Advanced Chemistry Spring Final Exam Review 2026 Study Notes

Advanced Chemistry Spring Final Exam Overview and Logistics

• Exam Date: Spring 2026.

• General Advice for Preparation:

  • Review the year in reverse order.

  • Complete the practice final exam.

  • Review all classroom notes, reading notes, problem sets, homework, and labs.

• Provided Materials:

  • Periodic table.

  • Conversion sheet.

  • Polyatomic ion sheet.

  • Solubility rules.

  • Formula sheet.

Course Syllabus and Unit Topics

• Unit 1 (Chapter 2): Matter & Measurement, including Dimensional Analysis, Significant Figures, and Density.

• Unit 2 (Chapter 3.1-3.5): Classification of Matter, Chemical & Physical Properties, and Changes.

• Unit 3 (Chapter 4): Atomic Structure & Periodic Table.

• Unit 4 (Chapters 5 & 6): Modern Atomic Theory & Periodic Table.

• Unit 5 (Chapters 7, 8, & 9): Nomenclature and Chemical Bonding.

• Unit 6 (Chapter 10): Chemical Composition and the Mole.

• Unit 7 (Chapters 11 & 12): Reactions, Stoichiometry, and Redox reactions.

• Unit 8 (Chapter 14): Gases.

• Unit 9 (Chapters 16 & 17): Solutions, Acid-Bases, and Equilibrium.

Matter & Measurement Principles

• Identification of Substances: Intensive properties, such as Specific Heat, are useful for identifying unknown substances because they do not depend on the amount of matter present. Extensive properties like volume, moles, and enthalpy vary with amount.

• Classification of Matter:

  • A mixture is represented by chemical symbols indicating multiple substances or a substance dissolved in another, such as $NaCl(aq)$ (sodium chloride dissolved in water).

  • Pure substances are represented as single formulas like $NaCl(s)$, $H_2O(l)$, or $H_2O(g)$.

• Density Calculations ($D = \frac{m}{V}$):

  • Displacement: If $52.4\,g$ of iron ($density = 7.86\,g/cm^3$) is added to $75.0\,mL$ of water, the volume of iron is calculated as $\frac{52.4\,g}{7.86\,g/cm^3} = 6.66\,cm^3$ ($6.67\,mL$). The final volume reading is $75.0\,mL + 6.67\,mL = 81.7\,mL$.

  • Volume from Mass: A gold nugget with a mass of $63.3\,g$ has a volume of approximately $3.28\,mL$.

• Experimental Accuracy and Precision:

  • Percent Error Formula: $\text{Percent Error} = \frac{|\text{Experimental Value} - \text{Accepted Value}|}{\text{Accepted Value}} \times 100$

  • Example: Experimental boiling point of octane is $124.1^{\circ}C$, accepted is $125.7^{\circ}C$. Percent error is approximately $1.273\%$.

  • Precision vs. Accuracy: Data that are close to one another but far from the true value are considered "inaccurate but precise." In a case where a student gets $0.120\,M$, $0.114\,M$, and $0.116\,M$ for an acid with a true value of $0.100\,M$, the average ($0.117\,M$) is inaccurate but the trials are precise relative to each other.

• Laboratory Equipment: A volumetric flask is the most appropriate equipment for making a solution of a specific concentration.

• Physical vs. Chemical Changes:

  • Physical: Powdering sugar, condensing steam, magnetizing iron, filtration.

  • Chemical: Decomposition of water (breaking chemical bonds to form new substances).

• Observations of Matter:

  • A pure substance that yields a gas and a different solid upon heating (chemical change) is classified as a compound.

  • Measurement: When using a graduated cylinder, the measurement should be recorded to one decimal place beyond the graduations. For a cylinder marked in mL, a reading like $15.1\,mL$ indicates precise estimation.

Atomic Structure and Modern Atomic Theory

• Subatomic Particles:

  • Atomic Number: Determined by the number of protons in the nucleus. This defines the identity of the element.

  • Isotopes: Atoms of the same element with the same number of protons but different numbers of neutrons.

  • Ions: Charged particles where the number of electrons differs from the number of protons. $^{52}_{24}Cr^{3+}$ has $21$ electrons ($24 - 3 = 21$).

  • Carbon Isotopes: Carbon-14 ($^{14}_{6}C$) has 8 neutrons ($14 - 6 = 8$).

• Atomic Mass Calculation: Average atomic mass is the weighted average of all isotopes. If element X has isotopes $^{40}X$ ($72.0\%$), $^{41}X$ ($9.00\%$), and $^{42}X$ ($19.0\%$), the atomic mass is:

  • $(40 \times 0.72) + (41 \times 0.09) + (42 \times 0.19) = 40.5\,amu$.

• Historical Atomic Models:

  • Dalton's Theory: The fundamental particle of an element is the atom.

  • Rutherford: The alpha-particle scattering experiment led to the conclusion that the atom has a dense, positively charged nucleus and is mostly empty space.

• Modern Atomic Theory Principles:

  • Heisenberg Uncertainty Principle: The location and momentum of an electron cannot be known simultaneously.

  • Wave-Particle Duality: All matter exhibits both wave and particle properties.

  • Probabilistic Nature: Scientists cannot predict with $100\%$ certainty the exact location of an electron; they use probability distributions (orbitals).

Electron Configurations and Periodicity

• Quantum Rules:

  • Aufbau Principle: Electrons fill lower energy orbitals first before moving to higher ones. A configuration like $1s^2 2s^2 2p^6 3s^2 3p^5 4s^2$ violates this as the $3p$ orbital is not full before the $4s$ fills.

  • Pauli Exclusion Principle: An orbital can hold a maximum of two electrons with opposite spins.

  • Hund's Rule: Electrons fill degenerate orbitals singly first before pairing.

• Energy Levels and Orbitals:

  • The third energy level ($n=3$) can hold a maximum of $18$ electrons ($s=2, p=6, d=10$).

  • Valence Electrons: Electrons in the highest principal energy level, involved in chemical bonding.

  • Unpaired Electrons: Cobalt ($[Ar] 4s^2 3d^7$) has 3 unpaired electrons in the d-subshell.

• Electromagnetic Radiation:

  • Wavelength and Energy: Shorter wavelengths have higher energy. Blue light has higher energy than red, yellow, or green light.

  • Energy Equation: $E = \frac{h \times c}{\lambda}$ or $E = h \times \nu$. For a wavelength of $2.40 \times 10^{-7}\,m$, the energy is $8.29 \times 10^{-19}\,J$.

• Periodic Trends:

  • Atomic Radius: Increases moving down a group and left across a period. Rubidium (Rb) has a larger radius than Potassium (K), Calcium (Ca), or Iodine (I).

  • Ionization Energy: Increases moving up and to the right. Elements S, Cl, and F ordered by increasing ionization energy are S < Cl < F.

  • Electronegativity: The ability of an atom to attract electrons in a covalent bond. Generally higher for nonmetals than metals.

  • Reactivity: Cesium (Cs) is one of the most reactive metals. Halogens (Group 17) have a tendency to gain one electron.

Chemical Bonding and Nomenclature

• Bond Types:

  • Covalent Bonds: Formed between nonmetals; electrons are shared. Bond dipoles can form if there is an electronegativity difference.

  • Ionic Bonds: Formed via electron transfer, typically between a metal and a nonmetal (e.g., Calcium and Oxygen).

• Molecular Geometry (VSEPR):

  • Bicarbonate ion ($HCO_3^-$): The carbon atom exhibits trigonal planar geometry.

• Advanced Bonding Concepts:

  • Formal Charge: Used to determine the most plausible Lewis Dot Structure.

  • Resonance: Carbon dioxide structure and stability can be explained through resonance structures.

  • Polarity: Carbon disulfide ($CS_2$) is nonpolar due to its linear, symmetrical shape despite polar bonds.

• Compounds and Naming:

  • Molecular compounds consist of nonmetals (e.g., $HCN$).

  • Naming Rules:

    • $SO_3$: Sulfur trioxide.

    • $HClO$: Hypochlorous acid.

    • $MnO_2$: Manganese (IV) oxide.

    • $Cu(OH)_2$: Copper (II) hydroxide.

    • $CoCl_2 \cdot 6H_2O$: Cobalt (II) chloride hexahydrate.

Chemical Composition and The Mole

• Molar Mass Calculations:

  • Calcium Phosphate ($Ca_3(PO_4)_2$): Molar mass is approximately $310\,g/mol$.

• Mole Conversions:

  • $50\,g$ of Iron (III) oxide ($Fe_2O_3$) is approximately $0.3\,mol$.

  • Molecules in $11\,g$ of $CO_2$: $\frac{11\,g}{44\,g/mol} = 0.25\,mol$. $0.25 \times 6.022 \times 10^{23} = 1.5 \times 10^{23}\,molecules$.

• Composition:

  • Mass Percent: Nitrogen in ammonium nitrate ($NH_4NO_3$) is $35.0\%$.

  • Empirical Formulas: Simplest whole-number ratio. $N_2H_4$ is not an empirical formula (it simplifies to $NH_2$).

  • Calculation: A compound with $85.71\%$ C and $14.29\%$ H has an empirical formula of $CH_2$.

  • Molecular Formula: If the empirical formula is $C_2H_3O$ and molar mass is $172\,g$, the empirical mass is $43\,g$. The multiplier is $172 / 43 = 4$. Molecular formula is $C_8H_{12}O_4$.

  • Hydrates: Manganese (II) nitrate tetrahydrate ($Mn(NO_3)_2 \cdot 4H_2O$) is approximately $29\%$ water by mass.

Chemical Reactions and Stoichiometry

• Balancing and Reaction Types:

  • $4Fe(s) + 3O_2(g) \rightarrow 2Fe_2O_3(s)$. Coefficient for $O_2$ is $3$.

  • Synthesis: $A + B \rightarrow AB$.

  • Redox / Single Replacement: $Ba(s) + 2HCl \rightarrow BaCl_2 + H_2(g)$.

• Specific Reaction Characteristics:

  • Combustion: Requires oxygen as a reactant and typically produces water and carbon dioxide (if a hydrocarbon is burned). It is exothermic (releases heat).

  • Oxidation States: In molybdenum polyatomic ion $Mo_2O_7^{2-}$, Mo has an oxidation state of $+6$.

  • Precipitation: Reactions between aqueous $CuCl_2$ and $AgNO_3$ produce a precipitate of $AgCl$. Reactions between $Li_2SO_4$ and $Pb(NO_3)_2$ produce $LiNO_3$ and $PbSO_4$.

• Law of Conservation: In chemical reactions, atoms and mass are conserved, but the total number of moles and compounds are not necessarily conserved.

• Stoichiometry Calculations:

  • Mass to Mass: To react with $1.00\,g$ of diborane ($B_2H_6 + 3O_2 \rightarrow B_2O_3 + 3H_2O$), $3.48\,g$ of oxygen is required.

  • Mole to Mole: From $0.50\,mol$ of $O_2$ in reaction $2H_2S + 3O_2 \rightarrow 2H_2O + 2SO_2$, $0.33\,mol$ of $SO_2$ is produced.

  • Limiting Reactants: $32\,g$ of $O_2$ reacting with $32\,g$ of $H_2$ produces $36\,g$ of water ($O_2$ is the limiting reactant).

  • Percent Yield: $\frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100$. For an experimental mass of $50.0\,g$ and theoretical of $60.0\,g$, yield is $83.3\%$.

Gas Laws

• Constants and Conditions:

  • $R = 0.0821\,atm \cdot L / K \cdot mol$.

  • $0^{\circ}C = 273.15\,K$.

  • STP: $1\,atm$ and $273.15\,K$. $1\,mol$ of any gas at STP occupies $22.4\,L$.

• Gas Law Relationships:

  • Boyle's Law: If volume doubles at constant temp/mass, pressure is reduced by half ($1/2$).

  • Charles' Law: If volume of $6.24\,L$ at $25^{\circ}C$ is heated to $55^{\circ}C$, new volume is $6.87\,L$.

  • Combined Gas Law/STP: Oxygen occupies $2.15\,L$ at $0.572\,atm$ and $25^{\circ}C$. At STP, it occupies $1.13\,L$.

  • Ideal Gas Law ($PV=nRT$): In a $4.0\,L$ container at $1520\,torr$ ($2\,atm$) and $127^{\circ}C$ ($400\,K$), there are $0.24\,mol$ of hydrogen.

• Dalton's Law of Partial Pressure: Total pressure is the sum of partial pressures. If ammonia is collected over water at $20^{\circ}C$, total pressure is $756\,mmHg$ and water vapor pressure is $17.5\,mmHg$. Pressure of ammonia is $756 - 17.5 = 739\,mmHg$.

• Gas Stoichiometry:

  • $12.3\,L$ of $O_2$ at STP reacting to form $NO_2$ ($2NO + O_2 \rightarrow 2NO_2$) will produce $24.6\,L$ of $NO_2$.

  • Decomposition of potassium chlorate to produce $5.0\,L$ of $O_2$ at STP requires $18\,g$ of $KClO_3$.

  • Mass of calcium metal reacting with oxygen in $500.0\,mL$ at $90.0\,kPa$ and $27^{\circ}C$ is $1.4\,g$.

Solutions and Solubility

• Intermolecular Forces (IMFs):

  • London Dispersion forces are temporary dipoles found in all molecules, including nonpolar $CF_4$ and polar $H_2O$.

  • Oil and water do not mix because oil is nonpolar and water is polar ("like dissolves like").

  • Miscibility: Ethanol and water are miscible because they form a single phase when mixed.

• Concentration:

  • Molarity ($M$): Moles of solute per liter of solution. $14\,g$ of $KOH$ ($0.25\,mol$) in $150.0\,mL$ of water is $1.7\,M$.

  • Ion Concentration: In a $0.15\,M$ sodium sulfate ($Na_2SO_4$) solution, the concentration of sodium ions ($Na^+$) is $0.30\,M$ because there are 2 moles of sodium ions per mole of formula unit.

• Solubility Factors:

  • Solubility of a gas in a liquid is increased by increasing pressure and lowering the temperature of the solvent.

• Dilution: Using $M_1V_1 = M_2V_2$, to make $2.0\,L$ of $0.06\,M\,CaCl_2$ from a $0.25\,M$ stock solution, $480\,mL$ of stock is needed.

Acids and Bases

• Properties of Acids:

  • Hydronium concentration is greater than hydroxide concentration ([H_3O^+] > [OH^-]).

  • They act as proton donors.

  • They have a pH less than $7$.

• Calculations:

  • Ion Product of Water ($K_w$): At $25^{\circ}C$, $K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$. If $[H_3O^+] = 4.0 \times 10^{-4}\,M$, then $[OH^-] = 2.5 \times 10^{-11}\,M$.

  • pH Scale: If $[OH^-] = 3.4 \times 10^{-5}\,M$, $pOH = 4.47$. Since $pH + pOH = 14$, the $pH = 9.53$.

• Neutralization and Titration:

  • If $50.00\,mL$ of $1.000\,M\,HCl$ is neutralized by $35.4\,mL$ of $KOH$, the molarity of the $KOH$ is calculated using $M_aV_a = M_bV_b$ (for 1:1 ratio), resulting in $1.41\,M$.

Advanced Chemistry Spring Final Exam Overview and Logistics

• Exam Date: Spring 2026.
• General Advice for Preparation:
  • Review the year in reverse order.
  • Complete the practice final exam.
  • Review all classroom notes, reading notes, problem sets, homework, and labs.
• Provided Materials:
  • Periodic table.
  • Conversion sheet.
  • Polyatomic ion sheet.
  • Solubility rules.
  • Formula sheet.

Course Syllabus and Unit Topics

• Unit 1 (Chapter 2): Matter & Measurement, including Dimensional Analysis, Significant Figures, and Density.
• Unit 2 (Chapter 3.1-3.5): Classification of Matter, Chemical & Physical Properties, and Changes.
• Unit 3 (Chapter 4): Atomic Structure & Periodic Table.
• Unit 4 (Chapters 5 & 6): Modern Atomic Theory & Periodic Table.
• Unit 5 (Chapters 7, 8, & 9): Nomenclature and Chemical Bonding.
• Unit 6 (Chapter 10): Chemical Composition and the Mole.
• Unit 7 (Chapters 11 & 12): Reactions, Stoichiometry, and Redox reactions.
• Unit 8 (Chapter 14): Gases.
• Unit 9 (Chapters 16 & 17): Solutions, Acid-Bases, and Equilibrium.

Matter & Measurement Principles

• Identification of Substances: Intensive properties, such as Specific Heat, are useful for identifying unknown substances because they do not depend on the amount of matter present. Extensive properties like volume, moles, and enthalpy vary with amount.
• Classification of Matter:
  • A mixture is represented by chemical symbols indicating multiple substances or a substance dissolved in another, such as $NaCl(aq)$ (sodium chloride dissolved in water).
  • Pure substances are represented as single formulas like $NaCl(s)$, $H<em>2O(l)$, or $H</em>2O(g)$.
• Density Calculations ($D = \frac{m}{V}$):
  • Displacement: If $52.4 ext{ g}$ of iron ($ext{ density} = 7.86 ext{ g/cm}^3$) is added to $75.0 ext{ mL}$ of water, the volume of iron is calculated as $\frac{52.4 ext{ g}}{7.86 ext{ g/cm}^3} = 6.66 ext{ cm}^3$ ($6.67 ext{ mL}$). The final volume reading is $75.0 ext{ mL} + 6.67 ext{ mL} = 81.7 ext{ mL}$.
  • Volume from Mass: A gold nugget with a mass of $63.3 ext{ g}$ has a volume of approximately $3.28 ext{ mL}$.
• Experimental Accuracy and Precision:
  • Percent Error Formula: $ext{Percent Error} = \frac{| ext{Experimental Value} - ext{Accepted Value}|}{ ext{Accepted Value}} imes 100$
  • Example: Experimental boiling point of octane is $124.1^{ ext{ }}C$, accepted is $125.7^{ ext{ }}C$. Percent error is approximately 1.273 ext{ %} .
  • Precision vs. Accuracy: Data that are close to one another but far from the true value are considered "inaccurate but precise." In a case where a student gets $0.120 ext{ M}$, $0.114 ext{ M}$, and $0.116 ext{ M}$ for an acid with a true value of $0.100 ext{ M}$, the average ($0.117 ext{ M}$) is inaccurate, but the trials are precise relative to each other.
  • Laboratory Equipment: A volumetric flask is the most appropriate equipment for making a solution of a specific concentration.
  • Physical vs. Chemical Changes:
  • Physical: Powdering sugar, condensing steam, magnetizing iron, filtration.
  • Chemical: Decomposition of water (breaking chemical bonds to form new substances).

Atomic Structure and Modern Atomic Theory

• Subatomic Particles:
  • Atomic Number: Determined by the number of protons in the nucleus. This defines the identity of the element.
  • Isotopes: Atoms of the same element with the same number of protons but different numbers of neutrons.
  • Ions: Charged particles where the number of electrons differs from the number of protons. $^{52}_{24}Cr^{3+}$ has $21$ electrons ($24 - 3 = 21$).
  • Carbon Isotopes: Carbon-14 ($^{14}_{6}C$) has 8 neutrons ($14 - 6 = 8$).
• Atomic Mass Calculation: Average atomic mass is the weighted average of all isotopes. If element X has isotopes $^{40}X$ ( 72.0 ext{ %} ), $^{41}X$ ( 9.00 ext{ %} ), and $^{42}X$ ( 19.0 ext{ %} ), the atomic mass is:
  • $(40 imes 0.72) + (41 imes 0.09) + (42 imes 0.19) = 40.5 ext{ amu}$.
• Historical Atomic Models:
  • Dalton's Theory: The fundamental particle of an element is the atom.
  • Thomson's Model: Introduced the idea of electrons embedded in a positively charged 'soup.'
  • Rutherford: The alpha-particle scattering experiment led to the conclusion that the atom has a dense, positively charged nucleus and is mostly empty space.
  • Bohr Model: Electrons reside in fixed orbits around the nucleus, with quantized energy levels.
  • Quantum Mechanical Model: The modern view where electrons are in orbitals, defined by probability distributions.
• Modern Atomic Theory Principles:
  • Heisenberg Uncertainty Principle: The location and momentum of an electron cannot be known simultaneously.
  • Wave-Particle Duality: All matter exhibits both wave and particle properties.
  • Probabilistic Nature: Scientists cannot predict with 100 ext{ %} certainty the exact location of an electron; they use probability distributions (orbitals).

Electron Configurations and Periodicity

• Quantum Rules:
  • Aufbau Principle: Electrons fill lower energy orbitals first before moving to higher ones. A configuration like $1s^2 2s^2 2p^6 3s^2 3p^5 4s^2$ violates this as the $3p$ orbital is not full before the $4s$ fills.
  • Pauli Exclusion Principle: An orbital can hold a maximum of two electrons with opposite spins.
  • Hund's Rule: Electrons fill degenerate orbitals singly first before pairing.
• Energy Levels and Orbitals:
  • The third energy level ($n=3$) can hold a maximum of $18$ electrons ($s=2, p=6, d=10$).
• Valence Electrons: Electrons in the highest principal energy level, involved in chemical bonding.
• Unpaired Electrons: Cobalt ($[Ar] 4s^2 3d^7$) has 3 unpaired electrons in the d-subshell.
• Electromagnetic Radiation:
  • Wavelength and Energy: Shorter wavelengths have higher energy. Blue light has higher energy than red, yellow, or green light.
  • Energy Equation: E = rac{h imes c}{ ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ }} ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } $
    ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ }$E = h imes <br />\nu$. For a wavelength of $2.40 imes 10^{-7} ext{ m}$, the energy is $8.29 imes 10^{-19} ext{ J}$.
• Periodic Trends:
  • Atomic Radius: Increases moving down a group and left across a period. Rubidium (Rb) has a larger radius than Potassium (K), Calcium (Ca), or Iodine (I).
  • Ionization Energy: Increases moving up and to the right. Elements S, Cl, and F ordered by increasing ionization energy are S < Cl < F.

Chemical Bonding and Nomenclature

• Bond Types:

  • Covalent Bonds: Formed between nonmetals; electrons are shared. Bond dipoles can form if there is an electronegativity difference.
  • Ionic Bonds: Formed via electron transfer, typically between a metal and a nonmetal (e.g., Calcium and Oxygen).

• Molecular Geometry (VSEPR):

  • Bicarbonate ion ($HCO_3^-$): The carbon atom exhibits trigonal planar geometry.

• Advanced Bonding Concepts:

  • Formal Charge: Used to determine the most plausible Lewis Dot Structure.
  • Resonance: Carbon dioxide structure and stability can be explained through resonance structures.
  • Polarity: Carbon disulfide ($CS_2$) is nonpolar due to its linear, symmetrical shape despite polar bonds.
  • Compounds and Naming:
  • Molecular compounds consist of nonmetals (e.g., $HCN$).
  • Naming Rules:
    • $SO_3$: Sulfur trioxide.
    • $HClO$: Hypochlorous acid.
    • $MnO_2$: Manganese (IV) oxide.
    • $Cu(OH)_2$: Copper (II) hydroxide.
    • $CoCl<em>2 \bullet 6H</em>2O$: Cobalt (II) chloride hexahydrate.

Chemical Composition and The Mole

• Molar Mass Calculations:
  • Calcium Phosphate ($Ca<em>3(PO</em>4)_2$): Molar mass is approximately $310 ext{ g/mol}$.
• Mole Conversions:
  • $50 ext{ g}$ of Iron (III) oxide ($Fe<em>2O</em>3$) is approximately $0.3 ext{ mol}$.
  • Molecules in $11 ext{ g}$ of $CO_2$: $\frac{11 ext{ g}}{44 ext{ g/mol}} = 0.25 ext{ mol}$; $0.25 imes 6.022 imes 10^{23} = 1.5 imes 10^{23} ext{ molecules}$.
• Composition:
  • Mass Percent: Nitrogen in ammonium nitrate ($NH<em>4NO</em>3$) is 35.0 ext{ %} .
  • Empirical Formulas: Simplest whole-number ratio. $N<em>2H</em>4$ is not an empirical formula (it simplifies to $NH_2$).
  • Calculation: A compound with 85.71 ext{ %} C and 14.29 ext{ %} H has an empirical formula of $CH_2$.
  • Molecular Formula: If the empirical formula is $C<em>2H</em>3O$ and molar mass is $172 ext{ g}$, the empirical mass is $43 ext{ g}$. The multiplier is $172 / 43 = 4$, making Molecular formula $C<em>8H</em>{12}O_4$.
• Hydrates: Manganese (II) nitrate tetrahydrate ($Mn(NO<em>3)</em>2 \bullet 4H_2O$) is approximately 29 ext{ %} water by mass.

Chemical Reactions and Stoichiometry

• Balancing and Reaction Types:
  • 4Fe(s) + 3O2(g) ightarrow 2Fe2O3(s). Coefficient for $O</em>2$ is $3$.
  • Synthesis: A + B
    ightarrow AB .
  • Redox / Single Replacement: Ba(s) + 2HCl
    ightarrow BaCl2 + H2(g) .
• Specific Reaction Characteristics:
  • Combustion: Requires oxygen as a reactant and typically produces water and carbon dioxide (if a hydrocarbon is burned). It is exothermic (releases heat).
  • Oxidation States: In molybdenum polyatomic ion $Mo<em>2O</em>7^{2-}$, Mo has an oxidation state of $+6$.
  • Precipitation: Reactions between aqueous $CuCl<em>2$ and $AgNO</em>3$ produce a precipitate of $AgCl$. Reactions between $Li<em>2SO</em>4$ and $Pb(NO<em>3)</em>2$ produce $LiNO<em>3$ and $PbSO</em>4$.
  • Law of Conservation: In chemical reactions, atoms and mass are conserved, but the total number of moles and compounds are not necessarily conserved.
• Stoichiometry Calculations:
  • Mass to Mass: To react with $1.00 ext{ g}$ of diborane ( B2H6 + 3O2 ightarrow B2O3 + 3H2O ), $3.48 ext{ g}$ of oxygen is required.
  • Mole to Mole: From $0.50 ext{ mol}$ of $O<em>2$ in reaction 2H2S + 3O2 ightarrow 2H2O + 2SO2 , $0.33 ext{ mol}$ of $SO</em>2$ is produced.
  • Limiting Reactants: $32 ext{ g}$ of $O<em>2$ reacting with $32 ext{ g}$ of $H</em>2$ produces $36 ext{ g}$ of water ($O_2$ is the limiting reactant).
  • Percent Yield: rac{ ext{Actual Yield}}{ ext{Theoretical Yield}} imes 100 $. For an experimental mass of 50.0 ext{ g}$and theoretical of$60.0 ext{ g}$, yield is$83.3 ext{ %}.

Gas Laws

• Constants and Conditions:
  • R = 0.0821 ext{ atm } ext{ L} / ext{ K } ext{ mol} .
  • 0^{ ext{ }}C = 273.15 ext{ K} .
  • STP: 1 ext{ atm} $and$ 273.15 ext{ K} $, where$ 1 ext{ mol} $of any gas at STP occupies$ 22.4 ext{ L} .
• Gas Law Relationships:
  • Boyle's Law: If volume doubles at constant temperature/mass, pressure is reduced by half ( 1/2 ).
  • Charles' Law: If volume 6.24 ext{ L} $at$ 25^{ ext{ }}C $is heated to$ 55^{ ext{ }}C $, new volume is$ 6.87 ext{ L} .
  • Combined Gas Law/STP: Oxygen occupies 2.15 ext{ L} $at$ 0.572 ext{ atm} $and$ 25^{ ext{ }}C $; at STP, it occupies$ 1.13 ext{ L} .
  • Ideal Gas Law ( PV=nRT $):</strong> In a$ 4.0 ext{ L} $container at$ 1520 ext{ torr} $($ 2 ext{ atm} $) and$ 127^{ ext{ }}C $($ 400 ext{ K} $), there are$ 0.24 ext{ mol} of hydrogen.
  • Dalton's Law of Partial Pressure: Total pressure is the sum of partial pressures. If ammonia is collected over water at 20^{ ext{ }}C $, total pressure is$ 756 ext{ mmHg} $and water vapor pressure is$ 17.5 ext{ mmHg} $; pressure of ammonia is$ 756 - 17.5 = 739 ext{ mmHg} .
• Gas Stoichiometry:
  • 12.3 ext{ L} $of$ O2 $at STP reacting to form$ NO2 $($ 2NO + O2 ightarrow 2NO2 $) will produce$ 24.6 ext{ L} $of$ NO_2 .
  • Decomposition of potassium chlorate to produce 5.0 ext{ L} $of$ O2 $at STP requires$ 18 ext{ g} $of$ KClO3 .
  • Mass of calcium metal reacting with oxygen in 500.0 ext{ mL} $at$ 90.0 ext{ kPa} $and$ 27^{ ext{ }}C $is$ 1.4 ext{ g} .

Solutions and Solubility

• Intermolecular Forces (IMFs):
  • London Dispersion forces are temporary dipoles found in all molecules, including nonpolar CF4 $and polar$ H2O .
  • Oil and water do not mix because oil is nonpolar and water is polar ("like dissolves like").
• Miscibility: Ethanol and water are miscible because they form a single phase when mixed.
• Concentration:
  • Molarity ( M $):</strong> Moles of solute per liter of solution.$ 14 ext{ g} $of$ KOH $($ 0.25 ext{ mol} $) in$ 150.0 ext{ mL} $of water is$ 1.7 ext{ M} .
  • Ion Concentration: In a 0.15 ext{ M} $sodium sulfate ($ Na2SO4 $) solution, the concentration of sodium ions ($ Na^+ $) is$ 0.30 ext{ M} because there are 2 moles of sodium ions per mole of formula unit.
• Solubility Factors:
  • Solubility of a gas in a liquid is increased by increasing pressure and lowering the temperature of the solvent.
• Dilution: Using M1V1 = M2V2 $, to make$ 2.0 ext{ L} $of$ 0.06 ext{ M } CaCl_2 $from a$ 0.25 ext{ M} $stock solution,$ 480 ext{ mL} of stock is needed.

Acids and Bases

• Properties of Acids:
  • Hydronium concentration is greater than hydroxide concentration ( [H_3O^+] > [OH^-] ).
  • They act as proton donors.
  • They have a pH less than 7.
• Calculations:
  • Ion Product of Water ( Kw $):</strong> At$ 25^{ ext{ }}C $,$ Kw = [H3O^+][OH^-] = 1.0 imes 10^{-14} $. If$ [H3O^+] = 4.0 imes 10^{-4} ext{ M} $, then$ [OH^-] = 2.5 imes 10^{-11} ext{ M} .
  • pH Scale: If [OH^-] = 3.4 imes 10^{-5} ext{ M} $,$ pOH = 4.47 $. Since$ pH + pOH = 14 $,$ pH = 9.53 .
• Neutralization and Titration:
  • If 50.00 ext{ mL} $of$ 1.000 ext{ M} HCl $is neutralized by$