Chemistry Notes: Balancing Equations and Moles

  • Balancing chemical equations: core idea

    • You cannot change the given formulas for the reactants and products.
    • You balance by putting coefficients in front of whole formulas (not by changing subscripts).
    • Coefficients multiply all atoms in that formula; subscripts stay fixed inside each molecule/ion.
    • After adding coefficients, always recount all elements to confirm balance.
    • If you need more of a species to balance, multiply that species (or sides) by an integer as a whole.
    • If any element is unbalanced, adjust coefficients and then recheck all elements.
    • A common rule of thumb: balance hydrogen and oxygen last, as they tend to be trickiest.

  • Worked example: balancing Ba(OH)₂ with HF to form BaF₂ and H₂O

    • Target unbalanced equation (illustrative): Ba(OH)₂ + HF → BaF₂ + H₂O
    • Reasoning:
    • Ba has to be balanced (Ba:1 on both sides).
    • Ba(OH)₂ provides 2 OH⁻ groups; to balance the fluoride side, you need fluorides to cancel Ba²⁺ charge
      and to supply H for water formation.
    • A typical balanced form is: ext{Ba(OH)}2 + 2 ext{HF} ightarrow ext{BaF}2 + 2 ext{H}_2 ext{O}
    • Check counts:
    • Barium: 1 on both sides.
    • Oxygen: 2 on left (from Ba(OH)₂) and 2 on right (in 2 H₂O).
    • Hydrogen: 2 (from Ba(OH)₂) + 2 (from 2 HF) = 4 on left; 2×2 = 4 on right (in 2 H₂O).
    • Fluorine: 2 on left (from 2 HF); 2 on right (in BaF₂).
    • Takeaway: adding a coefficient in front of HF (2) balances the fluorine and hydrogen counts without changing the formulas.
    • Note about front coefficients vs subscripts: putting a 2 in front of HF multiplies the whole HF molecule; using a subscript (e.g., HF₂) would change the species itself, which is not what we want for balancing this reaction. The placement (front vs subscripts) matters only in how the counts are achieved, but the final total counts must be correct.

  • More on balancing strategy (conceptual)

    • If a balance attempt yields odd numbers for some element, you may need to double one or more coefficients to get even counts and then reassess.
    • After adjusting, recount all elements, including elements that appear in multiple places (e.g., O or H spread across compounds).
    • A practical approach: once the counts appear correct for some elements, verify the rest and adjust as necessary until all elements balance.

  • Example discussion: a phosphorus-containing balancing step (illustrative)

    • Start with one phosphorus on one side; you may set a coefficient like 4 for a phosphorus-containing species to balance P.
    • This can lead to other element counts (e.g., hydrogens) that require adjusting another coefficient to balance (e.g., making another coefficient 6).
    • You may find you need to double certain coefficients to balance all elements (e.g., ensure you have 12 hydrogens on the side that needs them).
    • After each adjustment, recount all elements to ensure a complete balance.
    • This illustrates that balancing can require iterative changes and sometimes doubling of coefficients.

  • Practical tips during balancing

    • Always go back and recount everything after changing coefficients.
    • If an element appears in more than one compound, distribute the element counts across all affected species when checking balance.
    • Oxygen and hydrogen are often balanced last due to their prevalence and placement in many reactions.

  • The mole concept: what a mole represents in chemistry

    • A mole is a unit of amount of substance (amount of substance), used to measure how many particles are present.
    • One mole corresponds to Avogadro’s number: N_A = 6.022 imes 10^{23} particles.
    • In chemistry, a mole can count different particle types: molecules, formula units, atoms, or ions.
    • Clarification: For covalent/molecular compounds, the basic counting unit is the molecule; for ionic compounds, the basic unit is the formula unit.
    • Example particle types:
    • Molecules: smallest unit in covalent/molecular compounds (e.g., water is made of molecules).
    • Formula units (f.u.): smallest repeating unit in ionic compounds (e.g., NaCl or BaCl₂ in a crystal).
    • Atoms: individual atoms used in counting when dealing with elemental substances.
    • Ions: charged particles used when counting ionic species (e.g., Cl⁻ or Na⁺).

  • Ionic vs molecular compounds: smallest unit terminology

    • Ionic compounds: smallest unit is a formula unit (f.u.). Example for BaCl₂: the unit shows a 1:2 ratio of Ba to Cl (BaCl₂).
    • Molecular (covalent) compounds: smallest unit is a molecule. Example for water: H₂O is a molecule; the smallest unit is a molecule, not a formula unit.
    • Do not refer to a water sample as a formula unit; that term is reserved for ionic compounds.
    • When you count particles corresponding to a mole, you may refer to molecules, formula units, atoms, or ions, depending on the substance.

  • The particle test: how many particles correspond to a mole

    • If you have 6.02 × 10²³ molecules of water, you have one mole of water.
    • If you have 6.02 × 10²³ chloride ions (Cl⁻), you have one mole of chloride ions.
    • If you have an ionic solid like NaCl, the smallest repeating unit is a formula unit, so 6.02 × 10²³ formula units correspond to one mole of NaCl.
    • If you have 6.02 × 10²³ BaCl₂ formula units, that is one mole of BaCl₂, not one mole of Ba and two moles of Cl separately; the formula unit already encodes the ratio.

  • Dimensional analysis for converting particles to moles (and vice versa)

    • General relationship: n = rac{N}{N_A} where n is the amount in moles and N is the number of particles.
    • Example: If you have N = 6.8 imes 10^{24} molecules of some substance, then
    • $$n = rac{6.8 imes 10^{24}}{6.022 imes 10^{23}} \