The Mole Concept and Molar Mass

• The mole concept is a way of expressing the amount of a substance
• Stoichiometry deals with the quantitative relationships between reactants and products in chemical reactions

The Mole

• A mole (symbol: mol) is the base unit of amount of substance in the International System of Units (SI)
• It is defined as exactly 6.02214076 × 10²³ elementary entities
• This number is known as Avogadro's constant (NA)
• Elementary entities can be atoms, molecules, ions, or other specified particles
• One mole of any substance contains the same number of entities as there are atoms in 12 grams of carbon-12

Molar Mass

• Molar mass (M) is the mass of one mole of a substance
• It is typically expressed in grams per mole (g/mol)
• The molar mass of an element is numerically equal to its atomic mass in atomic mass units (amu or u)
• The molar mass of a compound is the sum of the molar masses of all the atoms in its chemical formula

Calculating Molar Mass

• To calculate the molar mass of a compound, add the atomic masses of each element in the formula, multiplied by its subscript
• Example: For water (H₂O), the molar mass is (2 × 1.008 g/mol for H) + (1 × 16.00 g/mol for O) = 18.016 g/mol

Mole Conversions

• Moles to mass: mass = moles × molar mass (m = n × M)
• Mass to moles: moles = mass / molar mass (n = m / M)
• Moles to particles: number of particles = moles × Avogadro's number (N = n × NA)
• Particles to moles: moles = number of particles / Avogadro's number (n = N / NA)

Stoichiometry

• Stoichiometry is the study of the quantitative relationships or ratios between two or more substances undergoing a physical or chemical change
• It is based on the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction
• Stoichiometry is essential for balancing chemical equations and determining the amount of reactants and products involved in a reaction

Balancing Chemical Equations

• A balanced chemical equation has the same number of atoms of each element on both sides of the equation
• Balancing is achieved by adding coefficients in front of the chemical formulas
• Never change the subscripts within a chemical formula when balancing an equation
• Follow a systematic approach: Balance metals, then non-metals, then hydrogen, and finally oxygen

Stoichiometric Coefficients

• The coefficients in a balanced chemical equation represent the relative number of moles of each reactant and product
• These coefficients are used to determine the mole ratios between substances in the reaction

Mole Ratios

• A mole ratio is a conversion factor derived from the coefficients of a balanced chemical equation
• It is used to convert between moles of one substance and moles of another substance in a chemical reaction
• Example: In the reaction 2H₂(g) + O₂(g) → 2H₂O(g), the mole ratio between H₂ and H₂O is 2:2, or 1:1
• To perform stoichiometric calculations, convert given quantities to moles, use mole ratios to find moles of desired substances, and then convert back to the desired units

Limiting Reactant

• The limiting reactant is the reactant that is completely consumed in a chemical reaction
• It determines the maximum amount of product that can be formed
• The other reactants are present in excess
• To identify the limiting reactant, calculate the moles of each reactant and compare their ratios to the stoichiometric ratios in the balanced equation
• The reactant that would produce the least amount of product is the limiting reactant

Theoretical Yield

• The theoretical yield is the maximum amount of product that can be produced from a given amount of limiting reactant
• It is calculated using stoichiometry based on the balanced chemical equation

Actual Yield

• The actual yield is the amount of product that is actually obtained from a chemical reaction
• It is often less than the theoretical yield due to factors such as incomplete reactions, side reactions, and loss of product during purification

Percent Yield

• The percent yield is the ratio of the actual yield to the theoretical yield, expressed as a percentage
• Percent yield = (Actual yield / Theoretical yield) × 100%
• It indicates the efficiency of a chemical reaction

Empirical Formula

• The empirical formula is the simplest whole-number ratio of atoms in a compound
• To determine the empirical formula:
  • Convert the mass percentages of each element to grams
  • Convert grams to moles using the molar mass of each element
  • Divide each mole value by the smallest mole value to obtain the simplest mole ratio
  • If necessary, multiply the ratios by a whole number to obtain whole-number subscripts

Molecular Formula

• The molecular formula is the actual number of atoms of each element in a molecule
• It is a whole-number multiple of the empirical formula
• To determine the molecular formula:
  • Calculate the empirical formula
  • Determine the molar mass of the empirical formula
  • Divide the molar mass of the compound by the molar mass of the empirical formula to get a whole number (n)
  • Multiply the subscripts in the empirical formula by n to obtain the molecular formula