Silverman's Special Final Review - Pre-IB and Honors Chemistry Complete Study Notes

Matter, Density, and Physical/Chemical Changes

• Definition of Matter: Matter is defined as anything that has mass and takes up space (volume).

• Fundamental Property - Density:

  • Density is the most fundamental property of all matter.

  • It represents the ratio of mass to volume: $D = \frac{m}{V}$.

  • It expresses how close particles are to one another.

  • The most common unit for density is $g/mL$.

• Classification of Matter:

  • Solution: A homogeneous mixture where particles are distributed evenly.

  • Suspension: A heterogeneous mixture containing large particles that settle out over time.

  • Colloid: A mixture containing mid-sized particles that do not settle.

• States of Matter and Phase Changes:

  • Matter exists as solid, liquid, and gas, differing in particle motion.

  • Phase changes are physical changes between these states.

• Properties and Changes:

  • Physical Properties/Changes: Characteristics or transitions that do not change the chemical identity of the substance.

  • Chemical Properties/Changes: Characteristics or transitions that describe the ability of a substance to change into a different substance.

Measurement and Metric Conversions

• Metric Prefixes (Descending Order):

  • Kilo- ($k$): $1000$

  • Hecto- ($h$): $100$

  • Deka- ($da$ or $dk$): $10$

  • Base Unit (e.g., meter, liter, gram): $1$

  • Deci- ($d$): $0.1$

  • Centi- ($c$): $0.01$

  • Milli- ($m$): $0.001$

• Mnemonic: ‐King Henry Died Merrily Drinking Chocolate Milk.‐

• Conversion Rule: Units can be converted by moving the decimal point based on the prefix values.

Significant Figures (SF) and Scientific Notation

• Significance Rules:

  • Nonzero digits are always significant.

  • Captured Zeros: Zeros between non-zeros are always significant.

  • Preceding Zeros: Zeros to the left of non-zeros are never significant. Note: The "courtesy zero" to the left of a decimal point is not significant.

  • Trailing Zeros: Zeros at the end of a number are significant only if a decimal is present anywhere in the number.

• Mathematical Operations with SF:

  • Multiplication/Division: The result must have the same number of significant figures as the least accurate measurement.

    • Example: $\frac{3.45\,cm}{2.5628\,cm} = 1.34618361\dots\,cm^2 = 1.35\,cm^2$

  • Addition/Subtraction: The result must be rounded to the same decimal place as the number with the fewest decimal places.

    • Example: $4.2\,g + 12.2635\,g = 16.4635\,g = 16.5\,g$

  • Logarithms: For the common logarithm of a measured quantity, the number of digits after the decimal point in the result equals the number of significant figures in the original number.

    • Example: $log(23.5)$. Since $23.5$ has $3$ SF, the answer is $1.371$ (3 numbers after the decimal).

• Scientific Notation: Used for very large or small numbers. Significant figures apply to the non-exponent digits.

  • Example: $2.34 \times 10^{-3}$ has $3$ SF.

Chemical Nomenclature and Ion Formulas

• Cations (Memorize):

  • Ammonium: $NH_4^{+}$

  • Hydrogen: $H^{+}$

  • Lithium: $Li^{+}$

  • Mercury(I): $Hg^{+}$

  • Potassium: $K^{+}$

  • Silver: $Ag^{+}$

  • Sodium: $Na^{+}$

  • Barium: $Ba^{2+}$

  • Calcium: $Ca^{2+}$

  • Magnesium: $Mg^{2+}$

  • Mercury(II): $Hg^{2+}$

  • Strontium: $Sr^{2+}$

  • Zinc: $Zn^{2+}$

  • Aluminum: $Al^{3+}$

• Anions (Memorize):

  • Acetate: $C_2H_3O_2^{-}$

  • Bromide: $Br^{-}$

  • Chlorate: $ClO_3^{-}$

  • Chloride: $Cl^{-}$

  • Fluoride: $F^{-}$

  • Bicarbonate: $HCO_3^{-}$

  • Hydroxide: $OH^{-}$

  • Hypochlorite: $ClO^{-}$

  • Iodide: $I^{-}$

  • Nitrate: $NO_3^{-}$

  • Nitrite: $NO_2^{-}$

  • Permanganate: $MnO_4^{-}$

  • Carbonate: $CO_3^{2-}$

  • Chromate: $CrO_4^{2-}$

  • Dichromate: $Cr_2O_7^{2-}$

  • Oxide: $O^{2-}$

  • Peroxide: $O_2^{2-}$

  • Sulfate: $SO_4^{2-}$

  • Sulfide: $S^{2-}$

  • Sulfite: $SO_3^{2-}$

  • Thiosulfate: $S_2O_3^{2-}$

  • Phosphate: $PO_4^{3-}$

  • Nitride: $N^{3-}$

  • Silicate: $SiO_4^{4-}$

Formula Writing Rules

• Ionic Compounds: Compounds of oppositely charged ions (usually metal and nonmetal).

  • Total charge must add up to zero.

  • Crossing Rule: Swap the magnitude of the charges to use as subscripts for the other ion. Drop the signs.

  • Never change internal polyatomic subscripts; use parentheses if a subscript is added to a polyatomic ion.

  • Binary compounds contain two parts; Ternary contain three.

  • Example: $\text{Sodium carbonate} = Na_2CO_3$

• Molecular Compounds: Made of two nonmetals. Uses prefixes to dictate subscripts.

  • 1: Mono; 2: Di; 3: Tri; 4: Tetra; 5: Penta; 6: Hexa; 7: Hepta; 8: Octa; 9: Nona; 10: Deca.

  • Example: $\text{Diiodine heptachloride} = I_2Cl_7$

• Acids: Compounds with $H^{+}$ as the cation.

  • No oxygen: Hydro-stem-ic acid (from stem-ide ion).

  • With Oxygen (-ate ion): Stem-ic acid.

  • With Oxygen (-ite ion): Stem-ous acid.

• Hydrates: Salts with water bound in the crystal.

  • Name the salt + prefix + hydrate.

  • Example: $CuSO_4 \cdot 5H_2O$ is Copper (II) sulfate pentahydrate.

Chemical Reactions and Balancing

• Law of Conservation of Mass: Equations must be balanced for moles of reactants and products.

• Balancing Guidelines: Never change subscripts; only change coefficients. Leave oxygen and hydrogen until the end, and solo elements last.

• Basic Reaction Types:

  • Synthesis: $A + B \rightarrow AB$

  • Decomposition: $AB \rightarrow A + B$

  • Single Displacement: $A + BC \rightarrow AC + B$ (Cationic) or $A + BC \rightarrow BA + C$ (Anionic). Use Activity Series to predict.

  • Double Displacement: $AB + CD \rightarrow AD + CB$. Often forms a precipitate.

  • Combustion: $\text{Fuel} + O_2(g) \rightarrow \text{Product} + \text{energy}$. Hydrocarbon combustion produces $CO_2(g) + H_2O(g) + \text{heat}$.

  • Oxidation-Reduction (Redox): Transfer of electrons. Oxidation (Loss), Reduction (Gain) (‐OIL RIG‐).

• Net Ionic Equations: Remove spectator ions (ions appearing unchanged on both sides) from a double displacement reaction.

• Diatomics (Standing Alone): $H_2$, $N_2$, $O_2$, $F_2$, $Cl_2$, $Br_2$, $I_2$.

Stoichiometry and Yields

• The Mole: $1\,mol = 6.02 \times 10^{23}$ particles.

• Molar Mass: Sum of atomic masses in a formula (units: $g/mol$).

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

• Dilution Formula: $M_1V_1 = M_2V_2$.

• Stoichiometry Pattern:

  1. Convert given to moles.

  2. Use mole-to-mole ratio from balanced equation coefficients.

  3. Convert result to requested units.

• Yields:

  • Actual Yield (AY): Amount actually formed/measured in lab.

  • Theoretical Yield (TY): Calculated amount using stoichiometry.

  • Percent Yield: $\frac{AY}{TY} \times 100\%$

Percent Composition and Empirical Formulas

• Percent Composition: $\frac{\text{mass of element}}{\text{molar mass of compound}} \times 100\%$

• Empirical Formula (EF): The most reduced whole-number mole ratio of elements in a compound.

• Determining EF:

  1. Assume $100\,g$ sample (convert % to grams).

  2. Convert grams to moles.

  3. Divide all by the smallest mole value.

  4. Multiply by a small whole number if ratios are not near whole numbers (e.g., $1.33 \times 3$).

• Molecular Formula (MF): The actual formula of the compound. $n(EF) = MF$.

  • $n = \frac{\text{Molar Mass of MF}}{\text{Molar Mass of EF}}$

Gas Laws and Kinetic Molecular Theory

• Ideal Gas Properties: High kinetic energy, negligible intermolecular attractions, perfectly elastic collisions.

• Pressure Units: $1\,atm = 760\,mmHg = 760\,Torr = 101.325\,kPa$.

• STP (Standard Temp & Pressure): $1\,atm$ and $273\,K$ ($0\,^{\circ}C$).

• Gas Laws:

  • Boyle’s Law: $P_1V_1 = P_2V_2$ (Inverse relationship).

  • Charles’ Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (Direct relationship).

  • Gay-Lussac’s (Amontons's) Law: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ (Direct relationship).

  • Combined Gas Law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$.

  • Ideal Gas Law: $PV = nRT$.

    • Universal Gas Constant ($R$): $0.0821\,L\cdot atm/mol\cdot K$ or $8.314\,L\cdot kPa/mol\cdot K$.

• Molar Volume at STP: $22.4\,L/mol$.

• Dalton’s Law of Partial Pressure: $P_{total} = P_1 + P_2 + P_3 + \dots$

• Mole Fraction ($X$): $X_A = \frac{n_A}{n_{total}}$.

• Graham’s Law of Effusion: $\frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}}$.

Atomic Structure and Quantum Theory

• Atom Particles:

  • Protons: Positive charge ($+1$), mass $\approx 1\,amu$ ($1.66 \times 10^{-27}\,kg$). Found in nucleus.

  • Neutrons: Neutral charge ($0$), mass $\approx 1\,amu$. Found in nucleus.

  • Electrons: Negative charge ($-1$), negligible mass. Found in orbitals.

• Electron Configuration: $\text{Energy Level (n)} + \text{Orbitals (l)} + \text{Electrons (exponent)}$. Example: $1s^2$.

• Quantum Constants:

  • Orbitals in energy level $n$: $n^2$.

  • Max electrons in energy level $n$: $2n^2$.

• Sublevel Capacities:

  • $s$: 1 orbital, max 2 electrons.

  • $p$: 3 orbitals, max 6 electrons.

  • $d$: 5 orbitals, max 10 electrons.

  • $f$: 7 orbitals, max 14 electrons.

• Order of Filling: $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p$.

Nuclear Chemistry

• Particles and Rays:

  • Alpha ($\alpha$): Helium-4 nucleus ($He^{2+}$), mass $4$, charge $+2$. Stopped by skin/paper.

  • Beta ($\beta$): High-speed electron ($e^{-}$), mass $\approx 0$, charge $-1$. Stopped by Al foil.

  • Positron ($\beta^{+}$): Positive electron ($e^{+}$), mass $\approx 0$, charge $+1$.

  • Gamma ($\gamma$): High-energy radiation, mass $0$, charge $0$. Stopped by several cm of lead.

• Types of Decay:

  • Alpha Decay: Mass decreases by $4$, atomic number decreases by $2$.

  • Beta Decay: Neutron becomes a proton (emits $e^{-}$). Atomic number increases by $1$.

  • Electron Capture: Proton captures an electron to become a neutron. Atomic number decreases by $1$.

• Half-Life ($t_{1/2}$): Time for half of a sample to decay. $\text{Remaining mass} = mi \times (0.5)^{\frac{t}{t_{1/2}}}$.

Periodic Trends

• Divisions: Metals (left, reactive, shiny, conductive), Nonmetals (right, dull, poor conductors), Metalloids (boundary/stairs, semiconductors like Si and Ge).

• Atomic Radius: Decreases across a period (greater nuclear pull), increases down a group (more shells).

• Ionization Energy (IE): Energy to remove an electron. Increases across a period, decreases down a group.

• Electron Affinity: Energy to add an electron. Follows the same pattern as IE.

Thermodynamics and Thermochemistry

• Enthalpy ($H$): Sum of kinetic and potential energy.

• Exothermic Reaction: Releases energy. $\Delta H = (-)$. Environment feels hotter.

• Endothermic Reaction: Absorbs energy. $\Delta H = (+)$. Environment feels colder.

• Activation Energy ($E_a$): Energy required to start a reaction. $E_a = H_{max} - H_{reactants}$.

• Calorimetry Equation: $q = mC\Delta T$

  • $q$: Heat energy ($J$ or $kJ$).

  • $m$: Mass ($g$).

  • $C$: Specific Heat (Water $C = 4.18\,J/g\cdot ^{\circ}C$).

  • $\Delta T$: $T_{final} - T_{initial}$.

• Standard Heat of Formation ($\Delta H_f^{\circ}$): $\Delta H^{\circ} = \Sigma \Delta H_{f}^{\circ}(\text{products}) - \Sigma \Delta H_{f}^{\circ}(\text{reactants})$.

• Entropy ($S$): Measure of disorder. Universe tends toward increasing entropy.

Solutions and Acids/Bases

• Factors Speeding Dissolution: Stirring, heating, grinding (for solids in liquids); cooling and pressure (for gases in liquids).

• Saturation Levels: Saturated (on the line), Supersaturated (above line), Unsaturated (below line).

• Colligative Properties:

  • Freezing Point Depression: Solute lowers freezing point.

  • Boiling Point Elevation: Solute raises boiling point.

• Acids/Bases Definitions:

  • Arrhenius: Acid ($H^{+}$ producer), Base ($OH^{-}$ producer).

  • Br%C3%B8nsted-Lowry: Acid (proton donor), Base (proton acceptor).

  • Lewis: Acid (electron pair acceptor), Base (electron pair donor).

• Ion-Product of Water ($K_w$): $K_w = [H^{+}][OH^{-}] = 1.0 \times 10^{-14}$.

• Logarithmic Scales:

  • $pH = -log[H^{+}]$

  • $pOH = -log[OH^{-}]$

  • $pH + pOH = 14$

  • $[H^{+}] = 10^{-pH}$

• Neutralization: $\text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water}$. Titration point of neutralization is the equivalence point.

• Buffers: Systems resisting pH change using a weak acid/base and its conjugate salt.

Kinetics and Equilibrium

• Collision Theory: Reactions require correct orientation and sufficient energy.

• Le Ch%C3%A2telier’s Principle: Systems adjust to minimize stress (concentration, temperature, pressure).

• Catalysts: Lower $E_a$ to speed up reaction; not consumed.

• Equilibrium Constant ($K_{eq}$): Ratio of products to reactants.

• Solubility Product Constant ($K_{sp}$): Indicates solubility; lower $K_{sp}$ means lower solubility.

• Common Ion Effect: Solubility of a substance decreases when a common ion is added.

Organic Chemistry

• Hydrocarbons: Alkanes (single bonds, saturated), Alkenes (double bonds, unsaturated), Alkynes (triple bonds, unsaturated).

• Skeletal Structures: Alcohols (-OH), Ethers (R-O-R), Amines (contain N), Aldehydes (terminal carbonyl), Ketones (internal carbonyl), Carboxylic Acids (-COOH), Esters (-COOR).

• Polymers: Large molecules made of repeating monomers.

• Biological Compounds: Carbohydrates, Lipids, Proteins, Nucleic Acids.

Questions & Discussion

• How old is a fossil if the initial mass of Carbon-14 is $41.6\,\mu g$ and final mass is $1.3\,\mu g$ ($t_{1/2} = 5700\,yrs$)?

  • Ratio: $\frac{1.3}{41.6} = \frac{1}{32}$. Since $\frac{1}{32} = (0.5)^5$, 5 half-lives passed.

  • Age: $5 \times 5700 = 28,500\,years$.

• What is the composition of a neutron based on decay?

  • A neutron behaves as a proton and an electron combined (Beta decay emits an electron, leaves a proton behind).

• Does a new bicycle or a rusty one have greater entropy?

  • A rusty one has greater entropy due to the breakdown and disorder of the metal structure.