8.1 Chemical Equations, Types of Reactions & Net Ionic Equations

8.1 Chemical Equations, Types of Reactions & Net Ionic Equations

Quick Summary: Chemical equations symbolize chemical transformations, conserving atoms and electrical charge according to the Law of Conservation of Mass. Inorganic reactions are classified into combination, decomposition, single displacement (governed by the activity series), double displacement (driven by precipitate, water, or gas formation), and combustion. In aqueous solutions, reactions between electrolytes are represented by net ionic equations, which eliminate spectator ions to isolate the fundamental chemical transformation.

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1. Anatomy of Chemical Equations & Conservation of Mass

A chemical equation symbolizes the rearrangement of atoms during a chemical change. Reactants appear on the left of the reaction arrow, and products appear on the right. Physical state designations denote phase under ambient reaction conditions: solid $(s)$, liquid $(l)$, gas $(g)$, and aqueous solution $(aq)$. Reaction conditions, such as thermal input ($\Delta$) or specific catalysts, appear above or below the arrow.

Coefficients versus Subscripts

• Subscripts define the fixed, invariant stoichiometric ratio of atoms within a molecule or crystal lattice (e.g., in $\text{H}_2\text{O}$, the subscript $2$ indicates two hydrogen atoms bonded to one oxygen). Altering subscripts changes the fundamental chemical substance.
• Stoichiometric Coefficients are whole numbers placed before formulas to balance the total quantity of each atom between reactants and products.

The Law of Conservation of Mass

Established by Antoine Lavoisier in 1789, the Law of Conservation of Mass mandates that matter is neither created nor destroyed during chemical transformations. Every atom entering a reaction must exit in the product mixture. Consequently, balanced equations satisfy two criteria:

1. Mass Balance: The total number of atoms of each element is identical on both sides.
2. Charge Balance: The net electrical charge of reactants equals the net charge of products.

Balancing Equations by Inspection

Most non-redox equations on the exam can be balanced by inspection:

1. Write correct formulas for every reactant and product; never change a subscript.
2. Balance the element that appears in the fewest formulas first, usually a metal or carbon.
3. Balance polyatomic ions that survive unchanged as single units (for example, keep $\text{SO}_4^{2-}$ together).
4. Balance hydrogen and then oxygen last, because they usually appear in several formulas.
5. If a fractional coefficient appears, multiply every coefficient by the denominator, then confirm that the coefficients are the smallest whole numbers.

Worked Example 1: $\text{Fe}(s) + \text{O}_2(g) \to \text{Fe}_2\text{O}_3(s)$. Two Fe are needed on the left for each $\text{Fe}_2\text{O}_3$, and oxygen requires $\tfrac{3}{2}\,\text{O}_2$: $2\,\text{Fe} + \tfrac{3}{2}\,\text{O}_2 \to \text{Fe}_2\text{O}_3$. Doubling clears the fraction: $4\,\text{Fe} + 3\,\text{O}_2 \to 2\,\text{Fe}_2\text{O}_3$.

Worked Example 2 (combustion): $\text{C}_2\text{H}_6 + \text{O}_2 \to \text{CO}_2 + \text{H}_2\text{O}$. Carbon gives $2\,\text{CO}_2$; hydrogen gives $3\,\text{H}_2\text{O}$; the products now hold $4 + 3 = 7$ O atoms, so $\tfrac{7}{2}\,\text{O}_2$ is needed. Doubling gives $2\,\text{C}_2\text{H}_6 + 7\,\text{O}_2 \to 4\,\text{CO}_2 + 6\,\text{H}_2\text{O}$ (check: 4 C, 12 H, and 14 O on each side).

Redox equations whose electrons do not balance by inspection are handled with the half-reaction method in Section 10.1.

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2. Five Major Reaction Classifications

Single Displacement & The Activity Series

In a single displacement reaction, an elemental metal or halogen displaces a less active counterpart from an aqueous compound. The Activity Series ranks elements by their relative tendency to undergo oxidation (lose electrons):

$\text{Li} > \text{K} > \text{Ba} > \text{Ca} > \text{Na} > \text{Mg} > \text{Al} > \text{Mn} > \text{Zn} > \text{Cr} > \text{Fe} > \text{Ni} > \text{Sn} > \text{Pb} > \mathbf{H_2} > \text{Cu} > \text{Ag} > \text{Pt} > \text{Au}$

• Active metals ($\text{Li}$–$\text{Na}$) reduce cold water to yield $\text{H}_2(g)$ and aqueous metal hydroxides.
• Moderately active metals ($\text{Mg}$–$\text{Pb}$) reduce aqueous hydronium in dilute acids ($\text{HCl}, \text{H}_2\text{SO}_4$) to liberate $\text{H}_2(g)$, but do not react with cold water.
• Metals below hydrogen ($\text{Cu}, \text{Ag}, \text{Pt}, \text{Au}$) lie below hydrogen and cannot displace $\text{H}_2(g)$ from non-oxidizing acids.

Halogen activity parallels electronegativity and reduction potentials: $\text{F}_2 > \text{Cl}_2 > \text{Br}_2 > \text{I}_2$. Chlorine displaces bromide and iodide ions from solution, but cannot displace fluoride.

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3. Aqueous Solutions: Molecular, Complete & Net Ionic Equations

When soluble ionic compounds dissolve in water, solvent dipoles dissociate them into independent hydrated ions. Aqueous reactions are formulated through three distinct representations:

1. Molecular Equation: Written with all reactants and products depicted as intact neutral compounds: $\text{Pb(NO}_3)_2(aq) + 2\,\text{KI}(aq) \longrightarrow \text{PbI}_2(s) + 2\,\text{KNO}_3(aq)$
2. Complete (Total) Ionic Equation: Dissociates all dissolved strong electrolytes into separated aqueous ions. Weak electrolytes, precipitates, pure liquids, and gases remain undissociated: $\text{Pb}^{2+}(aq) + 2\,\text{NO}_3^-(aq) + 2\,\text{K}^+(aq) + 2\,\text{I}^-(aq) \longrightarrow \text{PbI}_2(s) + 2\,\text{K}^+(aq) + 2\,\text{NO}_3^-(aq)$
3. Net Ionic Equation: Eliminates spectator ions—species that appear identically on both sides without chemical alteration—revealing the fundamental chemical process: $\text{Pb}^{2+}(aq) + 2\,\text{I}^-(aq) \longrightarrow \text{PbI}_2(s)$

Systematic Protocol for Net Ionic Equations

• Identify Strong Electrolytes: Fully dissociate soluble salts, the six strong acids ($\text{HCl}, \text{HBr}, \text{HI}, \text{HNO}_3, \text{HClO}_4, \text{H}_2\text{SO}_4$), and strong bases (Group 1 hydroxides, $\text{Ca(OH)}_2, \text{Sr(OH)}_2, \text{Ba(OH)}_2$).
• Retain Intact Formulas: Keep weak acids (e.g., $\text{HF}, \text{CH}_3\text{COOH}$), weak bases ($\text{NH}_3$), insoluble solids ($(s)$), pure liquids ($(l)$, notably $\text{H}_2\text{O}$), and gases ($(g)$) in molecular form.
• Cancel Spectator Ions: Eliminate identical ions in equal numbers from both sides.

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4. Gas-Evolution Reactions via Unstable Intermediates

Certain double displacement reactions produce intermediate acids or bases that are thermodynamically unstable in water, decomposing spontaneously into volatile gases and liquid water:

• Carbonates and Bicarbonates: React with acid to produce carbonic acid ($\text{H}_2\text{CO}_3$), which spontaneously decomposes: $\text{NaHCO}_3(s) + \text{H}^+(aq) \longrightarrow \text{Na}^+(aq) + \text{H}_2\text{O}(l) + \text{CO}_2(g)$
• Sulfites and Bisulfites: React with acid to yield sulfurous acid ($\text{H}_2\text{SO}_3$), decomposing into sulfur dioxide gas: $\text{SO}_3^{2-}(aq) + 2\,\text{H}^+(aq) \longrightarrow \text{H}_2\text{O}(l) + \text{SO}_2(g)$
• Ammonium Salts: React with strong bases to form ammonium hydroxide, which decomposes into ammonia gas: $\text{NH}_4^+(aq) + \text{OH}^-(aq) \longrightarrow \text{NH}_3(g) + \text{H}_2\text{O}(l)$
• Metal Sulfides: React directly with acids to generate toxic hydrogen sulfide gas without forming an intermediate: $\text{FeS}(s) + 2\,\text{H}^+(aq) \longrightarrow \text{Fe}^{2+}(aq) + \text{H}_2\text{S}(g)$