Chapter 3: Stoichiometry of Formulas and Equations

Chemistry The Molecular Nature of Matter and Change - Chapter 3 Study Notes

Overview

  • Textbook: Chemistry The Molecular Nature of Matter and Change, 9th Edition
  • Authors: Martin S. Silberberg and Patricia G. Amateis
  • Copyright: © 2021 McGraw Hill

Chapter 3: Stoichiometry of Formulas and Equations

Sections Covered

3.1 The Mole
3.2 Determining the Formula of an Unknown Compound
3.3 Writing and Balancing Chemical Equations
3.4 Calculating Quantities of Reactant and Product

3.1 The Mole

  • Definition: The mole (mol) is a unit of measurement for the amount of substance. It is defined as containing the same number of entities as there are atoms in exactly 12 g of carbon-12.
  • Entities Defined: The term "entities" may refer to atoms, ions, molecules, formula units, or electrons, essentially any particle type.
  • Avogadro’s Number: One mole (1 mol) contains 6.022 imes 10^{23} entities.
  • Mass Comparison: The mass of one atom (in atomic mass units, amu) corresponds numerically to the mass (in grams) of 1 mole of that substance. For example, 1 atom of sulfur (S) has a mass of 32.07 amu, therefore 1 mol (or 6.022 imes 10^{23} atoms) of sulfur has a mass of 32.07 g.
  • Significant Figures: All mass readings should be taken to four significant figures as per standards in chemistry.
  • Table of Elements:
    • Aluminum: 26.98 g, 1 mol = 6.022 imes 10^{23} atoms
    • Copper: 63.55 g, 1 mol = 6.022 imes 10^{23} atoms
    • Iron: 55.85 g, 1 mol = 6.022 imes 10^{23} atoms
    • Sulfur: 32.07 g, 1 mol = 6.022 imes 10^{23} atoms
    • Iodine: 126.9 g, 1 mol = 6.022 imes 10^{23} atoms
    • Mercury: 200.6 g, 1 mol = 6.022 imes 10^{23} atoms

Molar Mass

  • Molar Mass (M): The mass of one mole of entities (atoms/molecules/formula units) of a substance. For example,
    • Molar mass of Neon (Ne) = 20.18 g/mol.
  • For compounds:
    • The molar mass is calculated by summing the products of the number of mols of each atom and their respective atomic masses from the periodic table:
    • For example, the molar mass of water (H₂O):
      ext{Molar mass} = (2 imes ext{M of H}) + (1 imes ext{M of O})
      = (2 imes 1.008 ext{ g/mol}) + (1 imes 16.00 ext{ g/mol}) = 18.02 ext{ g/mol}

Calculating Molar Mass Example: Propane

  • Chemical Formula: C₃H₈
  • Calculation:
  • Molar Mass: = (3 imes 12.01) + (8 imes 1.008) = 44.09 ext{ g/mol}

3.2 Determining the Formula of an Unknown Compound

Empirical and Molecular Formulas

  • Empirical Formula: Simplest whole number ratio of elements in a compound (e.g., hydrogen peroxide is H₂O).
  • Molecular Formula: Actual number of atoms of each element in a molecule of the compound (e.g., H₂O₂ is the molecular formula for hydrogen peroxide).
  • Structural Formula: Shows relative placements of atoms (e.g., H-O-O-H for hydrogen peroxide).

Determining Empirical Formulas

  1. Determine the number of moles of each element in the compound.
  2. Identify the element with the least number of moles.
  3. Divide each quantity of moles by the smallest quantity to get the ratio.
  4. Multiply by the lowest integer to make all values whole numbers (if necessary).

Example of Empirical Formula Determination

  • Given: 5.08 g Zn, 1.60 g P, 3.32 g O
  • Steps:
    1. Convert grams to moles using atomic masses.
    2. Write preliminary formula (ZnₓPᵧO𝓏).
    3. Divide by the smallest mole number.
    4. If ratios are not whole numbers, multiply to obtain whole numbers.
    • Result: Empirical formula = Zn₃P₂O₈.

3.3 Writing and Balancing Chemical Equations

Chemical Equations

  • Definition: A representation of a chemical change using chemical formulas to define identities and quantities of reactants and products.
  • Components:
    • Reactants: Substances consumed in the reaction
    • Products: Substances produced in the reaction
  • Balancing Equations: Must have equal numbers of each type of atom on both sides.
    • Steps to Balance a Chemical Equation:
    1. Write the skeleton equation without coefficients.
    2. Count the number of each atom in reactants and products.
    3. Adjust coefficients to balance.
    4. Ensure smallest whole number coefficients are used in adjustments.
    5. Indicate states of matter for all substances.

Features of Balanced Equations

  • Example: C₈H₁₈ + 12.5 O₂ → 8 CO₂ + 9 H₂O
  • Stoichiometric Coefficients: Numbers placed before reactants/products to indicate the ratio in which they react or are produced.

3.4 Calculating Quantities of Reactant and Product

Stoichiometric Calculations

  • Uses: Calculate amounts of reactants/products in a chemical reaction.
  • Stoichiometry Definition: Relationship between relative quantities (in moles) of substances in a reaction.
    • Example: 1 mole of substance A will react with x moles of substance B, described by stoichiometric coefficients.

Calculating Yield and Limiting Reactants

  • Limiting Reactant: The reactant that is fully consumed and thus limits the amount of product formed.
  • Theoretical Yield: Maximum amount of product formed based on balanced equation.
  • Actual Yield: Amount of product actually obtained from the reaction.
  • Percent Yield Formula: ext{Percent Yield} = rac{ ext{actual yield}}{ ext{theoretical yield}} imes 100