Stoichiometry: Calculations with Chemical Formulas and Equations

Chemical Equations

Chemical equations are symbolic representations of chemical reactions, showing the reactants and products involved. The coefficients in front of chemical formulas indicate the relative number of molecules or moles of each substance participating in the reaction. A balanced chemical equation has equal numbers of atoms of each element on both sides, reflecting the law of conservation of mass.

• Reactants: Substances consumed during the reaction.

• Products: Substances formed as a result of the reaction.

• Coefficients: Numbers placed before formulas to indicate the quantity of molecules or moles.

• Subscripts: Numbers within formulas that indicate the number of atoms in a molecule; changing subscripts alters the identity of the substance.

Example: The reaction of hydrogen and oxygen to form water:

2 H2 + O2 → 2 H2O

Balancing Chemical Equations

Balancing chemical equations ensures that the number of atoms for each element is the same on both sides. Only coefficients should be changed, never subscripts.

• Start by balancing elements that appear only once on each side.

• Balance hydrogen and oxygen last, especially in combustion reactions.

• Use whole-number coefficients; if necessary, use fractional coefficients and multiply all coefficients to clear fractions.

Example: Balancing the combustion of methane:

CH4 + 2 O2 → CO2 + 2 H2O

Types of Chemical Reactions

• Combination (Synthesis): Two or more reactants form a single product. Example: C (s) + O2 (g) → CO2 (g)

• Decomposition: A single reactant breaks into two or more products. Example: 2 KClO3 (s) → 2 KCl (s) + 3 O2 (g)

• Single Replacement: One element replaces another in a compound. Example: Fe (s) + CuSO4 (aq) → FeSO4 (aq) + Cu (s)

• Double Replacement: Exchange of ions between two compounds. Example: Na2CO3 (aq) + 2 AgNO3 (aq) → 2 NaNO3 (aq) + Ag2CO3 (s)

• Combustion: Rapid reaction with oxygen producing a flame, usually forming CO2 and H2O.

Formula Weights and Percentage Composition

The formula weight (FW) or molecular weight is the sum of atomic weights of all atoms in a chemical formula. Percentage composition is the mass percentage of each element in a compound.

• Formula Weight:

• Percentage Composition:

Example: For C12H22O11:

• %C = 42.1%

• %H = 6.5%

• %O = 51.4%

Avogadro’s Number and the Mole

The mole is the counting unit for atoms, molecules, or ions. One mole contains Avogadro’s number () of particles.

• 1 mol of any substance = particles

• Molar mass (MM) in grams per mole is numerically equal to the formula weight in amu.

Example: 1 mol H2O = molecules H2O

Mole Relationships Table

This table summarizes the formula weight, molar mass, and number of particles in one mole for various substances.

Converting Masses, Moles, and Particles

Stoichiometric calculations often require converting between mass, moles, and number of particles. The relationships are:

• Mass (g) → Moles:

• Moles → Particles:

• Particles → Moles:

Empirical and Molecular Formulas

The empirical formula gives the simplest whole-number ratio of elements in a compound. The molecular formula is a whole-number multiple of the empirical formula, determined by the molar mass.

• Empirical Formula: Calculated from percent composition or elemental analysis.

• Molecular Formula: , where

Quantitative Information from Balanced Equations

Balanced equations provide mole ratios for converting between reactants and products. These ratios are used in stoichiometric calculations to determine the amount of product formed or reactant consumed.

• Mole Ratio: Derived from coefficients in the balanced equation.

• Mass-Mass Calculations: Convert mass to moles, use mole ratio, then convert moles to mass.

Limiting Reactants

The limiting reactant is the substance that is completely consumed first, thus determining the maximum amount of product formed. The excess reactant is left over after the reaction.

• Identify the limiting reactant by comparing the stoichiometric equivalents for each reactant.

• Theoretical yield is calculated based on the limiting reactant.

Example: Making sandwiches with limited cheese illustrates the concept of limiting reactants.

Theoretical and Percent Yield

The theoretical yield is the maximum amount of product that can be formed from the limiting reactant. The actual yield is the amount obtained experimentally. Percent yield is calculated as:

Example: If the theoretical yield of Zn(NO3)2 is 1.39 g and the actual yield is 1.12 g, the percent yield is 80.6%.

Additional info: These notes cover the essential concepts of stoichiometry, including chemical equations, reaction types, formula weights, mole relationships, empirical and molecular formulas, limiting reactants, and yield calculations, as required for General Chemistry.