Chemical Reactions and Reaction Stoichiometry Study Notes

Chemical Reactions and Reaction Stoichiometry

Stoichiometry

• Definition: Stoichiometry is the study of mass relationships in chemistry.

• Foundation: It is based on the Law of Conservation of Mass, which was formulated by Antoine Lavoisier in 1789.

  • Law of Conservation of Mass Statement: "We may lay it down as an incontestable axiom that, in all the operations of art and nature, nothing is created; an equal amount of matter exists both before and after the experiment. Upon this principle, the whole art of performing chemical experiments depends."

Chemical Equations

• Definition: Chemical equations are concise representations of chemical reactions.

• Structure of a Chemical Equation: Essential Components

  • Reactants: Substances that undergo reaction, represented on the left side.

  • Products: Substances formed as a result of the reaction, represented on the right side.

  • Example: For the reaction of hydrogen and oxygen to form water, the balanced equation is:
    $2 H<em>2 + O</em>2 <br>ightarrow 2 H_2O$

What Is in a Chemical Equation?

• Example provided:

  • $CH<em>4(g) + 2O</em>2(g) <br>ightarrow CO<em>2(g) + 2H</em>2O(g)$

  • Reactants:

  • $CH<em>4(g)$ and $2O</em>2(g)$ on the left side of the equation.

  • Products:

  • $CO<em>2(g)$ and $2H</em>2O(g)$ on the right side of the equation.

  • Physical States Notation: States of reactants/products are denoted as follows:

  • (g) - gas

  • (l) - liquid

  • (s) - solid

  • (aq) - in aqueous solution

Balancing Chemical Equations

• Purpose of Coefficients: Coefficients are inserted to balance the equation to adhere to the law of conservation of mass.

• Reason for Adding Coefficients Instead of Changing Subscripts:

  • Hydrogen and oxygen can yield either water (H₂O) or hydrogen peroxide (H₂O₂).

  • Water formation:

    • $2 H<em>2(g) + O</em>2(g) <br>ightarrow 2 H_2O(l)$

  • Hydrogen peroxide formation:

    • $H<em>2(g) + O</em>2(g) <br>ightarrow H<em>2O</em>2(l)$

Types of Reactions

• Three Primary Types of Reactions:

  1. Combination reactions

  2. Decomposition reactions

  3. Combustion reactions

Combination Reactions

• Definition: In combination reactions, two or more substances react to form one product.

• Examples:

  • $2 Mg(s) + O_2(g) <br>ightarrow 2 MgO(s)$

  • $N<em>2(g) + 3 H</em>2(g) <br>ightarrow 2 NH_3(g)$

  • $C<em>3H</em>6(g) + Br<em>2(l) ightarrow C</em>3H<em>6Br</em>2(l)$

Decomposition Reactions

• Definition: In a decomposition reaction, one substance breaks down into two or more substances.

• Examples:

  • $CaCO<em>3(s) ightarrow CaO(s) + CO</em>2(g)$

  • $2 KClO<em>3(s) ightarrow 2 KCl(s) + O</em>2(g)$

  • $2 NaN<em>3(s) ightarrow 2 Na(s) + 3 N</em>2(g)$

Combustion Reactions

• Definition: Combustion reactions are generally rapid reactions that produce a flame and often involve oxygen as a reactant.

• Examples:

  • $CH<em>4(g) + 2 O</em>2(g) <br>ightarrow CO<em>2(g) + 2 H</em>2O(g)$

  • $C<em>3H</em>8(g) + 5 O<em>2(g) ightarrow 3 CO</em>2(g) + 4 H_2O(g)$

Molecular Weight (Molar Mass)

• Definition: A molecular weight is the sum of the atomic weights of the atoms in a molecule.

• Example for Ethane (C₂H₆):

  • Carbon: $2 imes 12.011 ext{ amu} = 30.070 ext{ amu}$

  • Hydrogen: $6 imes 1.00794 ext{ amu}$

Ionic Compounds and Formulas

• Definition: Ionic compounds exist in a three-dimensional arrangement of ions, making them different from molecular compounds.

• Formulation: They utilize empirical formulas for representation; molecular weights are not applicable.

Percent Composition

• Definition: Percent composition is the percentage of the mass of a compound that comes from each element.

• Formula:

  • ext{% Element} = rac{( ext{number of atoms}) imes ( ext{atomic weight})}{ ext{FW of the compound}} imes 100

• Example for Carbon in Ethane:

  • Calculation:

  • ext{%C} = rac{(2)(12.011 ext{ amu})}{30.070 ext{ amu}} imes 100 = 79.887 ext{%}

Avogadro’s Number

• Definition: Avogadro’s number is the quantity of 6.02 × 10²³ atoms or molecules, defined as one mole.

• Relation to Carbon: One mole of $^{12}C$ has a mass of 12.000 g.

Molar Mass

• Definition: Molar mass is the mass of one mole of a substance, expressed in g/mol.

  • Atomic Weight: For elements, it equals the atomic weight; for diatomic elements, it’s double that atomic weight.

  • Relationship: Formula weight in atomic mass units (amu) equals the molar mass in g/mol.

Using Moles

• Function: Moles serve as a bridge from the molecular scale to practical applications in the real world.

Mole Relationships

• Key Points:

  • One mole of atoms, ions, or molecules corresponds to Avogadro’s number of that entity.

  • The mole of molecules/formula units contains Avogadro’s number multiplied by the number of constituent atoms or ions.

Determining Empirical Formulas

• Process:

  1. Starting Point: Use the percent composition.

  2. Mole Calculation: Convert masses to moles of each component using molar mass.

  3. Ratio Calculation: Divide each mole quantity by the smallest number of moles present to obtain whole-number ratios.

Example for PABA

• Percent Composition:

  • Carbon (C): 61.31%

  • Hydrogen (H): 5.14%

  • Nitrogen (N): 10.21%

  • Oxygen (O): 23.33%

Assuming 100 g of PABA:

$C: rac{61.31 g }{12.01 g/mol} = 5.105 mol C$

$H: rac{5.14 g}{1.01 g/mol} = 5.09 mol H$

$N: rac{10.21 g}{14.01 g/mol} = 0.7288 mol N$

$O: rac{23.33 g }{16.00 g/mol} = 1.456 mol O$

• Mole Ratio Calculation:

  • Divide by smallest mole value:

  • $C: rac{5.105}{0.7288} <br>ightarrow 7.005 ext{ (≈ 7)}$

  • $H: rac{5.09}{0.7288} <br>ightarrow 6.984 ext{ (≈ 7)}$

  • $N: rac{0.7288}{0.7288} <br>ightarrow 1.000$

  • $O: rac{1.456}{0.7288} <br>ightarrow 2.001 ext{ (≈ 2)}$

• Empirical Formula Result:

  • $C<em>7H</em>7NO_2$

Determining a Molecular Formula

• Definition: The molecular formula is a whole-number multiple of the empirical formula. To find it:

  • If the molar mass is known, compute the ratio of molar mass to empirical formula mass.

• Example Calculation:

  • Given empirical formula $CH$, with molar mass of 78 g/mol:

  • Whole-number multiple = $rac{78}{13} = 6$

  • Molecular formula = $C<em>6H</em>6$

Combustion Analysis

• Usage: Compounds containing C, H, and O can be analyzed through combustion.

  • Carbon Determination: Identified via mass of CO₂ produced.

  • Hydrogen Determination: Identified via mass of H₂O produced.

  • Oxygen Determination: Established by difference after Carbon and Hydrogen are accounted for.

Quantitative Relationships

• Coefficient Role: Coefficients in balanced equations are indicative of:

  • Relative numbers of molecules of reactants/products.

  • Relative moles of reactants/products, usable to calculate mass.

Limiting Reactants

• Definition: The limiting reactant is the one available in the least stoichiometric amount and limits the extent of a reaction, impacting product formation.

• Identification: Used in all stoichiometric calculations to determine product amounts and quantities of other reactants consumed in the reaction.

Theoretical Yield

• Definition: The theoretical yield represents the maximum possible amount of product that could be produced, as calculated via stoichiometry.

• Distinction from Actual Yield: Actual yield is the quantity actually measured and produced in practice.

Percent Yield

• Formula:
  $ext{Percent Yield} = rac{ ext{actual yield}}{ ext{theoretical yield}} imes 100$

• Purpose: Comparative measure of the quantity obtained versus the maximum potential yield.

Solutions

• Definition: Solutions are homogeneous mixtures of two or more pure substances.

  • Solvent: Substance present in greatest abundance.

  • Solutes: All other components in lesser amounts.

  • Aqueous Solutions: When the solvent is water.

Aqueous Solutions

• Dissolution Mechanism:

  • Ionic compounds dissolve via dissociation, where water molecules separate and surround ions.

  • Molecular compounds may dissolve without dissociation; some react with water during dissolution.

Electrolytes and Nonelectrolytes

• Electrolyte Definition: A substance that dissociates into ions in water.

• Nonelectrolyte Definition: A substance that may dissolve in water but does not dissociate into ions.

Electrolytes

• Classification:

  • Strong Electrolytes: Completely dissociate in solution.

  • Weak Electrolytes: Partially dissociate in solution.

  • Nonelectrolytes: Do not dissociate in water.

Solubility of Ionic Compounds

• Dissolution Limitations: Not all ionic compounds are soluble in water; solubility rules guide which combinations dissolve.

Precipitation Reactions

• Definition: Occurs when two solutions containing soluble salts yield an insoluble product, denoted as a precipitate.

Metathesis (Exchange) Reactions

• Definition: Involves the apparent exchange of ions between the reactant compounds.

• Example Reaction:

  • $AgNO<em>3(aq) + KCl(aq) ightarrow AgCl(s) + KNO</em>3(aq)$

Completing and Balancing Metathesis Equations

• Steps for Balancing:

  1. Identify the ions from reactants.

  2. Write formulas for the products using cations and anions from reactants.

  3. Apply solubility rules to identify any precipitate formation.

  4. Balance the resulting equation.

Ways to Write Metathesis Reactions

1. Molecular Equation: Lists reactants/products without indicating ionic nature.

2. Complete Ionic Equation: Displays all strong electrolytes as dissociated ions.

3. Net Ionic Equation: Eliminates spectator ions, reflecting only the changing ions.

Molecular Equation Example

• Chemical Representation:

  • $AgNO<em>3(aq) + KCl(aq) ightarrow AgCl(s) + KNO</em>3(aq)$

Complete Ionic Equation

• Representation:

  • $Ag^+(aq) + NO<em>3^−(aq) + K^+(aq) + Cl^−(aq) ightarrow AgCl(s) + K^+(aq) + NO</em>3^−(aq)$

Net Ionic Equation

• Derivation:

  • Resulting equation: $Ag^+(aq) + Cl^−(aq) <br>ightarrow AgCl(s)$

  • Spectator Ions Identified: $K^+(aq)$ and $NO_3^−(aq)$ excluded.

Writing Net Ionic Equations

• Procedure:

  1. Start with a balanced molecular equation.

  2. Dissociate all strong electrolytes.

  3. Exclude unchanged species (spectator ions).

  4. Present the net ionic equation with remaining species.

Acids

• Arrhenius Definition: Acids increase H⁺ concentration in water.

• Brønsted-Lowry Definition: Acids are proton donors.

Bases

• Arrhenius Definition: Bases increase OH⁻ concentration in water.

• Brønsted-Lowry Definition: Bases function as proton acceptors.

Strong or Weak Acids and Bases

• Strong Acids: Completely dissociate in water.

• Weak Acids: Partially dissociate in water.

• Strong Bases: Fully dissociate to form metal cations and hydroxide ions.

• Weak Bases: Partially generate hydroxide ions.

Acid-Base Reactions

• Nature of Reaction: Acid gives a proton (H⁺) to a base.

• Terminology: These interactions are termed neutralization reactions, often producing salt and water.

Neutralization Reactions

• Example:

  • $HCl(aq) + NaOH(aq) <br>ightarrow NaCl(aq) + H_2O(l)$

  • Net ionic representation:

  • $H^+(aq) + OH^−(aq) <br>ightarrow H_2O(l)$

Gas-Forming Reactions

• Observation: Occur when reacting carbonates/bicarbonates with acids, producing gas (CO₂) alongside salt and water.

• Example Reaction:

  • $CaCO<em>3(s) + 2 HCl(aq) ightarrow CaCl</em>2(aq) + CO<em>2(g) + H</em>2O(l)$

Oxidation-Reduction Reactions (Redox)

• Key Concepts:

  • Oxidation: Loss of electrons.

  • Reduction: Gain of electrons.

  • Interdependence: Both processes occur simultaneously in reactions.

Oxidation Numbers

• Purpose: Assigning oxidation numbers aids in determining if redox reactions have occurred.

Rules to Assign Oxidation Numbers

1. Zero for Elements in Standard Form

2. Monatomic Ions: Oxidation number equals its charge.

3. Nonmetals: Often possess negative oxidation states, but may be positive. Stable oxidation states include:

   • Oxygen: -2 (or -1 in peroxides).

   • Hydrogen: -1 with metals; +1 with nonmetals.

4. Fluorine: Always has -1.

5. Other Halogens can possess positive states in oxyanions.

6. Sum Rule: Oxidation numbers in neutral compounds sum to zero; polyatomic ions equal their charge.

Displacement Reactions

• Example Reaction:

  • $Cu(s) + 2 Ag^+(aq) <br>ightarrow Cu^{2+}(aq) + 2 Ag(s)$

• Nature of Reaction: Here, silver ions oxidize copper metal.

Activity Series

• Concept: Elements higher on the series are more reactive and tend to exist as ions.

Metal/Acid Displacement Reactions

• Behavior: Metals above hydrogen in the activity series react with acids, producing hydrogen gas through oxidation to create cations.

Molarity

• Definition: Molarity measures concentration as moles of solute per volume of solution in liters.

• Formula:
  $ext{Molarity (M)} = rac{ ext{moles of solute}}{ ext{volume of solution in liters}}$

Mixing a Solution

• Procedure: To prepare a solution of known molarity, weigh the solute accurately and add it to a volumetric flask before diluting to volume with solvent.

Dilution

• Process Description: Achieved by transferring a known volume of solution into a new volumetric flask and filling with solvent up to the requested volume.

• Calculation: Use the formula $M<em>c imes V</em>c = M<em>d imes V</em>d$ Where:

  • $M_c$ = Molarity of concentrated solution

  • $V_c$ = Volume of concentrated solution

  • $M_d$ = Molarity of diluted solution

  • $V_d$ = Volume of diluted solution

Using Molarities in Stoichiometric Calculations

• Overview of Steps:

  1. Convert grams of substance A to moles using molar mass.

  2. Use coefficients from a balanced equation for stoichiometric relationships of substance A to substance B.

  3. Calculate moles of substance B using molarity and volume of solution containing it.

Titration

• Definition: Titration is an analytical method to determine solute concentration within a solution.

• Components: A standard solution of known concentration is utilized to ascertain the unknown concentration under the equivalence point during the reaction.