Chapter 4: Chemical Reactions, Stoichiometry, and Electrolytes

Chemical Equations and Balancing

Writing and Balancing Chemical Equations

Chemical equations represent the reactants and products in a chemical reaction. To accurately reflect the law of conservation of mass, equations must be balanced so that the number of atoms of each element is the same on both sides.

• Balanced Equation: An equation with the smallest possible whole-number coefficients for all reactants and products.

• Steps to Balance:

  1. If an element occurs in only one compound on each side, balance it first.

  2. Balance elements that appear in two or more reactants or products last.

  3. Balance polyatomic ions as a unit if they appear unchanged on both sides.

  4. Check your work by counting atoms of each element on both sides.

• States of Matter: Indicate the physical state: (g) gas, (l) liquid, (s) solid, (aq) aqueous.

• Example: Combustion of methane: $\mathrm{CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)}$

• Example: Double displacement reaction: $\mathrm{CaCl_2(aq) + 2AgNO_3(aq) \rightarrow Ca(NO_3)_2(aq) + 2AgCl(s)}$

Stoichiometry and Mole Ratios

Stoichiometric Calculations

Stoichiometry involves using balanced chemical equations to calculate the relationships between reactants and products in a reaction, often using mole ratios.

• Mole Ratio: The ratio of moles of one substance to moles of another as indicated by the coefficients in a balanced equation.

• Example: For $2H_2 + O_2 \rightarrow 2H_2O$, the mole ratio is 2:1:2 for $H_2:O_2:H_2O$.

• Application: Used to convert between masses, moles, and numbers of particles.

Limiting Reactants

In a chemical reaction, the limiting reactant is the substance that is completely consumed first, thus limiting the amount of product formed.

• Definition: The reactant that is used up before the others in a chemical reaction.

• Identifying the Limiting Reactant: Compare the mole ratio of reactants used to the ratio in the balanced equation.

• Example: If 10 mol $H_2$ and 7 mol $O_2$ react to form $H_2O$, $H_2$ is the limiting reactant because it will be used up first according to the reaction $2H_2 + O_2 \rightarrow 2H_2O$.

Theoretical and Percent Yield

Theoretical yield is the maximum amount of product that can be formed from given reactants, while actual yield is the amount actually obtained. Percent yield compares these values.

• Theoretical Yield: Calculated from stoichiometry, assuming complete reaction.

• Actual Yield: The measured amount of product obtained from a reaction.

• Percent Yield Formula: $\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\%$

• Example: If 3.00 g of titanium reacts with 6.00 g of $Cl_2$ to form 7.7 g of $TiCl_4$, percent yield is calculated using the above formula.

Electrolytes and Ionic Compounds in Solution

Electrolytes

Electrolytes are substances that dissolve in water to produce a solution that conducts electricity due to the presence of ions.

• Strong Electrolytes: Dissociate completely into ions (e.g., soluble ionic compounds).

• Weak Electrolytes: Dissociate only partially into ions (e.g., weak acids and bases).

• Nonelectrolytes: Do not produce ions in solution (e.g., most molecular compounds).

• Electrical Conductivity: Depends on the concentration and extent of ionization.

Dissociation and Ionization

• Dissociation: Separation of an ionic compound into its constituent ions in water. Example: $MgCl_2(s) \rightarrow Mg^{2+}(aq) + 2Cl^-(aq)$

• Ionization: Formation of ions from molecular compounds, often by reaction with water. Example: $CH_3COOH(aq) + H_2O(l) \rightarrow CH_3COO^-(aq) + H_3O^+(aq)$

Precipitation Reactions

Formation of Precipitates

Precipitation reactions occur when two solutions are mixed and an insoluble solid (precipitate) forms.

• Precipitate: An insoluble solid formed from a reaction in solution.

• Solubility Rules: Used to predict whether a compound will dissolve in water or form a precipitate.

Solubility Table (Main Purpose: Classification of Ionic Compounds as Soluble or Insoluble)

Soluble Compounds	Exceptions
Compounds of Group 1A ions, NH4+	None
Nitrates (NO3-), Acetates (C2H3O2-), Most chlorides, bromides, iodides	Ag+, Pb2+, Hg22+
Sulfates (SO42-)	Ba2+, Pb2+, Ca2+, Sr2+
Insoluble Compounds	Exceptions
Carbonates (CO32-), Phosphates (PO43-), Hydroxides (OH-), Sulfides (S2-)	Group 1A, NH4+ (and Ba2+ for OH- and S2-)

• Example: $AgNO_3(aq) + NaCl(aq) \rightarrow AgCl(s) + NaNO_3(aq)$

Types of Equations for Ionic Reactions

• Balanced Chemical Equation (BCE): Shows all reactants and products as compounds.

• Complete Ionic Equation (CIE): Shows all strong electrolytes as ions.

• Net Ionic Equation (NIE): Shows only the species that actually change during the reaction.

• Example:

  • BCE: $Pb(NO_3)_2(aq) + 2KI(aq) \rightarrow PbI_2(s) + 2KNO_3(aq)$

  • CIE: $Pb^{2+}(aq) + 2NO_3^-(aq) + 2K^+(aq) + 2I^-(aq) \rightarrow PbI_2(s) + 2K^+(aq) + 2NO_3^-(aq)$

  • NIE: $Pb^{2+}(aq) + 2I^-(aq) \rightarrow PbI_2(s)$

Acid-Base Reactions

Acids and Bases in Aqueous Solution

Acids ionize in water to form hydrogen ions ($H^+$), while bases produce hydroxide ions ($OH^-$).

• Strong Acids: Ionize completely (e.g., HCl, HNO3, H2SO4).

• Weak Acids: Ionize partially (e.g., CH3COOH).

• Strong Bases: Group 1 and 2 metal hydroxides (e.g., NaOH, KOH).

• Weak Bases: Ammonia (NH3), amines.

• Example: $HCl(aq) \rightarrow H^+(aq) + Cl^-(aq)$

Gas-Forming Reactions

• Some reactions produce a gas as a product, such as CO2, SO2, or NH3.

• Example Table (Main Purpose: List of Common Gas-Forming Reactions)

Ion	Reaction
CO32-	$CO_3^{2-}(aq) + 2H^+(aq) \rightarrow CO_2(g) + H_2O(l)$
SO32-	$SO_3^{2-}(aq) + 2H^+(aq) \rightarrow SO_2(g) + H_2O(l)$
S2-	$S^{2-}(aq) + 2H^+(aq) \rightarrow H_2S(g)$
NH4+	$NH_4^+(aq) + OH^-(aq) \rightarrow NH_3(g) + H_2O(l)$

Oxidation-Reduction (Redox) Reactions

Redox Concepts

Redox reactions involve the transfer of electrons between substances. Oxidation is the loss of electrons, and reduction is the gain of electrons.

• Oxidizing Agent: Causes another substance to be oxidized and is itself reduced.

• Reducing Agent: Causes another substance to be reduced and is itself oxidized.

• Assigning Oxidation Numbers: Used to track electron transfer in redox reactions.

• Rules for Assigning Oxidation Numbers:

  1. Elemental form: 0

  2. Monatomic ion: charge of the ion

  3. Oxygen: usually -2

  4. Hydrogen: +1 with nonmetals, -1 with metals

  5. Fluorine: always -1

  6. Sum of oxidation numbers equals the charge of the species

• Example: In the reaction $Cd(s) + 2NiO_2(s) + 2H_2O(l) \rightarrow Cd(OH)_2(s) + 2Ni(OH)_2(s)$, identify oxidized and reduced species by assigning oxidation numbers.

Additional info: Some explanations and examples have been expanded for clarity and completeness, and tables have been reconstructed for study purposes.