Stoichiometry and Reaction Fundamentals Vocabulary
Mole Concepts, Molar Mass, and Avogadro's Number
At the heart of quantitative chemistry lies the mole, the SI unit for amount of substance. Understanding AP Chemistry key concepts begins with the ability to interconvert between macroscopic mass and microscopic particle counts. Avogadro’s number ($6.022 \times 10^{23}$) serves as the proportionality constant that defines the number of constituent particles (atoms, molecules, or formula units) in one mole of a substance. When performing calculations, students must distinguish between the relative atomic mass found on the periodic table and the molar mass, which is the mass in grams of one mole of that substance ($g/mol$). In the context of the AP exam, precision in using these terms is vital for dimensional analysis. A common pitfall is confusing the mass of a single molecule (measured in atomic mass units) with the molar mass of a bulk sample. Mastery of the law of definite proportions is also essential here, as it dictates that a specific chemical compound always contains its component elements in a fixed ratio by mass, a principle that underpins empirical formula determination.
Limiting Reactants, Theoretical Yield, and Percent Yield
In practical laboratory scenarios and exam problems, reactants are rarely present in exact stoichiometric proportions. The limiting reactant is the reagent that is entirely consumed first, thereby dictating the maximum amount of product that can be generated. Identifying this species requires comparing the molar amounts of reactants available to the coefficients in the balanced chemical equation. The theoretical yield represents the calculated maximum mass of product based on the limiting reactant. However, real-world constraints—such as incomplete reactions or side reactions—often result in an actual yield that is lower. The percent yield is the ratio of actual yield to theoretical yield, expressed as a percentage. On the AP exam, students are frequently asked to explain why a percent yield might exceed 100%, which usually points to impurities or insufficient drying of a precipitate rather than a violation of the law of conservation of mass.
Solution Concentration Terms: Molarity, Molality, and Dilution
Stoichiometry vocabulary extends into the behavior of aqueous systems, where concentration governs reactivity. Molarity ($M$) is the primary unit of concentration used in the course, defined as moles of solute per liter of solution. It is crucial to remember that the denominator is the total volume of the solution, not just the solvent. While molality ($m$)—moles of solute per kilogram of solvent—is less frequent in the current AP framework, it remains relevant in specific colligative property discussions because it is independent of temperature. The process of dilution involves adding solvent to a concentrated stock solution to achieve a lower molarity. This relationship is mathematically expressed by the equation $M_1V_1 = M_2V_2$. In the lab portion of the exam, candidates must be familiar with the use of a volumetric flask to ensure precise concentration, as graduated cylinders do not provide the analytical accuracy required for standardized solution preparation.
Atomic Structure and Bonding Terminology
Quantum Numbers, Orbitals, and Electron Configuration Language
Modern atomic theory is described through the lens of quantum mechanics, where electrons occupy orbitals rather than fixed orbits. Each electron in an atom is described by a unique set of quantum numbers that define its energy level, shape, and orientation. The Aufbau principle dictates that electrons fill lower-energy subshells before moving to higher ones, while Hund’s rule states that electrons will occupy degenerate orbitals singly before pairing to minimize electron-electron repulsion. The Pauli exclusion principle further clarifies that no two electrons in the same atom can have identical quantum sets. When writing an electron configuration, students must be adept at using the noble gas notation to highlight valence electrons, which are the outermost electrons responsible for chemical reactivity. Understanding the difference between a ground state and an excited state configuration is essential for explaining atomic emission spectra and the movement of electrons between energy levels.
Periodic Trends: Electronegativity, Ionization Energy, Atomic Radius
Predicting the behavior of elements relies on an understanding of periodic trends, all of which are driven by effective nuclear charge ($Z_{eff}$). This concept refers to the net positive charge experienced by valence electrons after accounting for the shielding effect of core electrons. Atomic radius generally decreases across a period as $Z_{eff}$ increases, pulling electrons closer to the nucleus. Ionization energy is the energy required to remove an electron from a gaseous atom; it increases across a period because the stronger nuclear attraction makes electron removal more difficult. Electronegativity measures an atom's ability to attract shared electrons in a bond. On the AP exam, simply stating a trend is insufficient for full credit; students must use Coulomb’s Law ($F = k q_1 q_2 / r^2$) to justify why the force of attraction increases or decreases based on the distance between the nucleus and the valence shell.
Chemical bonds are categorized by the distribution of electrons between nuclei. Ionic bonding involves the electrostatic attraction between cations and anions, typically formed through the transfer of electrons between metals and nonmetals. Covalent bonding occurs when atoms share electron pairs to achieve a stable octet. If the sharing is unequal due to differences in electronegativity, the bond is polar covalent, resulting in a dipole moment. Metallic bonding is characterized by a "sea of delocalized electrons" surrounding positive metal cores, explaining properties like conductivity and malleability. Within covalent molecules, the VSEPR theory (Valence Shell Electron Pair Repulsion) predicts the geometric arrangement of atoms. Understanding formal charge is a critical scoring component in drawing Lewis structures, as the most stable structure is generally the one where formal charges are closest to zero and negative charges reside on the most electronegative atoms.
Thermochemistry and Thermodynamics Key Terms
System, Surroundings, State Functions, and Processes
Thermodynamics distinguishes between the system (the chemical reaction itself) and the surroundings (everything else, including the solvent and the container). A state function is a property whose value depends only on the current state of the system, not the path taken to reach that state; examples include enthalpy, entropy, and internal energy. In contrast, heat ($q$) and work ($w$) are path functions. The First Law of Thermodynamics states that the change in internal energy ($Delta U$) is equal to the sum of heat and work. In AP Chemistry, most processes occur at constant pressure, meaning the heat exchanged is equal to the change in enthalpy ($Delta H$). Understanding the boundary of the system is vital for calorimetry problems, where the heat absorbed by the water (surroundings) is equal in magnitude but opposite in sign to the heat released by the reaction (system).
Enthalpy (ΔH), Entropy (ΔS), and Gibbs Free Energy (ΔG)
These three quantities form the core of thermodynamics terms AP Chem students must master. Enthalpy ($Delta H$) measures the heat of a reaction; a negative value indicates an exothermic process, while a positive value indicates an endothermic one. Entropy ($Delta S$) measures the dispersal of energy or matter; reactions that increase the number of gas moles typically have a positive $Delta S$. Gibbs Free Energy ($Delta G$) is the ultimate arbiter of spontaneity (or thermodynamic favorability). The relationship is defined by the Gibbs-Helmholtz equation: $Delta G = Delta H - TDelta S$. For a process to be spontaneous, $Delta G$ must be negative. Students must be able to predict how temperature changes affect the sign of $Delta G$ based on the relative signs of $Delta H$ and $Delta S$, a concept frequently tested in the context of phase changes and chemical equilibria.
Endothermic vs. Exothermic, Spontaneous vs. Nonspontaneous
An endothermic process absorbs thermal energy from the surroundings, resulting in a positive $Delta H$ and a decrease in the temperature of the surroundings. Conversely, an exothermic process releases energy, yielding a negative $Delta H$. The concept of spontaneity (often referred to as being thermodynamically favored) describes a process that occurs without continuous external intervention. It is important to distinguish between thermodynamic favorability and the speed of a reaction; a reaction can be highly spontaneous ($Delta G ll 0$) but proceed at an imperceptible rate due to high kinetic barriers. This is known as being under kinetic control. When $Delta G = 0$, the system has reached equilibrium, and no further net change occurs. Mastery of these terms allows students to explain why certain reactions, like the combustion of hydrocarbons, are favored even if they require an initial spark to overcome the activation energy.
Kinetics: Describing Reaction Rates and Mechanisms
Rate Law, Rate Constant (k), Reaction Orders, and Half-Life
Chemical kinetics focuses on the speed of reactions and the pathways they follow. The rate law is an expression that relates the reaction rate to the molar concentrations of the reactants, typically formatted as $Rate = k[A]^m[B]^n$. The exponents ($m$ and $n$) are the reaction orders, which must be determined experimentally—they cannot be reliably predicted from the balanced equation's coefficients. The rate constant ($k$) is specific to a reaction at a given temperature; its units vary depending on the overall order of the reaction. For first-order reactions, the half-life ($t_{1/2}$) is constant and independent of the initial concentration, a principle used extensively in radioactive decay and certain pharmacological models. In the AP curriculum, students are expected to use integrated rate laws to determine the order of a reaction by identifying which plot (concentration, natural log of concentration, or reciprocal concentration vs. time) yields a linear relationship.
Activation Energy, Transition State, and Reaction Coordinate Diagrams
For a reaction to occur, reactant particles must collide with sufficient energy and correct orientation, a concept known as collision theory. The minimum energy required is the activation energy ($E_a$). At the peak of the energy barrier sits the transition state (or activated complex), a temporary, high-energy arrangement of atoms where old bonds are breaking and new ones are forming. A reaction coordinate diagram visualizes these energy changes over the course of the reaction. The difference in energy between the reactants and the transition state is the $E_a$, while the difference between reactants and products is the $Delta H$. Students must be able to identify these features on a graph and understand that the Arrhenius equation relates the rate constant $k$ to the temperature and $E_a$, showing that as temperature increases, a larger fraction of molecules possess the kinetic energy necessary to surpass the activation barrier.
Most chemical reactions occur through a series of elementary steps known collectively as the reaction mechanism. The slowest step in this sequence is the rate-determining step, which governs the overall rate law. A reaction intermediate is a species produced in one step and consumed in a subsequent one; it does not appear in the overall balanced equation. In contrast, a catalyst is a substance that increases the reaction rate by providing an alternative pathway with a lower activation energy. Unlike intermediates, catalysts are present at the start of the reaction and regenerated at the end. In kinetics vocabulary, distinguishing between these two is vital. On the exam, a common task is to propose a mechanism that is consistent with an experimentally determined rate law, requiring a deep understanding of how molecularity (unimolecular, bimolecular) in elementary steps translates to the exponents in the rate expression.
Equilibrium and Solution Chemistry Definitions
Dynamic Equilibrium, Equilibrium Constant (K), and Reaction Quotient (Q)
Dynamic equilibrium occurs in a reversible reaction when the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products. The equilibrium constant ($K$) is the ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients (the law of mass action). Only aqueous and gaseous species are included in this expression; pure solids and liquids are omitted. The reaction quotient ($Q$) uses the same mathematical form as $K$ but is calculated using initial or non-equilibrium concentrations. By comparing $Q$ to $K$, one can predict the direction in which the reaction will shift to reach equilibrium: if $Q < K$, the reaction proceeds forward; if $Q > K$, it shifts toward the reactants. This quantitative comparison is a cornerstone of AP Chemistry problem-solving in Unit 7.
Le Chatelier's Principle and Common Ion Effect
Le Chatelier's Principle states that if a system at equilibrium is subjected to a stress (change in concentration, pressure, or temperature), the system will shift its equilibrium position to counteract the stress. For example, increasing the temperature of an exothermic reaction will shift the equilibrium toward the reactants, decreasing the value of $K$. It is critical to note that only temperature changes can alter the value of $K$; changes in concentration or pressure merely change the position of the equilibrium. The common ion effect is a specific application of this principle, where the addition of an ion already present in a solution decreases the solubility of an ionic compound. This concept is frequently tested in the context of precipitation reactions and buffer systems, where the presence of a shared ion suppresses the ionization of a weak acid or base.
Solubility Product (Ksp), Common Ion Effect, and Complex Ions
For sparingly soluble salts, the solubility product constant ($K_{sp}$) represents the equilibrium between the solid compound and its dissolved ions in a saturated solution. A higher $K_{sp}$ generally indicates greater solubility, though comparisons can only be made directly between salts with the same cation-to-anion ratio. Molar solubility is the number of moles of the salt that can dissolve in one liter of solution before precipitation occurs. The formation of complex ions—where a central metal ion bonds to surrounding molecules or ions called ligands—can significantly increase the solubility of an otherwise insoluble salt. For instance, adding ammonia to silver chloride forms the $[Ag(NH_3)_2]^+$ complex, shifting the solubility equilibrium to the right. Understanding these interactions requires a synthesis of equilibrium, bonding, and Lewis acid-base theory.
Acid-Base Chemistry and Buffers Vocabulary
Strong vs. Weak Acids/Bases, Conjugate Acid-Base Pairs
In the Brønsted-Lowry framework, an acid is a proton ($H^+$) donor and a base is a proton acceptor. A strong acid or base ionizes completely in aqueous solution, whereas a weak acid or base exists in equilibrium with its non-ionized form. This distinction is a matter of the extent of ionization, not the concentration. Every acid has a conjugate base, the species remaining after the proton is donated, and every base has a conjugate acid. The strength of an acid is inversely proportional to the strength of its conjugate base; the conjugate of a strong acid like $HCl$ is a negligible base ($Cl^-$). Amphiprotic substances, such as water or $HCO_3^-$, can act as either an acid or a base depending on the reaction environment. On the AP exam, identifying these pairs is the first step in solving titration or buffer problems.
pH, pOH, Ka, Kb, pKa, and the Autoionization of Water (Kw)
Quantitative acid-Base chemistry relies on logarithmic scales to manage the wide range of hydronium ($H_3O^+$) and hydroxide ($OH^-$) concentrations. pH is defined as $-log[H_3O^+]$, and pOH as $-log[OH^-]$. The autoionization of water is the process where water reacts with itself to form ions, governed by the constant $K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$ at $25^circ C$. Consequently, $pH + pOH = 14$. For weak acids, the acid dissociation constant ($K_a$) measures the strength of the acid; the smaller the $K_a$, the weaker the acid and the higher its pKa. Students must be comfortable using the relationship $K_w = K_a imes K_b$ for conjugate pairs to interconvert between acid and base strengths. In FRQ responses, providing the mathematical definition of these terms often serves as the foundation for justifying the pH of a solution.
Buffer Solutions, Buffer Capacity, and Henderson-Hasselbalch Equation
A buffer solution consists of a weak acid and its conjugate base (or a weak base and its conjugate acid) in significant concentrations. Buffers resist changes in pH when small amounts of strong acid or base are added. This resistance is quantified as buffer capacity, which depends on the absolute concentrations of the buffer components. The pH of a buffer is calculated using the Henderson-Hasselbalch equation: $pH = pK_a + log([A^-]/[HA])$. When the concentrations of the acid and conjugate base are equal, $pH = pK_a$, a condition known as the half-equivalence point in a titration. Understanding this relationship is essential for selecting an appropriate indicator for a titration or for designing a buffer that maintains a specific pH. The AP exam frequently tests the ability to explain, at the particulate level, how a buffer neutralizes added $H^+$ or $OH^-$ ions.
Electrochemistry and Redox Reaction Language
Oxidation, Reduction, Oxidizing/Reducing Agents, and Half-Reactions
Electrochemistry definitions center on the transfer of electrons. Oxidation is the loss of electrons, resulting in an increase in oxidation number, while reduction is the gain of electrons, resulting in a decrease in oxidation number. The mnemonic "OIL RIG" (Oxidation Is Loss, Reduction Is Gain) is a standard tool for students. An oxidizing agent is the species that undergoes reduction, thereby causing another species to be oxidized. Conversely, the reducing agent is oxidized. To balance complex redox reactions, especially in acidic or basic solutions, the process is broken down into two half-reactions—one for oxidation and one for reduction. This method ensures that both mass and charge are conserved, a requirement that is strictly enforced in the scoring of free-response questions involving electrochemical equations.
Galvanic vs. Electrolytic Cells: Anode, Cathode, Salt Bridge
Electrochemical cells are divided into two types based on the spontaneity of the reaction. A galvanic (voltaic) cell uses a spontaneous redox reaction to generate electrical energy, whereas an electrolytic cell requires an external power source to drive a non-spontaneous reaction. In both cells, oxidation occurs at the anode and reduction occurs at the cathode ("An Ox, Red Cat"). In a galvanic cell, a salt bridge is necessary to maintain electrical neutrality by allowing ions to migrate between the half-cells, preventing the buildup of charge that would stop the reaction. Electrons always flow through the external wire from the anode to the cathode. On the AP exam, students are often asked to predict the movement of specific ions in the salt bridge or the change in mass of the electrodes as the cell operates.
Standard Reduction Potentials, Cell Potential (E°cell), and Faraday's Constant
The driving force of an electrochemical cell is the cell potential ($E_{cell}$), measured in volts. The standard cell potential ($E^circ_{cell}$) is calculated using standard reduction potentials found in a reference table: $E^circ_{cell} = E^circ_{cathode} - E^circ_{anode}$. A positive $E^circ_{cell}$ indicates a spontaneous reaction, which correlates to a negative $Delta G^circ$ through the equation $Delta G^circ = -nFE^circ_{cell}$. Here, $n$ is the number of moles of electrons transferred, and $F$ is Faraday’s constant (approximately $96,485 , C/mol, e^-$). This relationship bridges thermodynamics and electrochemistry. For non-standard conditions, the Nernst equation is used to determine how changes in concentration or pressure affect the cell potential. Mastery of these formulas and the underlying vocabulary is indispensable for calculating the amount of product formed during electrolysis or the voltage of a battery.