Chapter 6: Chemical Reactions – Mole and Mass Relationships

6.1 The Mole and Avogadro’s Number

This section introduces the concept of the mole, Avogadro’s number, and their importance in relating the mass of substances to the number of particles involved in chemical reactions.

• Atomic Weight: The average mass of an element’s atoms, typically expressed in atomic mass units (amu).

• Molecular Weight (MW): The sum of the atomic weights of all atoms in a molecule. For ionic compounds, this is called the formula weight.

• The Mole: A mole is the amount of a substance whose mass in grams is numerically equal to its molecular or formula weight. It is a counting unit for atoms, molecules, or formula units.

• Molar Mass: The mass in grams of 1 mole of a substance. Numerically equal to the molecular or formula weight (in amu).

• Avogadro’s Number: One mole of any substance contains particles (atoms, molecules, or formula units).

• Key Point: Samples of different substances with masses proportional to their molar masses contain the same number of particles.

Example: 1 mole of sulfur, copper, mercury, or helium each contains particles, but their masses differ due to different molar masses.

6.2 Gram-Mole Conversions

This section explains how to convert between the mass of a substance and the number of moles using molar mass as a conversion factor.

• Conversion Formula:

  • To convert grams to moles:

  • To convert moles to grams:

• Molar Mass as a Conversion Factor: Used to relate the mass of a sample to the number of moles present.

Example: If a bottle contains 0.082 mol of ibuprofen (MW = 206.3 g/mol), the mass is g.

6.3 Mole Relationships and Chemical Equations

Balanced chemical equations show the quantitative relationships between reactants and products in terms of moles.

• Chemical Equation Coefficients: Indicate the number of moles of each substance involved in the reaction.

• Mole Ratios: Derived from the coefficients, used as conversion factors in stoichiometric calculations.

Example: For the synthesis of ammonia:

• Mole ratio of to :

• Mole ratio of to :

6.4 Mass Relationships and Chemical Equations

This section describes how to use mole ratios and molar masses to calculate the mass of products or reactants in a chemical reaction.

• Types of Conversions:

  • Mole-to-mole: Use mole ratios from the balanced equation.

  • Mole-to-mass or mass-to-mole: Use molar mass as a conversion factor.

  • Mass-to-mass: Requires converting mass to moles, using mole ratios, then converting back to mass.

• Four-Step Problem Solving Strategy:

  1. Write the balanced chemical equation.

  2. Choose appropriate molar masses and mole ratios.

  3. Set up the factor-label (dimensional analysis) expression.

  4. Calculate and check the answer.

Example: If 1.0 mol of reacts, and the molar mass of the product is 63.0 g/mol, use the balanced equation and mole ratios to find the mass of product formed.

6.5 Limiting Reagent and Percent Yield

Not all chemical reactions proceed with all reactants being completely consumed. This section explains how to identify the limiting reagent and calculate theoretical and percent yields.

• Limiting Reagent: The reactant that is completely consumed first, thus limiting the amount of product formed.

• Theoretical Yield: The maximum amount of product that can be formed from the limiting reagent, assuming complete reaction.

• Actual Yield: The amount of product actually obtained from the reaction.

• Percent Yield: The ratio of actual yield to theoretical yield, expressed as a percentage. Formula:

Example: If the theoretical yield of is 88.0 g and the actual yield is 72.4 g, then:

Worked Examples Summary

• Calculating Molar Mass: Add atomic weights of all atoms in the molecular formula.

• Converting Mass to Molecules: Use molar mass to convert mass to moles, then multiply by Avogadro’s number to get number of molecules.

• Converting Atoms to Mass: Divide the number of atoms by Avogadro’s number to get moles, then multiply by atomic weight to get mass.

• Stoichiometry: Use balanced equations and mole ratios to relate quantities of reactants and products.

• Limiting Reagent Problems: Calculate moles of product from each reactant; the one producing less product is limiting.

• Percent Yield Problems: Calculate theoretical yield, then use actual yield to find percent yield.

Key Table: Types of Stoichiometric Conversions

Summary of Key Equations

• Moles from mass:

• Mass from moles:

• Number of particles:

• Percent yield:

Additional info:

• When performing stoichiometric calculations, always start with a balanced chemical equation.

• Unit analysis (factor-label method) is essential for ensuring correct conversions and canceling units appropriately.

• Estimating answers before calculation helps check for errors in the final result.