Advanced Chemistry Second Semester Exam Comprehensive Study Guide 2026

Prerequisite Knowledge and Fundamental Skills

To successfully complete the second-semester exam, proficiency in several first-semester foundational skills is required. These include: - Formula Writing: The ability to write correct chemical formulas for ionic compounds, molecular compounds, acids, hydrocarbons, and alcohols. - Chemical Equations: Writing complete balanced chemical equations. This includes predicting products based on the reactants provided for various reaction types. - Mathematical Calculations: Using dimensional analysis (the factor-label method) for all unit conversions and problem-solving steps. - Significant Figures: Presentation of all numerical answers with the correct number of significant figures based on the precision of the data provided.

Avogadro’s Number and Molar Calculations

Avogadro’s Number: Defined as the quantity $6.022 \times 10^{23}$ . This number represents the amount of elementary entities (atoms, molecules, or formula units) present in one mole of a substance.
Application: Avogadro's number is used as a conversion factor between the macroscopic scale (moles) and the microscopic scale (particles/atoms).
Calculation Example: To find the number of atoms in $4.80\,\text{mol Au}$ , the following calculation is performed: - $\text{Atoms} = 4.80\,\text{mol} \times 6.022 \times 10^{23}\,\text{atoms/mol} = 2.89 \times 10^{24}\,\text{atoms}$

Periodic Trends

Atomic Radius: - Definition: The distance from the center of the nucleus to the outermost electron shell. - Trend: Atomic radius increases as you move down a group (due to the addition of principal energy levels) and decreases as you move across a period from left to right (due to increased effective nuclear charge pulling electrons closer). - Ordering Example: Increasing atomic radius for $Ba$ , $S$ , $Ca$ , $F$ , and $Zn$ : - $F < S < Zn < Ca < Ba$
First Ionization Energy: - Definition: The energy required to remove the most loosely held electron from an atom in the gaseous state. - Trend: It increases across a period and decreases down a group. - Relationship with Atomic Radius: They are inversely related. As atomic radius decreases, the nucleus has a stronger grasp on its electrons, making them harder to remove (thus increasing ionization energy).
Electronegativity: - Definition: A measure of the ability of an atom in a chemical compound to attract shared electrons to itself. - Trend: It generally increases across a period and decreases down a group.
Shielding Effect: - The phenomenon where inner-shell electrons "shield" or block the positive charge of the nucleus from the outermost valence electrons. This effect remains relatively constant across a period but increases significantly down a group as more electron shells are added.

Chemical Bonding

Bond Types and Characteristics: - Ionic Bonds: Formed by the electrostatic attraction between cations and anions, typically involving a transfer of electrons. These usually form between a metal and a nonmetal. - Covalent (Molecular) Bonds: Formed by the sharing of electrons between atoms. These typically occur between two nonmetals. - Metallic Bonds: Occur between metal atoms; they are characterized not by discrete compound formation but by a “sea of electrons” where valence electrons are delocalized and free to move throughout the structure.
Specific Examples: - Phosphorus ( $P$ ) and Bromine ( $Br$ ): These form a covalent bond because both are nonmetals and share electrons.
Valence Electrons: These are the electrons specifically involved in the bonding process.

Percent Composition and Empirical Formulas

Percent Composition: - Calculation: Calculated as \text{% by mass} = \frac{\text{mass of element in 1 mol compound}}{\text{molar mass of compound}} \times 100\%. - This can be used to determine the specific mass of an element within a larger given mass of a compound.
Empirical Formulas: - Definition: The simplest whole-number ratio of atoms of each element present in a compound. - Determination from Percent Composition: 1. Assume a $100\,\text{g}$ sample to convert percentages to grams. 2. Convert grams to moles using molar masses. 3. Divide all mole values by the smallest mole value calculated. 4. Multiply to get whole numbers if necessary. - Example Calculation: A compound containing $32.38\%\,\text{Na}$ , $22.65\%\,\text{S}$ , and $44.99\%\,\text{O}$ . - Moles of $Na = \frac{32.38}{22.99} = 1.408$ - Moles of $S = \frac{22.65}{32.06} = 0.706$ - Moles of $O = \frac{44.99}{16.00} = 2.812$ - Ratio: $Na:S:O = 2:1:4$ . Empirical formula: $Na_2SO_4$
Molecular Formulas: - Determined by comparing the empirical formula mass to the actual molecular mass ( $n = \frac{\text{Molar Mass}}{\text{Empirical Mass}}$ ). - Example: Empirical formula $PCl_5$ (MW $= 208.22\,\text{g/mol}$ ) and a given molar mass of $132.84\,\text{g/mol}$ . (Note: There appears to be a discrepancy in the transcript values versus expected molar masses for $PCl_5$ ; students should follow the formula $n \times \text{(Empirical Formula)}$ ).

Stoichiometry and Reaction Yields

Definitions: - Stoichiometry: The calculation of quantities in chemical reactions. - Mole Ratio: Derived from the coefficients of a balanced chemical equation, used to convert between moles of different substances.
Conversions: - Mole-to-Mole: Using the mole ratio directly. - Mole-to-Mass / Mass-to-Mole: Utilizing the mole ratio and the molar mass ( $g/mol$ ) of the substances. - Mass-to-Mass: Using molar mass of Reactant A \rightarrow mole ratio A:B \rightarrow molar mass of Substance B.
Yield and Reactants: - Theoretical Yield: The maximum amount of product that could be formed from given amounts of reactants. - Actual Yield: The amount of product actually produced in a laboratory setting. - Percent Yield: Calculated as $\frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$ . - Limiting Reactant: The reactant that is completely consumed first, limiting the amount of product formed. - Excess Reactant: The reactant that remains after the limiting reactant is exhausted.

Kinetic Molecular Theory (KMT) and States of Matter

Differences in Matter: Particles in a gas are far apart and move independently, whereas particles in a liquid are closer together but can still flow past one another.
KMT Assumptions for Gases: 1. Gases consist of large numbers of tiny particles that are far apart relative to their size. 2. Collisions between gas particles and between particles and container walls are elastic (no net loss of total kinetic energy). 3. Gas particles are in continuous, rapid, random motion. 4. There are no forces of attraction between gas particles. 5. The temperature of a gas depends on the average kinetic energy of the particles.
Ideal Gas: A hypothetical gas that perfectly fits all the assumptions of the kinetic-molecular theory.
Compressibility: Gases are highly compressible compared to solids and liquids because of the vast empty space between particles.
Kinetic Energy and Temperature: There is a direct relationship; as temperature increases, the average kinetic energy of the particles increases.

Gas Laws and Mathematical Relationships

Standard Temperature and Pressure (STP): - Temperature: $0^\circ\,\text{C}$ ( $273.15\,\text{K}$ ). - Pressure: $1.00\,\text{atm}$ , $101.3\,\text{kPa}$ , $760\,\text{mmHg}$ , or $760\,\text{torr}$ . - Molar Volume: $1\,\text{mole}$ of any gas at STP occupies $22.4\,\text{L}$ .
Gas Law Equations: - Charles’s Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ - Boyle’s Law: $P_1V_1 = P_2V_2$ - Gay-Lussac’s Law: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ - Ideal Gas Law: $PV = nRT$ - $P = \text{Pressure}$ - $V = \text{Volume}$ - $n = \text{Number of moles}$ - $R = \text{Ideal gas constant}$ - $T = \text{Temperature (must be in Kelvin)}$ - Dalton’s Law of Partial Pressures: $P_{\text{total}} = P_1 + P_2 + P_3...$ - Graham’s Law of Effusion: Rate of diffusion is inversely proportional to the square root of the molar mass: $\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{MM_2}{MM_1}}$ .

Thermochemistry

Definitions: - Heat ( $q$ ): The transfer of energy between objects due to a temperature difference. - Temperature: A measure of the average kinetic energy of particles. - Specific Heat ( $c$ ): The amount of heat required to raise the temperature of $1\,\text{g}$ of a substance by $1^\circ\,\text{C}$ . Units: $J/(g^\circ\text{C})$ . - Absolute Zero: $0\,\text{K}$ . It is the temperature at which all molecular motion theoretically stops. - Standard State: The most stable physical state of a substance at $1\,\text{atm}$ and a specified temperature (usually $298.15\,\text{K}$ ).
Measurements and Calculations: - $1\,\text{cal} = 4.184\,\text{J}$ . - Calorimetry Formula: $q = m \times c \times \Delta T$
Enthalpy and Reactions: - Heat of Formation ( $\Delta H_f$ ): Enthalpy change when one mole of a compound is formed from its elements in their standard states. - Heat of Reaction: Calculated as $\Delta H_{\text{rxn}} = \sum \Delta H_f \text{(products)} - \sum \Delta H_f \text{(reactants)}$ . - Exothermic: Energy is released ( $\Delta H$ is negative). Reaction feels hot. - Endothermic: Energy is absorbed ( $\Delta H$ is positive). Reaction feels cold.
Phase Changes: - Vaporization: Liquid to gas. - Condensation: Gas to liquid. - Fusion (Melting): Solid to liquid. - Solidification (Freezing): Liquid to solid. - Sublimation: Solid directly to gas. - Heat of Combustion: Energy released during the complete burning of one mole of a substance.

Practice Problems and Applications

Precipitation Stoichiometry: - Given $100.0\,\text{mL}$ of $0.200\,\text{M KOH}$ and $200.0\,\text{mL}$ of $0.150\,\text{M Fe}_2(SO_4)_3$ . - Eq: $6KOH(aq) + Fe_2(SO_4)_3(aq) \rightarrow 3K_2SO_4(aq) + 2Fe(OH)_3(s)$ . - Determine limiting reactant and calculate mass of $Fe(OH)_3$ .
Metabolic Gas Stoichiometry: - $C_6H_{12}O_6(aq) + 6O_2(g) \rightarrow 6CO_2(g) + 6H_2O(l)$ . - Calculate volume of $O_2$ at STP starting from $24.5\,\text{g}$ of glucose, and determine total number of oxygen atoms consumed.
Heat of Precipitation: - $Pb^{2+}(aq) + 2Cl^-(aq) \rightarrow PbCl_2(s)$ where $\Delta H = -359.4\,kJ$ . - Find $\Delta H$ for specific masses: $5.00\,g\,Pb^{2+}$ and $5.00\,g\,Cl^-$ .
Partial Pressure Example: - Total pressure $2.34\,\text{atm}$ , $P_{O_2} = 0.56\,\text{atm}$ , $P_{N_2} = 1.03\,\text{atm}$ . - $P_{H_2} = 2.34 - (0.56 + 1.03) = 0.75\,\text{atm}$ . This follows Dalton's Law.
Gas Diffusion/Effusion: - If a gas diffuses $2.5$ times faster than $NO$ (Molar Mass $\approx 30.01\,g/mol$ ), use Graham's Law to find the unknown molar mass: - $2.5 = \sqrt{\frac{30.01}{MM_{\text{unknown}}}}$ yield $MM_{\text{unknown}} = \frac{30.01}{6.25} \approx 4.80\,g/mol$ .