Mass Relationships in Chemical Reactions

Atomic Mass and Atomic Mass Unit (amu)

The atomic mass unit (amu) is a standard unit for expressing the mass of atoms and molecules. It is defined as exactly 1/12 the mass of a carbon-12 (12C) atom. Atomic mass is the mass of an atom in amu, and is often found on the periodic table.

• Definition: 1 amu = 1.66 × 10-24 g

• Example: The atomic mass of oxygen (16O) is 16.00 amu.

• Application: Atomic mass is used to calculate molar mass and to relate microscopic and macroscopic quantities.

Average Atomic Mass and Isotopes

The average atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes. Each isotope's contribution is based on its fractional abundance.

• Formula:

• Example: For carbon: amu

The Mole and Avogadro's Number

The mole (mol) is a fundamental unit in chemistry for counting particles. One mole contains Avogadro's number () of entities, which is .

• Definition: 1 mol = particles

• Application: Used to relate mass, number of particles, and volume in chemical calculations.

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). For elements, the molar mass is numerically equal to the atomic mass in amu.

• Formula: in grams per mole

• Example: 1 mol of carbon-12 = 12.00 g

Conversions Between Mass, Moles, and Atoms

To convert between mass, moles, and number of atoms, use the molar mass and Avogadro's number as conversion factors.

• Mass to moles:

• Moles to atoms:

• Example: How many atoms are in 0.551 g of potassium (K)?

Molecular Mass and Formula Mass

Molecular mass (or molecular weight) is the sum of the atomic masses in a molecule. Formula mass is the sum of atomic masses in a formula unit of an ionic compound.

• Formula:

• Example: SO2: amu

• Formula mass for NaCl: amu

Percent Composition

Percent composition expresses the mass percent of each element in a compound.

• Formula:

• Example: For C2H6O: %C = 52.14%, %H = 13.13%, %O = 34.73%

Empirical and Molecular Formulas

The empirical formula is the simplest whole-number ratio of elements in a compound. The molecular formula is a multiple of the empirical formula, based on the compound's molar mass.

• Steps to determine empirical formula:

  1. Convert mass percent to grams.

  2. Divide by molar mass to get moles.

  3. Divide by the smallest number of moles.

  4. Change to integer subscripts.

• Example: KMnO4 from percent composition.

Stoichiometry and Chemical Equations

Stoichiometry is the calculation of reactants and products in chemical reactions using balanced chemical equations.

• Steps:

  1. Write balanced chemical equation.

  2. Convert known quantities to moles.

  3. Use coefficients to find moles of sought quantity.

  4. Convert moles to desired units.

• Example: Combustion of methanol: 209 g CH3OH produces 235 g H2O.

Limiting Reagent and Reaction Yield

The limiting reagent is the reactant that is completely consumed first, limiting the amount of product formed. Theoretical yield is the maximum possible product, while actual yield is what is obtained experimentally. Percent yield compares actual to theoretical yield.

• Formula:

• Example: If 803 g CaO is produced, % yield = 33.8%.

Worked Examples and Applications

Numerous worked examples illustrate the application of mass relationships, mole concept, and stoichiometry in real-world and laboratory settings.

• Example: Calculation of moles, atoms, empirical and molecular formulas, and percent composition for various compounds.

• Application: Used in industrial processes, laboratory analysis, and chemical manufacturing.