Michael Farabaugh 2026 AP Chemistry Practice Exam Notes

Gas Properties and Particle Representations

• Partial Pressure and Particle Diagrams: In a gas mixture, the partial pressure of a specific gas is proportional to its mole fraction in the mixture. For a mixture of $Ar(g)$ and $O_2(g)$, if the total pressure is $3.0\,atm$ and the particle diagram shows 4 atoms of $Ar$ and 2 molecules of $O_2$ (total 6 particles), the partial pressure of $O_2$ is calculated as:     * $P_{O_2} = X_{O_2} \times P_{total} = \left( \frac{2}{6} \right) \times 3.0\,atm = 1.0\,atm$.     * Assumptions for gas problems (unless specified): $T = 298\,K$ and $P = 1.0\,atm$.

• Dalton’s Law in Rigid Containers: When an inert gas like $Ne(g)$ is added to a rigid container containing a mixture of gases (e.g., $CO(g)$ and $CO_2(g)$) at constant temperature:     * The partial pressures of the original gases remain constant because their moles, the volume of the container, and the temperature remain unchanged ($P = \frac{nRT}{V}$).     * The total pressure of the gas mixture increases due to the addition of the new gas particles ($P_{total} = P_{CO} + P_{CO_2} + P_{Ne}$).

• Ideal Gas Deviations: Real gases deviate most from ideal behavior under conditions of high pressure and low temperature. The likelihood of deviation increases with:     * Stronger Intermolecular Forces (IMFs): Larger, more polarizable electron clouds lead to stronger London dispersion forces.     * Significant Particle Volume: Larger molecules take up more space relative to the container volume.     * Example comparison: Among $H_2$, $O_2$, $CH_4$, and $CF_4$, the gas $CF_4$ is most likely to deviate due to its large size and polarizability.

• Maxwell-Boltzmann Distribution: The distribution of particle speeds is affected by temperature and molar mass:     * As temperature increases, the peak of the curve shifts to the right (higher average speed) and becomes flatter.     * At a constant temperature, lighter gas particles (lower molar mass) have a wider distribution and higher average speeds compared to heavier gas particles.     * Example: For curves at $300\,K$, $Ne(g)$ ($20.18\,g/mol$) would have a curve further to the right than $Ar(g)$ ($39.95\,g/mol$).

Kinetics and Reaction Rates

• Factors Affecting Reaction Rates: The rate of reaction between $CaCO_3(s)$ and $HCl(aq)$ is influenced by:     * Concentration: Increasing the concentration of $HCl(aq)$ increases collision frequency.     * Surface Area: Changing a single chunk of $CaCO_3$ to a fine powder increases the number of particles available for collision.     * Temperature: Higher temperature increases both collision frequency and the fraction of collisions with energy exceeding the activation energy ($E_a$).     * Stirring: Increases the rate of transport of reactants to the surface of the solid.     * Data comparison: Trial 1 ($342\,s$) and Trial 2 ($114\,s$). Trial 2 is three times faster, which could be explained by a higher concentration of $HCl$ in Trial 2.

• Rate Law and Orders of Reaction:     * Second-Order Reaction: For the decomposition $2\,NO_2(g) \rightarrow 2\,NO(g) + O_2(g)$, if the reaction is second order with respect to $NO_2$, the rate law is $\text{rate} = k[NO_2]^2$.     * Initial Rate Calculation: If the concentration of $NO_2$ triples (from $0.020\,M$ to $0.060\,M$), the initial rate of formation of $O_2(g)$ increases by a factor of $3^2 = 9$. For Trial 1 ($3.0 \times 10^{-4}\,M\,s^{-1}$), the Trial 2 rate is $9 \times (3.0 \times 10^{-4}) = 2.7 \times 10^{-3}\,M\,s^{-1}$.

• Kinetics Graphs and Half-Life:     * For the decomposition of $H_2O_2(aq)$, a constant half-life observed on a concentration vs. time graph indicates a first-order reaction.     * First-order integrated rate law: $\ln[A]_t = -kt + \ln[A]_0$.

• Reaction Mechanisms and Energy Profiles:     * The rate-determining step (RDS) is the slowest step in a mechanism and corresponds to the highest activation energy peak on an energy profile.     * Endothermic vs. Exothermic: If the potential energy of the products is lower than the reactants, the overall reaction is exothermic (\Delta H < 0).

Chemical Bonding and Molecular Geometry

• VSEPR Theory:     * T-shaped Geometry: Occurs in molecules with a central atom having five electron domains (trigonal bipyramidal electron geometry) with three bonding pairs and two lone pairs ($AX_3E_2$).

• Coulombic Attractions and Lattice Enthalpy:     * Lattice enthalpy ($\Delta H_{lattice}$) is the energy required to separate a solid crystal into gaseous ions (e.g., $NaCl(s) \rightarrow Na^+(g) + Cl^-(g)$).     * It depends on Coulomb’s Law: $F = k \frac{Q_1Q_2}{r^2}$.     * Attractions are strongest when ionic charges ($Q$) are high and ionic radii ($r$) are small.     * Comparison: $NaF$ has stronger attractions than $NaBr$ because $F^-$ has a smaller radius than $Br^-$. $MgF_2$ has stronger attractions than $NaF$ because $Mg^{2+}$ has a higher charge than $Na^+$ and a smaller radius.

• Bond Energy and Potential Energy Curves:     * The bond energy of a diatomic molecule is represented by the depth of the well (minimum potential energy) on a potential energy vs. internuclear distance graph. In the provided graph, this magnitude is approximately $275\,kJ/mol$.

• Resonance and Bond Order:     * When a molecule (like $NO_2^-$) has resonance structures, the actual bonds are an average of the structures. If there is one single bond and one double bond in two resonance structures, the bond order for both bonds is $1.5$.

• Formal Charge in Lewis Structures:     * The preferred Lewis structure is the one where formal charges are closest to zero and any negative formal charge resides on the most electronegative atom.     * Example for $SCN^-$: A structure placing a $-1$ formal charge on $N$ (electronegativity $3.0$) is generally preferred over structures placing it on $S$ or having higher magnitude charges.

Periodic Trends and Spectroscopy

• Atomic and Ionic Radii:     * Radii decrease across a period (due to increased effective nuclear charge, $Z_{eff}$) and increase down a group (due to additional electron shells).     * Anions are larger than their parent atoms (e.g., S < S^{2-}) due to increased electron-electron repulsion.     * Cations are smaller than their parent atoms (e.g., Mg^{2+} < Mg).     * Specific sequence example: Cl < S < S^{2-}.

• Photoelectron Spectroscopy (PES):     * PES peaks represent the binding energy of electrons in specific subshells. The peak with the highest binding energy corresponds to the electrons closest to the nucleus (e.g., the $1s$ orbital).     * Reason: electrons in the $1s$ orbital experience the strongest Coulombic attraction toward the nucleus.

• Mass Spectrometry:     * Mass spectra show the relative abundance of isotopes. For Rubidium ($Rb$), which has isotopes $^{85}Rb$ and $^{87}Rb$, a percent abundance of $72\%$ for $^{85}Rb$ results in a peak at mass 85 that is significantly taller than the peak at mass 87.

• Ionization Energy:     * First Ionization Energy generally increases up a group and to the right across a period. $Sr$ has a higher ionization energy than $Rb$ or $Ba$ due to its position in the periodic table ($Z_{eff}$ and shell number).

Thermodynamics and Thermochemistry

• Calorimetry Equations:     * Heat absorbed/released: $q = m \times c \times \Delta T$.     * Specific heat of water: $4.18\,J/(g \cdot ^\circ C)$.     * Enthalpy of reaction (per mole): $\Delta H = \frac{q}{n}$.     * Example calculation for metal: If $40.0\,g$ of metal at $100.0^\circ C$ is placed in $90.0\,g$ of water at $20.0^\circ C$, and the final temperature reaches $22.0^\circ C$:         * $q_{water} = 90.0\,g \times 4.18\,J/(g \cdot ^\circ C) \times 2.0^\circ C = 752.4\,J$.         * $c_{metal} = \frac{q_{metal}}{m \times \Delta T} = \frac{752.4\,J}{40.0\,g \times (100.0 - 22.0)^\circ C} \approx 0.24\,J/(g \cdot ^\circ C)$.

• Standard Enthalpy of Formation ($\Delta H_f^\circ$):     * $\Delta H_{rxn}^∘ = \sum \Delta H_f^∘(\text{products}) - \sum \Delta H_f^∘(\text{reactants})$.     * For $CCl_4(g) + 4\,HF(g) \rightarrow CF_4(g) + 4\,HCl(g)$ with $\Delta H^∘ = -106\,kJ/mol_{rxn}$:         * $-106 = [(-933) + 4(-92)] - [\Delta H_f^∘(CCl_4) + 4(-273)]$         * $-106 = [-1301] - [\Delta H_f^∘(CCl_4) - 1092]$         * $\Delta H_f^∘(CCl_4) = -103\,kJ/mol$.

• Entropy ($\Delta S^∘$):     * $\Delta S^∘$ is positive when disorder increases (e.g., solid to gas, or increase in the number of gas moles).     * $\Delta S^∘$ is closest to zero when the number of moles of gas is identical on both sides of the equation (e.g., $CH_4(g) + 2\,O_2(g) \rightarrow CO_2(g) + 2\,H_2O(g)$).

• Gibbs Free Energy and Favorability:     * $\Delta G^∘ = \Delta H^∘ - T\Delta S^∘$.     * A reaction is thermodynamically favorable if \Delta G^∘ < 0.     * The relationship between $\Delta G^∘$ and the equilibrium constant $K$ is $\Delta G^∘ = -RT \ln(K)$. Large $K$ values (e.g., $1.8 \times 10^{17}$) indicate a positive $E^∘$ and a negative $\Delta G^∘$.

Intermolecular Forces and States of Matter

• Boiling Point Determinants:     * Driven by IMFs: Hydrogen bonding > Dipole-Dipole > London Dispersion (for similar sizes).     * Polarizability: Larger atoms/molecules with larger electron clouds are more polarizable, leading to stronger dispersion forces. Example: $CH_3I$ (BP $316\,K$) vs. $CH_3Cl$ (BP $195\,K$) because iodine has a larger electron cloud.     * Ion-Dipole Forces: Present in aqueous ionic solutions (e.g., $KCl(aq)$). Water molecules orient their partial positive charges (H) towards anions ($Cl^-$) and partial negative charges (O) towards cations ($K^+$).

• Column Chromatography:     * Separation is based on the differential attraction to the stationary phase vs. the mobile phase (solvent).     * In a polar stationary phase with a nonpolar solvent: Nonpolar molecules (e.g., benzene) will travel faster as they are more attracted to the mobile phase. Polar molecules (e.g., phenol) move slower as they are more attracted to the stationary phase.

Chemical Equilibrium and Solubility

• Equilibrium Expressions:     * For $CH_3NH_2(aq) + H_2O(l) \rightleftharpoons CH_3NH_3^+(aq) + OH^-(aq)$, the base dissociation constant expression is $K_b = \frac{[CH_3NH_3^+][OH^-]}{[CH_3NH_2]}$. Pure liquids like $H_2O$ are omitted.

• Le Chatelier’s Principle:     * For the exothermic reaction $CO(g) + 2\,H_2(g) \rightleftharpoons CH_3OH(g)$, increasing temperature shifts the equilibrium to the left, increasing the moles of $CO$ and decreasing the value of $K_p$.

• Reaction Quotient ($Q$):     * Calculated using initial partial pressures: $Q_p = \frac{(P_{SO_2})^2(P_{O_2})}{(P_{SO_3})^2}$.     * If Q_p > K_p, the reaction shifts left (toward reactants), decreasing the pressure of products (like $O_2$).

• Solubility and Concentration:     * In a saturated solution of a salt like $CaSO_4$, the concentration ($[Ca^{2+}]$) is determined by the solubility product $K_{sp}$ and is independent of the total volume of the solution. However, the total number of moles of dissolved ions increases proportionally with the solvent volume.

Acid-Base Chemistry and Titrations

• Acid-Base Definitions:     * Brønsted-Lowry Base: Proton ($H^+$) acceptor (e.g., $NH_2OH$ in water).     * Brønsted-Lowry Acid: Proton donor.

• Titrations of Weak Acids:     * Equivalence Point: Point where moles of acid equal moles of base. In a titration of $HC_3H_5O_2$ with $NaOH$, the equivalence point occurs when the pH is greater than 7.     * Half-Equivalence Point: Point where half the acid is neutralized. At this point, $pH = pK_a$. Based on the titration curve for propanoic acid, $pK_a \approx 5$.     * Calculation of Concentration: $\text{Molarity}<em>{acid} \times \text{Volume}</em>{acid} = \text{Molarity}<em>{base} \times \text{Volume}</em>{base}$.

• Buffer Solutions:     * A buffer consists of a weak acid and its conjugate base. Buffer capacity is the ability of the buffer to resist pH change and is higher when the concentrations of the buffer components are higher.     * Example: Buffer Y ($1.0\,M$ HF/NaF) has a higher capacity than Buffer X ($0.10\,M$ HF/NaF). Adding $0.050\,mol$ $NaOH$ to Buffer X causes a larger pH increase than in Buffer Y.

Stoichiometry and Yield

• Limiting Reactants:     * Example reaction: $4\,Cr(s) + 3\,O_2(g) \rightarrow 2\,Cr_2O_3(s)$.     * Given $52\,g$ Cr ($1.0\,mol$) and $32\,g$ $O_2$ ($1.0\,mol$).     * Moles of Cr needed for $1\,mol$ $O_2$ is $4/3 = 1.33\,mol$. Since only $1.0\,mol$ Cr is available, Cr is the limiting reactant.     * Maximum product yield: $1.0\,mol\,Cr \times \left( \frac{2\,mol\,Cr_2O_3}{4\,mol\,Cr} \right) \times 152\,g/mol = 76\,g\,Cr_2O_3$.

• Gravimetric Analysis Errors:     * If a precipitate ($BaSO_4$) is not dried completely, the measured mass will be too high, leading to an overestimation of the concentration of the original salt ($K_2SO_4$).     * If some precipitate is lost (e.g., through a hole in the filter paper), the calculated concentration will be lower than the actual value.

Questions & Discussion

• Question 2: Why did Trial 2 take less time than Trial 1?     * Response: Trial 2 was faster because the concentration of hydrochloric acid was higher, leading to more frequent successful collisions.

• Question 11: What question is answered by calculating thermal energy in a coffee cup calorimeter for the reaction $MgO(s) + 2H^+(aq) \rightarrow Mg^{2+}(aq) + H_2O(l)$?     * Response: The experiment determines the $\Delta H$ for the specific reaction between magnesium oxide and hydrochloric acid.

• Question 18: How does temperature affect thermodynamic favorability given $\Delta H^∘ = +30\,kJ/mol_{rxn}$ and \Delta S^∘ > 0     * Response: Since the reaction is endothermic (\Delta H^∘ > 0), only the positive entropy change ($\Delta S^∘$) contributes to making the reaction favorable, typically at higher temperatures where the $T\Delta S$ term outweighs the $\Delta H$ term.

• Question 45: Comparison of final pH in Buffer X versus Buffer Y after adding base.     * Response: The final pH of Buffer X will be higher than Buffer Y. Because Buffer X has a smaller buffer capacity, the same amount of base neutralized a larger percentage of the weak acid, causing a more significant pH shift.