Chapter 6: Chemical Reactions – Mole and Mass Relationships

6.1 The Mole and Avogadro’s Number

The concept of the mole allows chemists to count atoms, molecules, or formula units by weighing them. This section introduces the mole, Avogadro’s number, and how to relate mass to the number of particles.

• 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.

• Mole (mol): The amount of a substance whose mass in grams is numerically equal to its molecular or formula weight.

• 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).

Example: The molecular weight of ethylene (C2H4) is 28.0 amu. Therefore, 1 mole of ethylene has a mass of 28.0 g and contains molecules.

Key Equations:

• Moles to particles:

• Particles to moles:

6.2 Gram-Mole Conversions

Molar mass serves as a conversion factor between the mass of a substance and the number of moles.

• Gram-Mole Conversion: Use the molar mass to convert between grams and moles.

Key Equations:

• Grams to moles:

• Moles to grams:

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 calculations.

Example: For the synthesis of ammonia:

• Mole ratio of N2 to NH3:

• Mole ratio of H2 to NH3:

6.4 Mass Relationships and Chemical Equations

Mass relationships in chemical reactions are determined using mole ratios and molar masses. Calculations often require converting between mass and moles for both reactants and products.

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

• Mole-to-Mass and Mass-to-Mole Conversions: Use molar mass as a conversion factor.

• Mass-to-Mass Conversions: Require converting mass to moles, using the mole ratio, then converting back to mass.

Four-Step Method for Mass Relationships:

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: To find the mass of product formed from a given mass of reactant, convert grams of reactant to moles, use the mole ratio to find moles of product, then convert to grams.

6.5 Limiting Reagent and Percent Yield

In most reactions, one reactant is used up first (the limiting reagent), which determines the maximum amount of product (theoretical yield) that can be formed. The actual yield is often less than the theoretical yield, and percent yield quantifies this efficiency.

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

• Theoretical Yield: The calculated amount of product formed from the limiting reagent, assuming complete reaction.

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

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

Key Equation:

• Percent yield:

Example: If the theoretical yield of CO2 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 grams to moles, then multiply by Avogadro’s number.

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

• Mass-to-Mass Conversions: Convert mass of reactant to moles, use mole ratio to find moles of product, then convert to mass.

• Limiting Reagent Problems: Calculate moles of product from each reactant; the smaller amount determines the limiting reagent and theoretical yield.

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

Table: Key Terms and Definitions

Additional info:

• When performing calculations, always check that units cancel appropriately and that the final answer makes sense (ballpark estimate).

• Balanced chemical equations are essential for determining correct mole ratios.

• Percent yield less than 100% is common due to side reactions, incomplete reactions, or loss of product during recovery.