ACS First Year Chemistry Comprehensive Review Notes

Atomic Structure and Fundamental Theory

• Definition of an Atom: An atom represents the smallest unit of matter that retains chemical and physical properties (Question 1).
• Nuclear Structure discovery: Ernest Rutherford is credited with discovering that the nucleus is extremely small compared to the overall volume of the atom (Question 47).
• Atomic Composition and Isotopes:
  • Protons define the element's identity (the atomic number).
  • Isotopes of a single element have the same number of protons but different mass numbers due to varying numbers of neutrons.
  • Example for $_{7}^{15}\text{N}^{2+}$ (Question 16, 88):
    • Atomic Number: $7$ (7 protons).
    • Mass Number: $15$
    • Neutron Count: $15 - 7 = 8$ neutrons.
    • Electron Count: For a charge of $+2$, the atom has $7 - 2 = 5$ electrons.
• Periodic Trends:
  • Atomic Radius: Generally decreases across a row as the atomic number increases because the addition of more protons increases the effective nuclear charge, pulling electrons closer to the nucleus (Question 36).
  • Ionization Energy (IE):
    • In the alkaline-earth group, atoms with the smallest radii possess the highest ionization energies (Question 66).
    • Elements like nitrogen and oxygen generally have high first ionization energies (Question 37).
    • Successive Ionization Energies: Significant jumps in IE indicate the removal of core electrons. For an unknown element with IE values of $590\,kJ/mol$, $1145\,kJ/mol$, $2412\,kJ/mol$, $9474\,kJ/mol$, and $12326\,kJ/mol$, the large jump after the third electron suggests the most common ion is $X^{3+}$ (Question 28).
    • Second Ionization Energy: Sodium (Na) has a very high second IE because its second electron is removed from a stable, filled inner shell (Question 63).
  • Electronegativity: Oxygen is characterized by having a higher electronegativity compared to sodium, chlorine, xenon, or sulfur (Question 32).
• Electronic Configuration:
  • Silicon (Si): In its ground state, silicon has $4$ valence electrons and $2$ unpaired electrons (Question 67).
  • Orbitals: There are exactly $5$ d-orbitals in the fourth energy level ($n = 4$) (Question 45).

Chemical Bonding and Molecular Geometry

• Molecular Shapes (VSEPR Theory):
  • Methane ($CH_4$): Tetrahedral geometry (Question 6).
  • Carbon Dioxide ($CO_2$): Linear geometry (Question 33).
  • Water ($H_2O$): Bent, angular, or V-shaped (Question 65).
  • Ammonia ($NH_3$): Trigonal pyramid (Question 86).
  • Aluminum Chloride ($AlCl_3$): Planar triangular (Question 82).
• Polarity and Intermolecular Forces:
  • Polar Molecules: Ammonia ($NH_3$) contains a permanent dipole (Question 15). Compounds like $CCl_4$, $CO_2$, and $Cl_2$ are non-polar.
  • Hydrogen Bonding: This explains why methanol ($CH_3OH$) has a higher boiling point than dimethyl ether ($CH_3OCH_3$) (Question 80).
  • Ionic Character: The bond between potassium (K) and chlorine (Cl) exhibits high ionic character due to the large electronegativity difference (Question 74).
• Lewis Structures: The hydroxide ion ($OH^-$) must show $8$ electrons in its Lewis structure ($1$ from Hydrogen, $6$ from Oxygen, and $1$ from the negative charge) (Question 53).
• Flame Tests: Sodium chloride ($NaCl$) produces a characteristic yellowish-orange flame when placed in a Bunsen burner (Question 38).

States of Matter and Gas Laws

• Kinetic Molecular Theory (KMT):
  • Average kinetic energy of gas molecules is determined solely by temperature. Different gases in identical conditions (same $T$ and $P$) have the same average kinetic energy (Question 5, 68).
  • Real gases most closely resemble ideal gases under conditions of low pressure and high temperature (Question 14).
• Gas Law Calculations:
  • Graham's Law of Effusion: Velocity is inversely proportional to the square root of molar mass ($v ∝ 1/\sqrt{M}$). If oxygen ($M = 32$) travels at $1000\,m/sec$, hydrogen ($M = 2$) travels at $4000\,m/sec$ because its mass is $16$ times smaller ($\sqrt{16} = 4$) (Question 4).
  • Combined Gas Law: Used to find new volume when $P$ and $T$ change ($\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$). For a sample at $300.0\,mL$, $1.00\,atm$, and $27.0^{\circ}C$ ($300\,K$), increasing temperature to $327^{\circ}C$ ($600\,K$) and decreasing pressure to $0.500\,atm$ results in a volume of $1200\,mL$ (Question 12).
  • Boyle’s Law: ($P_1V_1 = P_2V_2$). A $2.0\,L$ gas sample at $1.00\,atm$ compressed to $500.0\,mL$ requires a pressure of $4.0\,atm$ (Question 87).
  • Charles’s Law: ($\frac{V_1}{T_1} = \frac{V_2}{T_2}$). A $5.0\,L$ gas at $50.0^{\circ}C$ ($323\,K$) heated to $100.0^{\circ}C$ ($373\,K$) at constant pressure expands to $5.8\,L$ (Question 51).
  • Dalton’s Law of Partial Pressures: The partial pressure of a dry gas collected over water is the total pressure minus the water vapor pressure ($P_{\text{gas}} = P_{\text{total}} - P_{\text{H}_2\text{O}}$). At $600.0\,mmHg$ and $40^{\circ}C$ (vapor pressure $= 55.3\,mmHg$), the gas pressure is $544.7\,mmHg$ (Question 54).
• Phase Changes: During boiling, the temperature of a liquid remains constant while the potential energy increases (Question 8).

Stoichiometry and Molar Relationships

• Formula Weights and Molar Mass:
  • Calcium nitrate ($Ca(NO_3)_2$): $0.20\,moles$ has a mass of approximately $33\,g$ (Question 21).
  • Oxygen gas ($O_2$): $2.0\,moles$ has a mass of $64\,g$ ($2 \times 32\,g/mol$) (Question 27).
  • Magnesium chloride ($MgCl_2$): Molar mass is approximately $95.3\,g/mol$ (Question 44).
• Reaction Stoichiometry:
  • Water Yield: From $2H_2 + O_2 \rightarrow 2H_2O$, $6.00\,moles$ of $H_2$ and $6.00\,moles$ of $O_2$ produce a maximum of $108\,g$ of water (since $H_2$ is limiting, producing $6.00\,moles$ of $H_2O$) (Question 17).
  • Gas Volume to Mass: To produce $44.8\,L$ of methane ($CH_4$) at STP (which is $2.0\,moles$) via $C + 2H_2 \rightarrow CH_4$, one needs $4.0\,moles$ of $H_2$, weighing $8.0\,g$ (Question 77).
  • Decomposition: $2KClO_3 \rightarrow 2KCl + 3O_2$. The decomposition of $4.00\,mol$ of $KClO_3$ produces $6.00\,mol$ ($192\,g$) of oxygen (Question 55).
  • Haber Process: ($N_2 + 3H_2 \rightarrow 2NH_3$). Converting $12.0\,g$ of $H_2$ ($6.0\,mol$) requires $2.0\,mol$ of $N_2$ (Question 60).
• Empirical Formulas:
  • A compound with $64\,g$ of Oxygen ($4\,mol$) and $4\,g$ of Hydrogen ($4\,mol$) has an empirical formula of $HO$ (Question 75).
  • If empirical formula is $NO_2$ ($46\,amu$) and molecular mass is $85-95\,amu$, the molecular formula is $N_2O_4$ (Question 71).

Solutions and Titrations

• Concentration Calculations:
  • Molarity ($M$): Moles of solute per Liter of solution. For example, $120\,g$ of $NaOH$ ($3\,mol$) in $600\,mL$ ($0.6\,L$) results in a $5.0\,M$ solution (Question 84).
  • Volume and Concentration: A $0.40\,M \, NH_3$ solution containing $3.4\,g$ ($0.2\,mol$) of ammonia has a volume of $500\,mL$ (Question 46).
• Titrations:
  • Calculated using balanced equations ($n_{\text{acid}}M_AV_A = n_{\text{base}}M_BV_B$).
  • Titrating $100.0\,mL$ of $Ba(OH)_2$ with $200.0\,mL$ of $0.500\,M \, HNO_3$: Since $Ba(OH)_2$ produces two $OH^-$, the concentration is $0.500\,M$ (Question 2).
  • Titrating $50.0\,mL$ of $HCl$ with $40.0\,mL$ of $0.400\,M \, NaOH$ yields an $HCl$ molarity of $0.320\,M$ (Question 50).
  • In a strong acid/strong base titration, the pH at the end point is approximately $7.0$, and salt/water are the primary species present (Question 81).
• Solubility and Conductance:
  • Non-polar molecules like methane ($CH_4$) are not very soluble in water (Question 11).
  • Strong Electrolytes: Dissociate completely and conduct electricity well (e.g., $HNO_3$, $KCl$ solution) (Question 76, 90).
  • Weak Electrolytes: Dissociate only partially (Question 9).
  • Precipitates: Based on solubility guidelines, mixing $KBr$ and $Hg(NO_3)_2$ or $NH_4Cl$ and $Pb(NO_3)_2$ produces a precipitate (Question 39).
  • Net Ionic Equations: For silver nitrate and sodium sulfide: $2Ag^+(aq) + S^{2-}(aq) \rightarrow Ag_2S(s)$ (Question 40).
• Colligative Properties: Solutes like sugar in distilled water depress the freezing point and elevate the boiling point (Question 61).

Acids, Bases, and pH

• pH scale:
  • If $[H_3O^+] = 8.26 \times 10^{-5} \, M$, the pH is between $4$ and $5$ (Question 3).
  • Distilled water concentration of $OH^-$ is $10^{-7} \, M$ at neutral pH (Question 25).
  • A $10^{-4} \, M \, NaOH$ solution has a pH of $10$ (Question 62).
  • Basic substances ($pH > 7.0$) include dish soap (Question 23).
• Properties of Bases: They taste bitter, feel slippery, and turn red litmus paper blue (Question 13).

Chemical Equilibrium

• Le Châtelier’s Principle:
  • Pressure: In the system $2CO(g) + O_2(g) \rightleftharpoons 2CO_2(g)$, increasing total pressure shifts equilibrium toward the side with fewer gas moles ($CO_2$ increases, $CO$ decreases) (Question 18).
  • Concentration: In $CH_3COOH(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + CH_3COO^-(aq)$, $CH_3COOH$ is the species present in highest concentration because it is a weak acid (Question 7).
  • Temperature: Increasing temperature on an endothermic reaction (e.g., $CH_3OH + 101 \, kJ \rightleftharpoons CO + 2H_2$) shifts equilibrium to the products, increasing $[CO]$ (Question 59).
• Equilibrium Constant ($K$):
  • A very high value of $K$ indicates that products are heavily favored (Question 64).
  • Changing the concentration of reactants/products at a constant temperature does not change the value of the equilibrium constant $K$ (Question 85).

Thermochemistry and Nuclear Chemistry

• Thermodynamics:
  • Specific Heat: Energy ($Q$) absorbed by $10.0\,g$ of water heated from $10.0^{\circ}C$ to $40.0^{\circ}C$ is calculated as $10.0 \times 4.2 \times 30.0 = 1260\,J$ or $1.26\,kJ$ (Question 34).
  • Units: Energy as heat is measured in Joules ($J$) or Kilojoules ($kJ$) (Question 42).
  • Gibbs Free Energy: ($\Delta G = \Delta H - T\Delta S$). For a reaction where $\Delta H = -150\,kJ/mol$, $\Delta S = +200\,J/mol\cdot K$, and $T = 300\,K$, the value is $-210\,kJ/mol$, making the reaction spontaneous (Question 58).
  • Entropy and Enthalpy: The process of ice freezing is exothermic and results in a decrease in entropy (Question 73).
• Redox and Reactions:
  • Oxidation Numbers: Sulfur in $Na_2SO_4$ has an oxidation number of $+6$ (Question 10).
  • Single Replacement: Reactions such as $2NaBr + Cl_2 \rightarrow 2NaCl + Br_2$ (Question 35).
• Nuclear Chemistry:
  • Penetrating Power: Gamma radiation has greater penetrating power and velocity compared to alpha and beta radiation (Question 56).
  • Half-life: If $125\,g$ remains of a $500\,g$ sample (which is two half-lives, $1/4$ original) after $8.0$ years, the half-life is $4.0$ years (Question 78).
  • Balancing Nuclear Equations: Bombarding a nucleus with an alpha particle ($_{2}^{4}He$) results in transmutations that must conserve mass and atomic numbers (Question 69).

Measurement, Formulas, and Properties

• Scientific Notation and Sig Figs:
  • $0.00930 \, m$ is expressed as $9.30 \times 10^{-3} \, m$ (Question 22).
  • $50.0 \, cm$ is same as $500 \, mm$ when significant figures are considered (Question 83).
• Chemical vs. Physical Changes: Boiling and melting are physical changes; rusting and burning are chemical changes (Question 52).
• Naming Compounds:
  • $Fe(NO_3)_2$ is Iron(II) nitrate (Question 20).
  • Aluminum sulfate is $Al_2(SO_4)_3$ (Question 57).
  • Compound formed by lead(IV) and carbonate is $Pb(CO_3)_2$ (Question 48).
• Mixtures: A solution of sugar and water is a homogeneous mixture, whereas garden soil is heterogeneous (Question 31).