College Chemistry B Final Exam Comprehensive Study Notes

Quantitative Analysis and Measurement Standards

• Scientific Notation and Significant Figures:
  • Scientific notation requires expressing numbers as a coefficient between 1 and 10 multiplied by a power of 10 ($a \times 10^b$).
  • Significant figures (sig figs) are the digits in a number that carry meaningful contributions to its measurement resolution. Following the transcript, numbers must be rounded to exactly 3 significant figures:
    • $0.00213$ becomes $2.13 \times 10^{-3}$.
    • $0.008567$ becomes $8.57 \times 10^{-3}$.
    • $153,210$ becomes $1.53 \times 10^5$.
    • $1,652,231$ becomes $1.65 \times 10^6$.
• Accuracy vs. Precision in Data Interpretation:
  • Accuracy: Refers to how close a measured value is to the accepted, theoretical, or true value.
  • Precision: Refers to how close a series of measurements are to one another, reflecting the reproducibility of the data.
  • Example Evaluation: With a theoretical density value of $44.8 \text{ g/cm}^3$, Set A ($44.74 \text{ g/cm}^3$, $44.83 \text{ g/cm}^3$, and $44.84 \text{ g/cm}^3$) is both accurate (values reflect the true density) and precise (values are clustered tightly together).
  • Comparison of other sets:
    • Set B ($39.33 \text{ g/cm}^3$, $39.32 \text{ g/cm}^3$, $39.34 \text{ g/cm}^3$) is precise but not accurate.
    • Set C ($48.55 \text{ g/cm}^3$, $35.56 \text{ g/cm}^3$, $39.78 \text{ g/cm}^3$) is neither accurate nor precise.
• Density Calculations:
  • Density is defined as the mass of an object divided by its volume: $Density = \frac{Mass}{Volume}$.
  • Example Calculation: For an object with a volume of $95.5 \text{ ml}$ and a mass of $35.4 \text{ grams}$, the calculation is:
    • $D = \frac{35.4 \text{ g}}{95.5 \text{ ml}} = 0.37068 \text{ g/ml}$
    • Rounded to 3 significant figures: $0.371 \text{ g/ml}$.
  • Substances with a density lower than water ($1.0 \text{ g/cm}^3$) will float on top, while substances with a density greater than water will sink.

Classification of Matter and Physical/Chemical Changes

• Matter Classification Categories:
  • Pure Element: A substance consisting of only one type of atom (e.g., $O_2$ or Iron).
  • Pure Compound: A substance consisting of two or more elements chemically bonded in a fixed ratio (e.g., $H_2O$).
  • Mixture of Elements: Multiple types of elemental atoms or molecules present together but not chemically bonded.
  • Mixture of Compounds: Multiple types of molecules present together.
  • Mixture of Elements and Compounds: A blend of both pure elements and chemical compounds.
• Physical vs. Chemical Changes:
  • Physical Change: A change that alters the form or appearance of a substance but does not change its chemical composition. These include phase changes and structural alterations.
    • Examples: Tearing paper, boiling water, stretching metal into wire (ductility), crushing an aluminum can, evaporating liquid to gas.
  • Chemical Change: A process where one or more substances are altered into one or more new and different substances through the breaking and forming of chemical bonds.
    • Examples: Burning wood (combustion), rusting iron (oxidation), burning gasoline, rotting/spoiling food, cooking a steak on the BBQ.
• Phases of Matter:
  • Solid: Particles are packed tightly together, usually in a regular pattern, with limited motion (vibration only).
  • Liquid: Particles are close together but have no regular arrangement; they move past one another.
  • Gas: Particles are far apart with no regular arrangement and move rapidly in all directions.

Atomic Structure and the Periodic Table

• Ions and Charged Particles:
  • Cation: A positively charged ion formed when an atom loses electrons. Metal elements typically lose electrons to become cations.
  • Anion: A negatively charged ion formed when an atom gains electrons. Non-metal elements typically gain electrons to become anions.
• Isotopes and Subatomic Particles:
  • Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number. All isotopes of a given element have the same number of protons in each atom.
  • Protons (Black Circles): Determine the identity of the element.
  • Neutrons (White Circles): Contribute to the mass of the nucleus alongside protons.
  • Nuclei Composition Examples:
    • Boron-10 ($ ext{ }_5^{10} ext{B}$): 5 protons, 5 neutrons.
    • Beryllium-9 ($ ext{ }_4^9 ext{Be}$): 4 protons, 5 neutrons.
    • Lithium-7 ($ ext{ }_3^7 ext{Li}$): 3 protons, 4 neutrons.
    • Carbon-12 ($ ext{ }_6^{12} ext{C}$): 6 protons, 6 neutrons.
• Weighted Average Atomic Mass:
  • The atomic mass listed on the periodic table (e.g., $6.941 \text{ amu}$ for Lithium) is a weighted average of all naturally occurring isotopes. This value ($6.941$) is closer to $7$ than to $6$ because the isotope $\text{Li-7}$ is significantly more abundant in nature than $\text{Li-6}$.
• Electron Configuration and Valence:
  • Ground State: The lowest energy state of an atom.
  • Carbon ($Z=6$): Configuration: $1s^2 2s^2 2p^2$. Orbital notation includes two electrons in $1s$, two in $2s$, and two single electrons in two separate $2p$ orbitals.
  • Lithium ($Z=3$): Configuration: $1s^2 2s^1$.
  • Iron ($Z=26$): Configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6$.
  • Valence Electrons: Represented by Lewis dots, these correspond to the outermost electrons in the highest principal energy level.
    • $Li$, $K$: 1 dot.
    • $C$: 4 dots.
    • $N, P$: 5 dots.
    • $O, S$: 6 dots.
    • $Cl, Br$: 7 dots.
    • $Ne$: 8 dots.
• Atomic Radius Trends:
  • Atomic radius generally increases as you move down a group (due to additional energy levels) and decreases as you move across a period (due to increased nuclear charge pulling electrons closer).
  • Among the list Na, He, K, I, Cl, Ne, Br:
    • Largest: Potassium ($K$) [Lowest and leftmost on the Periodic Table].
    • Smallest: Helium ($He$) [Highest and rightmost].

Chemical Bonding and Molecular Geometry (VSEPR)

• Bond Types:
  • Ionic Bond: The transfer of electrons from a metal to a non-metal, creating ions that attract one another. Examples: $NaCl$, $CaBr_2$, $NaNO_3$.
  • Non-Polar Covalent Bond: The equal sharing of electrons between atoms.
  • Polar Covalent Bond: The unequal sharing of electrons due to differences in electronegativity. Electrons spend more time near the more electronegative atom, creating partial charges ($\text{positive } \rightarrow \text{ negative}$).
• Molecular Polarity:
  • Non-Polar Molecule: A molecule with a completely symmetric appearance and equal distribution of electrons.
  • Polar Molecule: A molecule that is asymmetrically shaped with unevenly distributed electrons, leading to one region being more electron-rich than another.
• VSEPR Geometry and Bond Angles:
  • $CO_2$ (Carbon Dioxide): Linear geometry, bond angle of $180^\text{o}$.
  • $BF_3$ (Boron Trifluoride): Trigonal Planar, bond angle of $120^\text{o}$.
  • $CCl_4$ (Carbon Tetrachloride): Tetrahedral, bond angle of $109.5^\text{o}$.
  • $NH_3$ (Ammonia): Trigonal Pyramidal, bond angle approximately $107^\text{o}$. (Based on tetrahedral parent geometry).
  • $H_2O$ (Water): Bent, bond angle approximately $104.5^\text{o}$.
  • $SH_2$ (Hydrogen Sulfide): Bent.
  • $PCl_3$ (Phosphorus Trichloride): Trigonal Pyramidal.

Intermolecular Forces (IMF)

• Types of Forces (Weakest to Strongest):
  1. Dispersion Force (London Dispersion): Caused by temporary, instantaneous dipole formation due to constant electron motion in non-polar molecules.
  2. Dipole-Dipole Interaction: Occurs between polar molecules where the positive end of one molecule is attracted to the negative end of another.
  3. Hydrogen Bonding: A specific, strong type of dipole-dipole force occurring when hydrogen is bonded to Nitrogen ($N$), Oxygen ($O$), or Fluorine ($F$).
• Influence on Boiling Temperature:
  • Stronger intermolecular forces between molecules result in higher boiling points because more energy (heat) is required to overcome the attractions and separate the molecules into a gas phase.

Stoichiometry and Solution Chemistry

• Molar Mass and Formula Writing:
  • Copper(II) Phosphide: $Cu_3P_2$.
  • Ammonium Carbonate: $(NH_4)_2CO_3$.
  • Lead(II) Nitrate: $Pb(NO_3)_2$.
  • Calcium Chloride: $CaCl_2$.
• Molarity ($M$) and Dilution:
  • Molarity Formula: $M = \frac{Moles \text{ of Solute}}{Liters \text{ of Solution}}$.
  • Dilution Equation: $M_1V_1 = M_2V_2$.
    • Example: If $634.5 \text{ ml}$ ($0.6345 \text{ L}$) of $0.75 \text{ M } K_2SO_4$ is diluted to $1.00 \text{ Liter}$, the new molarity is calculated as:
    • $(0.75 \text{ M}) \times (0.6345 \text{ L}) = (M_2) \times (1.00 \text{ L})$
    • $M_2 = 0.475875 \text{ M}$.
  • Mass from Molarity calculation: To find grams of $Mg(C_2H_3O_2)_2$ needed for $448.5 \text{ ml}$ ($0.4485 \text{ L}$) of $0.75 \text{ M}$ solution:
    • $Moles = M \times V = 0.75 \text{ M} \times 0.4485 \text{ L} = 0.336375 \text{ moles}$.
    • Multiply moles by molar mass ($142.39 \text{ g/mol}$) to find the grams required.
• Precipitation Reactions and Spectator Ions:
  • A precipitation reaction occurs when two aqueous solutions react to form an insoluble solid.
  • Example: Reaction between Sodium Carbonate ($Na_2CO_3$) and Copper(II) Sulfate ($CuSO_4$) forms Copper(II) Carbonate ($CuCO_3$) as the solid precipitate.
  • Spectator Ions: Ions that do not participate in the formation of the precipitate. In the reaction between Ammonium Chromate and Silver Nitrate, the spectator ions are Ammonium ($NH_4^+$) and Nitrate ($NO_3^-$).
• Percent Yield:
  • $\text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100$.

Reaction Types and Thermodynamics

• Classification of Chemical Reactions:
  • Synthesis: Two or more reactants form one product ($N_2 + 3H_2 \rightarrow 2NH_3$).
  • Decomposition: One reactant breaks down into two or more products ($CaCO_3 \rightarrow CaO + CO_2$).
  • Single Replacement: One element replaces another in a compound ($2AgNO_3 + Cu \rightarrow Cu(NO_3)_2 + 2Ag$).
  • Double Replacement: Ions of two compounds exchange places ($3K_2SO_4 + Ca_3(PO_4)_2 \rightarrow 2K_3PO4 + 3CaSO_4$).
  • Combustion: A substance reacts with Oxygen, producing energy, $CO_2$, and $H_2O$ ($C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O$).
• Properties of Gases:
  • Temperature: A measurement of the average Kinetic Energy (speed) of gas particles.
  • Ideal Gas Law: $PV = nRT$.
    • Variables: $P = \text{Pressure}$, $V = \text{Volume}$, $n = \text{moles}$, $R = \text{Gas Constant}$, $T = \text{Temperature in Kelvin}$.
    • Relationship: If pressure and moles are constant, volume is directly proportional to temperature (Charles's Law).
• Thermodynamics and Heat Energy:
  • Exothermic reaction: A process where energy is released from the system into the surroundings.
  • Specific Heat Equation: q = mc\text{\Delta}T.
    • Example: Calculate the mass if $q = 2967 \text{ Joules}$, \text{\Delta}T = 35.6 - 20.7 = 14.9^\text{o}\text{C}, and $c_{\text{water}} = 4.184 \text{ J/g}^\text{o}\text{C}$.
    • $2967 = m \times 4.184 \times 14.9$
    • $m = \frac{2967}{(4.184 \times 14.9)} \text{ grams}$.
• Acid Dissociation:
  • Strong Acid: Dissociates completely in water, meaning every molecule breaks apart into ions.
  • Weak Acid: Dissociates only partially in water, with many molecules remaining whole within the solution.