Chemical Reactions and Reaction Stoichiometry: Core Concepts and Calculations

Stoichiometry and the Law of Conservation of Mass

Introduction to Stoichiometry

Stoichiometry is the study of the quantitative relationships between the amounts of reactants and products in chemical reactions. It is fundamentally based on the Law of Conservation of Mass, which states that matter is neither created nor destroyed in a chemical reaction. This principle, established by Antoine Lavoisier in 1789, underpins all stoichiometric calculations in chemistry.

Chemical Equations

Structure and Interpretation

Chemical equations are concise representations of chemical reactions. They show the substances involved as reactants (on the left) and products (on the right), with their physical states indicated in parentheses: (g) for gas, (l) for liquid, (s) for solid, and (aq) for aqueous solution. Coefficients are used to balance equations, ensuring the law of conservation of mass is obeyed.

It is essential to balance chemical equations by adjusting coefficients, not subscripts, as changing subscripts alters the identity and properties of the compounds.

Types of Chemical Reactions

Classification of Reactions

Chemical reactions can be classified into several types, including:

• Combination reactions: Two or more substances combine to form one product.

• Decomposition reactions: A single substance breaks down into two or more products.

• Combustion reactions: A substance reacts rapidly with oxygen, often producing a flame.

Formula Weight, Molecular Weight, and Percent Composition

Calculating Formula and Molecular Weights

The formula weight (FW) is the sum of the atomic weights of all atoms in a chemical formula, typically used for ionic compounds. The molecular weight (MW) is the sum of atomic weights in a molecule, used for molecular compounds. For example, the formula weight of CaCl2 is calculated as:

$\text{FW of CaCl}_2 = 1 \times 40.08\ \text{amu} + 2 \times 35.453\ \text{amu} = 110.99\ \text{amu}$

Percent Composition

The percent composition of an element in a compound is calculated as:

$\%\ \text{Element} = \frac{(\text{number of atoms})(\text{atomic weight})}{\text{FW of the compound}} \times 100$

For example, the percent of carbon in ethane (C2H6):

$\%C = \frac{2 \times 12.011}{30.070} \times 100 = 79.887\%$

The Mole and Avogadro’s Number

Definition and Importance

The mole is a counting unit in chemistry, defined as $6.02 \times 10^{23}$ particles (Avogadro’s number). One mole of a substance contains this number of atoms, molecules, or formula units, allowing chemists to relate microscopic particles to macroscopic amounts.

Molar Mass

The molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). For elements, it is numerically equal to the atomic weight from the periodic table. For compounds, it is the sum of the atomic weights of all atoms in the formula.

Mole Relationships Table

The following table summarizes the relationships between formula, formula weight, molar mass, and the number of particles in one mole for various substances:

Name of Substance	Formula	Formula Weight (amu)	Molar Mass (g/mol)	Number and Kind of Particles in One Mole
Atomic nitrogen	N	14.0	14.0	$6.02 \times 10^{23}$ N atoms
Molecular nitrogen	N2	28.0	28.0	$6.02 \times 10^{23}$ N2 molecules
Silver	Ag	107.9	107.9	$6.02 \times 10^{23}$ Ag atoms
Silver ion	Ag+	107.9	107.9	$6.02 \times 10^{23}$ Ag+ ions
Barium chloride	BaCl2	208.2	208.2	$6.02 \times 10^{23}$ BaCl2 formula units

Empirical and Molecular Formulas

Determining Empirical Formulas

The empirical formula gives the simplest whole-number ratio of atoms in a compound. It can be determined from percent composition data using the following steps:

1. Obtain the mass percent of each element.

2. Assume a 100 g sample to convert percentages to grams.

3. Convert grams to moles using molar masses.

4. Divide by the smallest number of moles to get the simplest ratio.

5. Write the empirical formula.

Example: For para-aminobenzoic acid (PABA) with 61.31% C, 5.14% H, 10.21% N, and 23.33% O, the empirical formula is C7H7NO2.

Determining Molecular Formulas

The molecular formula is a whole-number multiple of the empirical formula. It is determined by dividing the compound’s molar mass by the empirical formula mass:

$\text{Whole-number multiple} = \frac{\text{Molar mass}}{\text{Empirical formula mass}}$

Example: If the empirical formula is CH and the molar mass is 78 g/mol, the molecular formula is C6H6.

Combustion Analysis

Experimental Determination of Composition

Combustion analysis is used to determine the amounts of C, H, and O in organic compounds. The sample is combusted in oxygen, and the resulting CO2 and H2O are collected and measured to calculate the original composition.

Stoichiometric Calculations

Quantitative Relationships in Reactions

The coefficients in a balanced chemical equation indicate the relative numbers of molecules (or moles) of reactants and products. These relationships allow conversion between masses of different substances in a reaction using the mole ratio from the equation.

Example: To find the grams of water produced from 1.00 g of glucose in the reaction C6H12O6 + 6 O2 → 6 CO2 + 6 H2O, convert grams of glucose to moles, use the mole ratio, and convert to grams of water.

Limiting Reactants and Theoretical Yield

Limiting and Excess Reactants

The limiting reactant is the reactant that is completely consumed first, limiting the amount of product formed. The excess reactant is present in a greater amount than necessary to react with the limiting reactant.

Theoretical and Percent Yield

The theoretical yield is the maximum amount of product that can be formed from the limiting reactant, as calculated from stoichiometry. The actual yield is the amount of product actually obtained from the reaction. The percent yield is calculated as:

$\text{Percent yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100$

Additional info: These notes provide a comprehensive overview of chemical reactions and stoichiometry, including the calculation of formula and molecular weights, percent composition, empirical and molecular formulas, combustion analysis, stoichiometric calculations, limiting reactants, and yield calculations. All images included directly reinforce the concepts discussed in the adjacent text.