23}\) molecules of adipic acid.

The mole concept, combined with molar mass, enables chemists to count and measure atoms and molecules in practical laboratory quantities, thus allowing us to perform experiments and obtain meaningful results that can be replicated and applied in real-world scenarios.