Chapter 3: Balancing Equations, Phases, and Acid Nomenclature

Phase concepts and terminology

• Three basic phases emphasized: solid, liquid, gas. These are foundational before introducing reactions.
• In reactions, many substances are dissolved in water to form solutions. When dissolved, the term for the substance expressed as a liquid is not just “liquid” but aqueous.
  • Aqueous means dissolved in water. Write as aqueous when a substance is dissolved in water (often abbreviated as (aq) in reaction notation).
• Oxygen in its diatomic form appears as a molecule in its standard state: $ext{O}_2$ (gas).
• The solvent water is a pure liquid; however, a solution is a mixture where solutes are dissolved in water (aqueous).
• In organic chemistry (not the focus here), other solvents exist, but this course emphasizes aqueous systems for reactions.

Writing and balancing chemical formulas

• When writing ionic compounds, charges must balance. Ionic compounds are neutral overall (total positive charge equals total negative charge).
• In covalent compounds, sharing governs bonds; the emphasis here is on balancing chemical equations more generally, regardless of ionic or covalent nature.
• A compound’s formula is built from its constituent ions or atoms in a fixed ratio (e.g., MgO is magnesium oxide with Mg$^{2+}$ and O$^{2-}$ in a 1:1 ratio).
• Physical state of compounds matters for the overall description: ionic compounds are typically solids; many dissolve in water to form aqueous solutions; some remain solids in water depending on solubility rules.

Balancing chemical equations: core concepts

• Goal: balance so that the number of atoms of each element is the same on both sides of the equation.
• Methodology overview:
  • Write the correct formulas for all reactants and products first (no coefficients yet).
  • Use coefficients (the large numbers in front of formulas) to balance atoms, not by changing subscript digits in the formulas.
  • If a coefficient of 1 is appropriate, explicitly include it for clarity.
  • If a balancing step produces fractions, multiply all coefficients by a common factor to clear fractions (usually a small integer).
  • The element that appears in the most places in the equation is usually balanced last; this often helps avoid unnecessary steps.
  • The most common balancing target is oxygen (O) and hydrogen (H) due to their presence in many combustion reactions; however, any element can be the starting point depending on the equation.
• Practical tip: choose the molecule with the most atoms as a starting point, typically locking a coefficient of 1 in place for the initial step to anchor balancing.
• Always check for balance after applying coefficients; leaving an equation unbalanced is not acceptable in this course.
• Time-management advice for exams:
  • Practice streamlined methods to avoid time drains (e.g., avoid long balancing lists unless necessary).
  • On the test, aim to complete within the allotted time and reserve a few minutes to re-check.
  • If you get stuck, start over or switch the starting molecule to reframe the balance problem.

Worked example: formation of magnesium oxide (MgO)

• Determine the correct formula: magnesium is Mg$^{2+}$, oxide is O$^{2-}$ → MgO in a 1:1 ratio.
• Formula and state:
  • Reactants: $ext{Mg (s)}$ (solid) and $ext{O}_2 ext{(g)}$ (diatomic oxygen gas).
  • Product: $ext{MgO (s)}$ (solid).
• Write the unbalanced equation with correct formulas:
  • ext{Mg} + ext{O}_2
    ightarrow ext{MgO}
• Balance using coefficients:
  • Start with Mg: set coefficient 1 for Mg on left, then O balance requires at least one MgO on right.
  • To balance O, use a coefficient of 2 in front of MgO: ext{Mg} + ext{O}_2
    ightarrow 2 ext{MgO}
  • Now left side has 1 Mg and 2 O atoms; right side has 2 Mg and 2 O atoms. Balance Mg by doubling the magnesium on the left: 2 ext{Mg} + ext{O}_2
    ightarrow 2 ext{MgO}
  • Check: Left has 2 Mg and 2 O; right has 2 Mg and 2 O. Balanced.
• Final balanced equation:
  • 2 ext{Mg} + ext{O}_2
    ightarrow 2 ext{MgO}
• Key points:
  • We did not change the formula for MgO; coefficients balanced the equation rather than subscripts.
  • MgO is a solid (s) under standard conditions since it is an ionic compound; it is typically solid unless dissolved in water to form an aqueous solution, which depends on solubility.

Worked example: combustion of methane (CH$_4$) with oxygen

• General form of combustion: hydrocarbon + O$<em>2$ → CO$</em>2$ + H$_2$O
• Write the unbalanced skeleton:
  • ext{CH}4 + ext{O}2
    ightarrow ext{CO}2 + ext{H}2 ext{O}
• Balance step-by-step (the common streamlined method):
  • Balance carbon first: one carbon in CH$<em>4$ and one in CO$</em>2$ → coefficient for CH$<em>4$ is 1, for CO$</em>2$ is 1.
  • Balance hydrogen next: CH$<em>4$ has 4 H, so 2 H$</em>2$O are needed to supply 4 H (since each H$_2$O has 2 H).
  • Now balance oxygen on the left: products have CO$<em>2$ (2 O) + H$</em>2$O (2 × 1 O) = 4 O atoms total.
  • Therefore, O$<em>2$ must supply 4 O atoms, requiring 2 O$</em>2$ molecules.
• Final balanced equation:
  • ext{CH}4 + 2 ext{O}2
    ightarrow ext{CO}2 + 2 ext{H}2 ext{O}
• Key points:
  • Coefficients reflect whole molecules; no fractions are used in the final balanced equation here.
  • Hydrogen and oxygen are balanced via the water and carbon dioxide products.
  • Combustion reactions commonly produce CO$<em>2$ and H$</em>2$O as products.

Combustion examples with fractions and doubling technique

• Some combustion problems yield fractional coefficients when balancing directly; common issue is obtaining fractions like 1/2 or 12.5.
• Rule of thumb: avoid fractions in final balanced equations by multiplying all coefficients by the least common multiple to clear fractions.
  • Example scenario described: balancing may lead to a half coefficient (e.g., 12.5) for O$_2$
  • Solution: multiply all coefficients by 2 to eliminate the fraction (e.g., 25 O$_2$ becomes 25; then doubling all coefficients yields whole numbers for all species).
• After doubling, re-check that both sides have equal numbers of each atom for all elements (C, H, O, etc.).
• Note: some chapters later allow fractional coefficients, but at this stage, whole-number coefficients are preferred.

Formation reactions and stoichiometry from elements

• Formation reaction concept: forming a compound from its elements; the reaction is written as element(s) + element(s) → compound.
  • Example: formation of water from elements:
  • Unbalanced skeleton: ext{H}2 + ext{O}2
    ightarrow ext{H}_2 ext{O}
  • Balanced form (formation of water): 2 ext{H}2 + ext{O}2
    ightarrow 2 ext{H}_2 ext{O}
• When writing formation from elements, use diatomic symbols for elements that occur as diatomic molecules in standard state: $ext{H}<em>2$, $ext{O}</em>2$, etc.
• For water, the physical state under standard conditions is liquid: $ext{H}<em>2 ext{O (l)}$; when dissolved in water, the aqueous form is denoted as $ext{H}</em>2 ext{O (aq)}$ (water as solvent).

Acids, polyatomic ions, and naming conventions discussed

• Naming acids (patterns highlighted):
  • If an acid name ends with -ic, it typically derives from a polyatomic ion that ends with -ate. Examples:
  • Nitrate ion NO$<em>3^-$ → nitric acid HNO$</em>3$
  • Sulfate ion SO$<em>4^{2-}$ → sulfuric acid H$</em>2$SO$_4$
  • Phosphate ion PO$<em>4^{3-}$ → phosphoric acid H$</em>3$PO$_4$
  • If an acid name ends with -ous, it typically derives from a polyatomic ion that ends with -ite. Examples:
  • Nitrite ion NO$<em>2^-$ → nitrous acid HNO$</em>2$
  • Sulfite ion SO$<em>3^{2-}$ → sulfurous acid H$</em>2$SO$_3$
• The general acid formation pattern is illustrated with HNO$<em>3$ (nitric acid) as a common example; HNO$</em>3$ is a polyatomic-derived acid.
• Examples used for practice: H$<em>2$O (water, liquid), NaNO$</em>3$ (sodium nitrate, solid), HNO$<em>3$ (nitric acid, aqueous when dissolved), CO$</em>2$ (carbon dioxide, gas).

Solubility, aqueous solutions, and common notes

• Solubility rules determine whether ionic compounds dissolve in water to form an aqueous solution or remain as solids. Some ionic compounds are soluble; others are not.
• In practice problems, you should indicate solubility when appropriate:
  • If the substance dissolves in water, indicate aqueous (aq).
  • If it remains a solid, indicate solid (s).
• The presence of a solution is often described as a “solution” (dissolution in water) or as aqueous.
• Example usage in problems:
  • If a reaction occurs in water with ionic species, you may denote species as (aq).
  • If no dissolution is specified, you may treat the substance as a solid (s) or as a gas (g) depending on the context.

Quick strategies and practice guidance

• Typical test workflow for a reaction problem:
  • Step 1: Write the correct formulas for all reactants and products.
  • Step 2: Check if the equation is already balanced; if not, proceed to balance.
  • Step 3: Balance by adding coefficients, not by altering subscripts.
  • Step 4: If a fractional coefficient appears, multiply all coefficients by the denominator to yield whole numbers.
  • Step 5: Re-check all atoms on both sides for all elements.
• Common pitfalls to avoid:
  • Changing subscripts while balancing.
  • Forgetting to place a coefficient of 1 where appropriate.
  • Not addressing fractions, leading to fractional coefficients in the final answer.
  • Assuming a given equation is balanced without verification.
• Collaboration and study approach:
  • Working with peers on homework problems is encouraged and can improve understanding and speed.
  • Two or three sets of eyes can help identify mistakes that one person might miss.

Quick reference formulas and notations used in this chapter

• Methane combustion (balanced):

  • ext{CH}4 + 2 ext{O}2
    ightarrow ext{CO}2 + 2 ext{H}2 ext{O}

• Magnesium oxide formation (balanced):

  • 2 ext{Mg} + ext{O}_2
    ightarrow 2 ext{MgO}

• Formation of water from elements (balanced):

  • 2 ext{H}2 + ext{O}2
    ightarrow 2 ext{H}_2 ext{O}

• Acid nomenclature examples (patterns):

  • Nitrate to nitric acid: ext{NO}3^- ightarrow ext{HNO}3
  • Nitrite to nitrous acid: ext{NO}2^- ightarrow ext{HNO}2

• Common polyatomic ions and corresponding acids (patterns):

  • Nitrate NO$<em>3^-$ → HNO$</em>3$
  • Sulfate SO$<em>4^{2-}$ → H$</em>2$SO$_4$
  • Phosphate PO$<em>4^{3-}$ → H$</em>3$PO$_4$

• Example entries from the initial list (practice items):

  • Li$<em>3$PO$</em>4$ (lithium phosphate) and Cu acetate (CuCH$_3$COO) or related acetate representations; three common ways to write acetate were noted; ensure you can recognize acetate in multiple notations.
  • Cu acetate can be written in several formats depending on resonance and ion pairing; the essential point is one copper per acetate unit in the simplest solid form.

Any chemistry problem set may include: writing formulas for salts like Li$<em>3$PO$</em>4$, identifying a spectator ion, balancing combustion or synthesis reactions, and naming/recognizing acids and polyatomic ions. Practice these core skills to be exam-ready.