Comprehensive College Chemistry: Foundations, Stoichiometry, and Gas Laws Study Guide

Chemical Foundations: Matter and Chemistry Overview

• Matter is defined as anything that takes up space, has mass, and exhibits inertia.

  • It is composed of atoms, of which there are only about 100 different types.

  • Water ($H_2O$) consists of one oxygen atom and two hydrogen atoms.

  • Passing an electric current through water separates these atoms, which then rearrange into two different types of molecules. Chemical reactions such as this are reversible.

• Chemistry is the study of matter and energy and, more significantly, the changes occurring between them.

• Motivations for studying chemistry include:

  • Developing problem-solving skills applicable to all life areas.

  • Safety considerations; for instance, the fall of the Roman civilization is attributed in part to their lack of understanding regarding lead poisoning.

  • Achieving a foundational understanding of all scientific disciplines.

The Scientific Method, Theories, and Laws

• The Scientific Method is a "plan of attack" for inquiry.

  • Key components include good experimental design and repetition.

• Theory/Model:

  • A theory is a set of tested hypotheses that attempt to explain why a natural phenomenon happens.

  • Models are used to explain observations; they are modified whenever new evidence is discovered.

• Robert Boyle's Contributions:

  • Conducted experiments with air and created the first vacuum pump.

  • Demonstrated that a coin and a feather fall at the same rate due to gravity in a vacuum, where there is no air resistance to impede motion.

  • Defined elements as substances that cannot be broken down into simpler substances.

  • Boyle’s Gas Law: $P_1V_1 = P_2V_2$.

• Scientific Laws:

  • A law provides a summary of observed, measurable behavior (it describes what happens).

  • A theory provides an explanation of behavior (it describes why it happens).

  • Law of Conservation of Mass: $\text{mass of reactants} = \text{mass of products}$.

  • Law of Conservation of Energy (First Law of Thermodynamics): Energy cannot be created nor destroyed; it can only change forms.

• Human Factors in Science:

  • Scientists are subject to data misinterpretations, emotional attachments to theories, loss of objectivity, politics, ego, profit motives, fads, wars, and religious beliefs.

  • Historical examples: Galileo was forced to recant astronomical observations due to religious resistance; Antoine Lavoisier (the "father of modern chemistry") was beheaded due to political affiliations during the French Revolution.

• War and Science:

  • The need for explosives (the rapid change of a solid or liquid to gas where molecules become approximately $2,000$ diameters farther apart) has led to the development of nitrogen-based fertilizers and nuclear devices.

Units of Measure and Measurement Systems

• Quantitative observations (measurements) always consist of two parts: a number and a unit.

• Systems of Measurement:

  • English System: Used primarily in the US and parts of Africa.

  • SI System (Metric): Established in 1960 (Le Système International) to standardize scientific communication.

• Volume:

  • Derived from length ($1.0 \text{ m} \times 1.0 \text{ m} \times 1.0 \text{ m} = 1.0 \text{ m}^3$).

  • $1\text{ dm}^3 = 1\text{ Liter (L)}$.

  • $(10\text{ cm})^3 = 1,000\text{ cm}^3 = 1\text{ L} = 1,000\text{ mL}$.

  • $1\text{ cm}^3 = 1\text{ mL} = 1\text{ gram of } H_2O$ at $4^\text{◦}C$.

• Mass vs. Weight:

  • Mass ($g$ or $kg$): A measure of the resistance of an object to a change in its state of motion (inertia); the quantity of matter present.

  • Weight: The response of mass to gravity, measured in Newtons as a force. Since gravity is constant on Earth, chemists often use these interchangeably, though it is technically incorrect.

  • Chemical quantities are weighed on a balance, not a scale.

Significant Figures and Calculations

• Determining Significant Figures:

  1. Nonzero digits are always significant.

  2. Zeros are significant only if they are "sandwiched" between significant figures or are both "terminating and right" of the decimal point.

  3. Exact/counting numbers and fundamental constants have an infinite ($∞$) number of significant figures.

• Calculation Rules:

  • Multiplication/Division: The result is limited by the term with the least number of significant figures.

  • Addition/Subtraction: The result is limited by the term with the least number of decimal places.

  • pH: The number of significant figures in the least accurate measurement determines the number of decimal places in the reported pH.

• Rounding Guidelines:

  • Round only at the end of the calculation sequence.

  • If the digit following the last significant figure is > 5, round up; if < 5, drop the remaining digits.

  • Do not "double round." Example: $7.348$ rounded to 2 significant figures is $7.3$, not $7.4$.

Classification and States of Matter

• Key Distinction: Changes of state involve altering Intermolecular Forces (IMFs), not chemical bonds.

• States of Matter:

  • Solid: Rigid, definite shape and volume; molecules vibrate about fixed points; virtually incompressible.

  • Liquid: Definite volume, takes the shape of its container; molecules vibrate, rotate, and translate; slightly compressible.

  • Gas: No definite volume or shape; molecules move independently and are far apart; highly compressible.

  • Vapor: The gas phase of a substance that is normally a solid or liquid at room temperature.

  • Fluid: Any substance that can flow (liquids and gases).

• Simple Mixtures:

  • Homogeneous: Visibly indistinguishable parts (solutions, air).

  • Heterogeneous: Visibly distinguishable parts.

  • Separation methods: Filtering, fractional crystallization, distillation, chromatography.

• Pure Substances:

  • Elements and Compounds (e.g., water, carbon dioxide).

  • Compounds can be broken down into elements by chemical means (electrolysis).

  • Elements consist of atoms, which break down into nuclei and electrons, then protons ($p^+$), neutrons ($n^0$), and electrons ($e^-$), then quarks.

Early History of Chemistry and Atomic Theory

• 1,000 B.C.: Ore processing for metals and embalming fluids.

• 400 B.C.: Greeks proposed four elements: fire, earth, water, and air.

• Democritus: Coined the term atomos for smallest particles.

• Alchemy (Next 2,000 years): Pseudoscience attempting to turn metals into gold; produced some valid chemical knowledge.

• 16th Century: Georg Bauer (metallurgy) and Paracelsus (medicinal minerals).

• Georg Stahl: Proposed "phlogiston" as a substance that flows out of burning materials.

• Joseph Priestley: Discovered oxygen, initially calling it "dephlogisticated air."

• Antoine Lavoisier: Explained combustion and published the first modern chemistry textbook; executed in 1794 during the French Revolution.

• Fundamental Laws:

  • Law of Conservation of Mass: Mass is neither created nor destroyed.

  • Law of Definite Proportions (Proust): A given compound always contains exactly the same proportions of elements by mass.

  • Law of Multiple Proportions (Dalton): When two elements form a series of compounds, the ratios of the masses of the second element that combine with 1 gram of the first element can be reduced to small whole numbers.

Dalton's Atomic Theory and the Nuclear Atom

• Dalton’s Atomic Theory of Matter (1808):

  1. All matter is made of atoms (indivisible and indestructible).

  2. Atoms of a given element are identical in weight and properties; atoms of different elements differ.

  3. Compounds are formed by atoms combining in small whole-number ratios.

  4. Reactions involve rearrangement; atoms are not created or destroyed.

  • Modifications: Discovery of subatomic particles and isotopes.

• Experiments to Characterize the Atom:

  • J.J. Thomson (1898–1903): Used cathode ray tubes to discover negative particles (electrons); measured charge-to-mass ratio ($e/m$). Proposed the "plum pudding" model.

  • Robert Millikan (1909): Oil drop experiment; determined the charge of an electron and its mass ($9.11 \times 10^{-31}\text{ kg}$).

  • Henri Becquerel: Discovered radioactivity (spontaneous emission from uranium).

  • Ernest Rutherford (1911): Gold foil experiment. Directed $α$ particles at foil; most passed through, but some deflected at large angles. Formulated the nuclear atom: a dense positive core (nucleus) containing most of the mass, surrounded by empty space.

Modern Atomic Structure and Isotopes

• Elements: 92 naturally occurring, others manmade.

• Subatomic Particles:

  • Nucleus: Consists of protons and neutrons (diameter $\text{ ≈ } 10^{-13}\text{ cm}$). Nuclear material is extremely dense (a pea-sized amount would weigh 250 million tons).

  • Proton ($p^+$): Charge $+1$, mass $\text{ ≈ } 1.67 \times 10^{-27}\text{ kg}$. Defines the element (atomic number, $Z$).

  • Neutron ($n^0$): Charge $0$, mass $\text{ ≈ } 1.67 \times 10^{-27}\text{ kg}$. Responsible for isotopes; alters mass number ($A$).

  • Electron ($e^-$): Charge $-1$, mass $\text{ ≈ } 9.11 \times 10^{-31}\text{ kg}$ ($1/2,000$ the mass of a proton). Responsible for bonding and ions.

• Isotopes: Atoms with the same atomic number but different mass numbers (different number of neutrons).

  • Hydrogen isotopes: Hydrogen ($0$ neutrons), Deuterium ($1$ neutron), Tritium ($2$ neutrons).

• Mass Number ($A$): Sum of protons and neutrons.

• Mass Defect: The reason actual masses are not integers; related to nuclear binding energy.

Molecules, Ions, and the Periodic Table

• Bonding:

  • Covalent: Atoms share electrons to form molecules.

  • Ionic: Formed by electron transfer; held by electrostatic forces. Strong forces results in solids.

• Ions:

  • Cations: Positive ions (usually metals).

  • Anions: Negative ions (usually nonmetals).

  • Polyatomic ions: Groups of atoms behaving as a single unit with a charge.

• Periodic Table Organization:

  • Metals: Malleable, ductile, luster; form cations in a "sea of electrons."

  • Nonmetals: Located to the right of the "stair-step" line.

  • Metalloids: Elements bordering the stair-step line.

  • Groups (Vertical): Have similar properties ($1A = \text{ Alkali Metals}$; $2A = \text{ Alkaline Earth Metals}$; $7A = \text{ Halogens}$; $8A = \text{ Noble Gases}$).

  • Periods (Horizontal): Progression from metals to nonmetals.

Naming Simple Compounds

• Binary Ionic Compounds:

  • Type I: Metal cation (fixed charge) + nonmetal anion (stem + "-ide").

  • Type II: Transition metals requiring Roman numerals to specify charge (e.g., $Fe^{3+} = \text{iron(III)}$).

  • Exceptions: $Ag^+$, $Cd^{2+}$, and $Zn^{2+}$ do not need Roman numerals. Mercury(I) is $Hg_2^{2+}$.

• Polyatomic Ions/Oxyanions:

  • Prefix "hypo-": Least oxygen.

  • Suffix "-ite": More oxygen.

  • Suffix "-ate": Even more oxygen.

  • Prefix "per-": Most oxygen.

• Binary Covalent Compounds (Type III):

  • Use Greek prefixes (mono, di, tri, tetra, penta, hexa, hepta, octa, nona, deca). Always end in "-ide."

• Acids:

  • If the anion ends in "-ide" → hydro [root] ic acid.

  • If the anion ends in "-ate" → [root] ic acid.

  • If the anion ends in "-ite" → [root] ous acid.

• Common Trivial Names:

  • Water ($H_2O$), Ammonia ($NH_3$), Hydrazine ($N_2H_4$), Phosphine ($PH_3$), Nitric Oxide ($NO$), Nitrous Oxide ($N_2O$).

Stoichiometry and the Mole

• Atomic Mass Standard: $^{12}C$ is defined as exactly $12\text{ atomic mass units (amu)}$.

• Mass Spectrometer: Measures mass by knocking electrons off atoms, accelerating cations through a magnetic field, and measuring the deflection proportional to mass.

• Average Atomic Mass: Weighted average of isotopes based on percent abundance.

• The Mole:

  • Avogadro’s Number: $6.02 \times 10^{23}$ particles per mole.

  • Definition: The number of Carbon atoms in exactly $12.0\text{ grams}$ of $^{12}C$.

• Molar Mass ($MM$): Sum of atomic masses in a chemical formula in units of $g/mol$. Always use two decimal places for molar mass calculations.

• Percentage Composition:

  • \text{Percent Composition} = \frac{\text{mass of element}}{\text{total mass of compound}} \times 100\text{%}.

• Formulas:

  • Empirical Formula: Simplest whole-number ratio of atoms in a compound.

  • Molecular Formula: Actual number of atoms; a whole-number multiple ($n$) of the empirical formula ($\text{Empirical Mass} \times n = \text{Molar Mass}$).

  • Hydrates: Compounds containing "dot waters" (waters of hydration) in the crystal structure.

• Diatomic Elements (The "Gens"): Hydrogen ($H_2$), Nitrogen ($N_2$), Oxygen ($O_2$), Fluorine ($F_2$), Chlorine ($Cl_2$), Bromine ($Br_2$), Iodine ($I_2$). Also Phosphorus ($P_4$) and Sulfur ($S_8$).

Balancing Equations and Stoichiometric Calculations

• Law of Conservation of Matter (Lavoisier): Matter is neither created nor destroyed.

• Balancing Tips:

  • Start with the most complicated molecule.

  • Balance elemental substances last.

  • Use state symbols: $(s)$, $(l)$, $(g)$, $(aq)$.

• Reaction Templates:

  • $\text{Metal} + \text{Halogen} \rightarrow \text{Salt } (M_aX_b)$.

  • $\text{Hydrocarbon} + O_2 \rightarrow CO_2 + H_2O$.

  • $H_2CO_3 \rightarrow CO_2 + H_2O$ (carbonic acid spontaneously decomposes).

  • $\text{Metal Carbonate} \rightarrow \text{Metal Oxide} + CO_2$.

• Stoichiometric Chart Method:

  1. Write balanced equation.

  2. Calculate moles of the given substance (Mass / MM).

  3. Use the mole-to-mole ratio from the balanced equation to find moles of all other species.

  4. Convert moles to desired units (mass or volume).

Limiting Reactants and Reaction Yields

• Limiting Reactant ($LR$): The reactant that is completely consumed and limits the amount of product formed.

• Excess Reactant: The reactant that remains after the reaction stops.

• Haber Process: $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$. A classic limiting reactant example for producing ammonia fertilizer.

• Yields:

  • Theoretical Yield: Maximum amount of product calculated from stoichiometry.

  • Actual Yield: The amount actually produced in the lab.

  • \text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\text{%}.

Solutions and Molarity

• Water Solubility:

  • Water is polar due to unequal charge distribution ($105^\text{◦}$ bond angle).

  • Hydration: Positive ends of water attract negative ions (and vice versa) to dissolve salts.

  • "Like dissolves like": Polar solvents dissolve polar/ionic solutes; nonpolar solvents dissolve nonpolar solutes.

• Electrolytes:

  • Solutions that conduct electricity.

  • Strong Electrolytes: Completely dissociate (soluble salts, strong acids like $HCl$, $HNO_3$, $H_2SO_4$, strong bases like $NaOH$).

  • Weak Electrolytes: Dissociate only slightly (\text{≈ } 1\text{%}), such as acetic acid ($HC_2H_3O_2$) or ammonia ($NH_3$).

  • Nonelectrolytes: Dissolve without forming ions (sugar, alcohols).

• Molarity ($M$):

  • $\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{Liters of solution}}$.

  • Concentration of ions: Multiply the molarity of the compound by the ion's subscript (e.g., $0.50\text{ M } Co(NO_3)_2$ contains $1.0\text{ M } NO_3^-$).

• Preparation and Dilution:

  • Standard Solution: Concentration is accurately known; prepared in a volumetric flask.

  • Dilution formula: $M_1V_1 = M_2V_2$ (Moles before dilution = Moles after dilution).

Types of Chemical Reactions in Aqueous Solution

• Synthesis ($A + B \rightarrow AB$).

• Decomposition ($AB \rightarrow A + B$).

• Single Replacement ($A + BC \rightarrow AC + B$).

• Double Replacement ($AB + CD \rightarrow AD + CB$).

• Combustion: Reaction with an oxidizer (usually $O_2$) to form oxides.

  • Cellular respiration is a controlled form of combustion: $C_6H_12O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O + \text{energy}$.

• Precipitation Reactions (Solubility Rules):

  1. "Big Mamma": All Nitrates ($NO_3^-$) are soluble.

  2. "Big Daddy": All Group IA metals and Ammonium ($NH_4^+$) salts are soluble.

  3. "Halides": Generally soluble except with Silver ($Ag^+$), Mercury ($Hg_2^{2+}$), or Lead ($Pb^{2+}$).

  4. "Strong Acids/Bases": Dissociate them in equations.

• Describing Reactions:

  1. Molecular Equation: Overall stoichiometry.

  2. Complete Ionic Equation: Represents strong electrolytes as ions.

  3. Net Ionic Equation: Shows only species undergoing change; omits spectator ions.

Acids, Bases, and Oxidation-Reduction

• Acid-Base Reactions:

  • Neutralization: $\text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water}$.

  • Equivalence point: $\text{Moles } OH^- = \text{Moles } H_3O^+$.

  • Titration: A volumetric analysis technique using a titrant (buret) and analyte (flask).

• Redox Reactions (Electron Transfer):

  • "OIL RIG": Oxidation is Loss, Reduction is Gain.

  • Oxidation Number Rules:

    • Elements = $0$.

    • Monatomic ions = Charge.

    • Fluorine = $-1$.

    • Oxygen = $-2$ (except in peroxides, then $-1$).

    • Hydrogen = $+1$ with nonmetals, $-1$ with metals.

• Balancing Redox via Half-Reaction Method:

  1. Divide into oxidation and reduction half-reactions.

  2. Balance non-O and non-H elements.

  3. Balance O using $H_2O$; balance H using $H^+$; balance charge using $e^-$.

  4. Equalize electrons and recombine.

  5. If basic, neutralize $H^+$ with $OH^-$ to form water.

Properties of Gases and Gas Laws

• Define a gas using: Quantity ($n$, moles), Temperature ($T$, Kelvins), Volume ($V$, Liters), and Pressure ($P$, atmospheres).

• Pressure Units:

  • $1.00\text{ atm} = 760\text{ torr} = 760\text{ mm Hg} = 101,325\text{ Pa}$.

• Gas Laws:

  • Boyle’s Law: $P_1V_1 = P_2V_2$ (Inverse relationship; constant $n, T$).

  • Charles’s Law: $V_1/T_1 = V_2/T_2$ (Direct relationship; constant $n, P$).

  • Gay-Lussac’s Law: $P_1/T_1 = P_2/T_2$ (Direct relationship; constant $n, V$).

  • Avogadro’s Law: $V_1/n_1 = V_2/n_2$ (Direct relationship; constant $P, T$).

  • Combined Gas Law: $P_1V_1T_2 = P_2V_2T_1$.

• Ideal Gas Law:

  • $PV = nRT$.

  • Ideal gas constant $R = 0.08206\text{ L} \times \text{atm} / (\text{mol} \times K)$.

  • Gases behave most ideally at low pressures and high temperatures.

Questions & Discussion

• Exercise 2.1 Solution: Compounds of Nitrogen and Oxygen.

  • Compound A: $1.750\text{ g N / 1 g O}$.

  • Compound B: $0.8750\text{ g N / 1 g O}$.

  • Compound C: $0.4375\text{ g N / 1 g O}$.

  • Ratios: $A/B = 2/1$, $B/C = 2/1$, $A/C = 4/1$. These whole numbers illustrate the Law of Multiple Proportions.

• Exercise 8 Solution (Density): A cleaning fluid with mass $19.625\text{ g}$ and volume $25.00\text{ cm}^3$.

  • $\text{Density} = 19.625 / 25.00 = 0.7850\text{ g/cm}^3$.

  • Identification: Match density to Isopropyl alcohol ($0.785\text{ g/cm}^3$).

• Stoichiometry Exercise (Propane): Mass of Oxygen for $96.1\text{ g}$ propane ($C_3H_8$).

  • Balance: $C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O$.

  • Moles propane: $96.1 / 44.1 = 2.18\text{ mol}$.

  • Moles Oxygen needed: $5 \times 2.18 = 10.9\text{ mol}$.

  • Mass Oxygen: $10.9 \times 32.00 = 349\text{ g}$.