11.4 Preparing for the MCAT: General Chemistry

The following presents the general chemistry content you are likely to see on Test Day. The High-Yield badges point out the topics that are tested most frequently.

Atomic Structure

A proton has a positive charge and a mass of around 1 amu; a neutron has no charge and a mass of around 1 amu; an electron has a negative charge and negligible mass. The nucleus contains the protons and neutrons, while the electrons move around the nucleus. The atomic number is the number of protons in a given element, while the mass number is the sum of an element’s protons and neutrons.

Atomic mass is essentially equal to the mass number, which is the sum of an element’s protons and neutrons. Atomic mass varies due to isotopes. Isotopes are atoms of a given element (elements with the same atomic number) that have different mass numbers. They differ in the number of neutrons. Most isotopes are identified by the element followed by the mass number (such as carbon-12, carbon-13, and carbon-14). Atomic weight is the weighted average of the naturally occurring isotopes of an element. The periodic table lists atomic weights, not atomic masses.

In the Bohr model of the atom, a dense, positively charged nucleus is surrounded by electrons revolving around the nucleus in orbits with distinct energy levels. The energy difference between energy levels is called a quantum, first described by Planck.

Figure 11.1. Atomic Emission of a Photon as a Result of a Ground-State Transition

Quantization means that there is not an infinite range of energy levels available to an electron; electrons can exist only at certain energy levels. The energy of an electron increases the farther it is from the nucleus. The atomic absorption spectrum of an element is unique. For an electron to jump from a lower energy level to a higher one, it must absorb an amount of energy precisely equal to the energy difference between the two levels. When electrons return from the excited state to the ground state, they emit an amount of energy that is exactly equal to the energy difference between the two levels. Every element has a characteristic atomic emission spectrum (see Figure 11.1). Sometimes the electromagnetic energy emitted corresponds to a frequency in the visible light range.

The quantum mechanical model posits that electrons are localized in orbitals and do not travel in definite orbits; an orbital is a region of space around the nucleus defined by the probability of finding an electron in that region of space. The Heisenberg uncertainty principle says it is impossible to know both an electron’s position and its momentum exactly at the same time. The principal quantum number, n, is one of four quantum numbers. It describes the average energy of a shell; as n increases, the average distance between the electron and the nucleus increases as does the potential energy of the electron.

Electrons fill from lower- to higher-energy subshells, according to the Aufbau principle. Each subshell fills completely before electrons begin to enter the next one. Electrons fill orbitals according to Hund’s rule: subshells with multiple orbitals fill electrons so that every orbital in a subshell gets one electron before any orbital gets a second.

Valence electrons are those in the outermost shell available for interaction (bonding) with other atoms. Many atoms form bonds that complete an octet in the valence shell.

The Periodic Table

The periodic table of the elements organizes the elements according to their atomic numbers. It reveals a pattern of similar chemical and physical properties among elements. Rows are called periods and are based on the same principal energy level, n, while columns are called groups. Elements in the same group have the same valence shell electron configuration.

The elements on the periodic table (see Figure 11.2) belong to one of three types.

Metals are shiny (lustrous), conduct electricity well, and both malleable and ductile. Metals are found on the left side and the middle of the periodic table.

Nonmetals are dull, poor conductors of electricity, and brittle. Nonmetals are found on right side of the periodic table.

Metalloids possess characteristics of both metals and nonmetals. They are found in a stair-step pattern starting with boron (B).

Key Concept

Effective nuclear charge (Zeff) is the net positive charge experienced by electrons in the valence shell; it forms the foundation for all periodic trends. Zeff increases from left to right across a period, with little change in value from top to bottom in a group. Valence electrons become increasingly separated from the nucleus as the principal energy level, n, increases from top to bottom in a group.

Atomic radius is the distance between the center of the nucleus and the outermost electron. Ionic radius is the size of a charged species. Cations (positive charge) are generally smaller than their corresponding neutral atom; anions (negative charge) are generally larger than their corresponding neutral atom. Ionization energy is the amount of energy necessary to remove an electron from the valence shell of a gaseous species. Electron affinity is the amount of energy released when a gaseous species gains an electron in its valence shell. Electronegativity is a measure of the attractive force of the nucleus for electrons within a bond. (See Figure 11.2.)

Figure 11.2. The Periodic Table of the Elements

Alkali metals typically take on an oxidation state of +1 and prefer to lose an electron to achieve a noble gas configuration (an octet). Both alkali metals and the alkaline earth metals are the most reactive of all metals. Alkaline earth metals take on an oxidation state of +2 and can lose two electrons to achieve noble gas configurations. Transition metals are unique because they take on multiple oxidation states.

Chalcogens take on oxidation states of −2 or +6 (depending on whether they are nonmetals or metals, respectively) in order to achieve a noble gas configuration. Halogens take on an oxidation state of −1 and prefer to gain an electron to achieve noble gas configurations; these nonmetals have the highest electronegativities. Noble gases have a fully filled valence shell in their standard state and prefer not to give up or take on additional electrons. Noble gases have very high ionization energies and virtually nonexistent electronegativities and electron affinities.

Bonding and Chemical Interactions

Elements form bonds to attain a noble gas electron configuration (an octet), and these bonds are either ionic or covalent. The octet rule states that elements are most stable with eight valence electrons. There are, however, a few exceptions. Some elements with an incomplete octet are stable (H, He, Li, Be, and B). Elements with an expanded octet are stable with more than eight electrons (all elements in Period 3 or greater). Compounds with an odd number of electrons cannot have eight electrons on each element.

An ionic bond is formed via the transfer of one or more electrons from an element with a relatively low ionization energy to an element with a relatively high electron affinity—usually between metals and nonmetals. The resulting electrostatic attraction between the ions causes them to remain in close proximity, forming the ionic bond and often crystalline lattices—large, organized arrays of ions. Ionic compounds have unique physical and chemical properties such as high melting points and the tendency to dissociate in polar solvents.

A covalent bond is formed via the sharing of electrons between two elements of similar electronegativities. Bond order refers to whether a covalent bond is a single bond, double bond, or triple bond. As bond order increases, bond strength increases, bond energy increases, and bond length decreases.

Covalent bonds can be categorized as either nonpolar or polar based on the nature of the elements involved. Nonpolar bonds result in molecules in which both atoms have exactly the same electronegativity. Some bonds are considered nonpolar when there is a very small difference in electronegativity between the atoms, even though they are technically slightly polar. Polar bonds form when there is a significant difference in electronegativities but not enough to transfer electrons and form an ionic bond. In a polar bond, the more electronegative element takes on a partial negative charge and the less electronegative element takes on a partial positive charge. Coordinate covalent bonds result when a single atom provides both bonding electrons while the other atom does not contribute any; coordinate covalent bonds are most often found in Lewis acid-base chemistry.

Lewis dot symbols are a chemical representation of an atom’s valence electrons; they require a balance of valence, bonding, and nonbonding electrons in a molecule or ion. Formal charges exist when an atom is surrounded by either more or fewer valence electrons than it has in its neutral state (assuming equal sharing of electrons in a bond). For any molecule with a π (pi) system of electrons, resonance structures exist. These represent all of the possible configurations of electrons—stable and unstable—that contribute to the overall structure.

The valence shell electron pair repulsion (VSEPR) theory predicts the three-dimensional molecular geometry of covalently bonded molecules. In this theory, electrons—whether bonding or nonbonding—arrange themselves to be as far apart as possible from each other in three-dimensional space, leading to characteristic geometries. Nonbonding electrons exert more repulsion than bonding electrons because nonbonding electrons reside closer to the nucleus. Electronic geometry refers to the position of all electrons in a molecule, whether bonding or nonbonding. Molecular geometry refers to the position of only the bonding pairs of electrons in a molecule.

The polarity of molecules depends on the dipole moment of each bond and the sum of the dipole moments in a molecular structure. All polar molecules contain polar bonds. However, nonpolar molecules may contain nonpolar bonds or may contain polar bonds with dipole moments that cancel each other. σ and π bonds describe the patterns of overlap observed when molecular bonds are formed. Sigma (σ) bonds are the result of head-to-head overlap, while pi (π) bonds are the result of the overlap of two parallel electron cloud densities.

Intermolecular forces are electrostatic attractions between molecules. They are significantly weaker than covalent bonds (which are weaker than ionic bonds). London dispersion forces are the weakest interactions but are present in all atoms and molecules. As the size of the atom or structure increases, so does the corresponding London dispersion force. Dipole–dipole interactions, which occur between the oppositely charged ends of polar molecules, are stronger than London dispersion forces. These interactions are evident in the solid and liquid phases but negligible in the gas phase due to the distance between particles. Hydrogen bonds are a specialized subset of dipole–dipole interactions involved in intra- and intermolecular attraction. Hydrogen bonding occurs when H is bonded to one of three very electronegative atoms—F, O, or N.

Compounds and Stoichiometry

Compounds are substances composed of two or more elements in a fixed proportion. Molecular weight is the mass (in amu) of the constituent atoms in a compound as indicated by the molecular formula. Molar mass is the mass of 1 mole (Avogadro’s number or 6.022 × 1023 particles) of a compound, usually measured in grams per mole.

Gram equivalent weight is a measure of the mass of a substance that can donate one equivalent of the species of interest. Normality is the ratio of equivalents per liter; normality is molarity multiplied by the number of equivalents present per mole of compound. Equivalents are moles of the species of interest, most often seen in acid-base chemistry (hydrogen ions or hydroxide ions) and oxidation-reduction reactions (moles of electrons).

The law of constant composition states that any pure sample of a compound contains the same elements in the same mass ratio. The empirical formula is the smallest whole-number ratio of the elements in a compound. The molecular formula is either the same as or a multiple of the empirical formula; it gives the exact number of atoms of each element in a compound. To calculate percent composition by mass, determine the mass of the individual element and divide by the molar mass of the compound.

Combination reactions occur when two or more reactants combine to form one product. Decomposition reactions occur when one reactant is chemically broken down into two or more products. Combustion reactions occur when a fuel and an oxidant (typically oxygen) react, forming the products water and carbon dioxide (if the fuel is a hydrocarbon). Neutralization reactions are those in which an acid reacts with a base to form a salt and, usually, water.

Displacement reactions occur when one or more atoms or ions of one compound are replaced with one or more atoms or ions of another compound. Single-displacement reactions occur when an ion of one compound is replaced with another element. Double-displacement reactions occur when elements from two different compounds trade places with each other to form two new compounds.

Chemical equations must be balanced to perform stoichiometric calculations. Balanced equations are determined using the following steps in order:

Balance the least common atoms.

Balance the more common atoms.

Balance the charge, if necessary.

Balanced equations can be used to determine the limiting reagent, which is the reactant that is consumed first in a chemical reaction. The other reactants present are termed excess reagents. The theoretical yield is the amount of product generated if all of the limiting reactant is consumed with no side reactions. However, the actual yield is typically lower than theoretical yield. Percent yield is the actual yield divided by the theoretical yield, which is then converted to a percentage.

Ionic charges are predictable by group number and type of element (metal or nonmetal) for representative elements. However, they are generally unpredictable for nonrepresentative elements. Metals form positively charged cations based on group number, while nonmetals form negatively charged anions based on the number of electrons needed to achieve an octet. Electrolytes contain equivalents of ions from molecules that dissociate in solution. The strength of an electrolyte depends on its degree of dissociation or solvation.

Chemical Kinetics

Chemical mechanisms propose a series of steps that make up the overall reaction. Intermediates are molecules that exist within the course of a reaction but are neither reactants nor products overall. The slowest step, also known as the rate-determining step, limits the maximum rate at which the reaction can proceed.

The collision theory states that a reaction rate is proportional to the number of effective collisions between the reacting molecules. For a collision to be effective, molecules must be in the proper orientation and have sufficient kinetic energy to exceed the activation energy. The Arrhenius equation is a mathematical way of representing collision theory.

The transition state theory states that molecules form a transition state or an activated complex during a reaction in which the old bonds are partially dissociated and the new bonds are partially formed. From the transition state, the reaction can proceed toward products or revert back to reactants. The transition state is the highest point on a free-energy reaction diagram.

Figure 11.3. Reaction Diagram for a Catalyzed and an Uncatalyzed Reaction

Key Concept

Reaction rates can be affected by a number of factors. Increasing the concentration of reactant increases the reaction rate (except for zero-order reactions) because there are more effective collisions per time. Increasing the temperature increases the reaction rate because the particles’ kinetic energy is increased. Changing the medium can increase or decrease reaction rate, depending on how the reactants interact with the medium. Adding a catalyst increases the reaction rate because it lowers the activation energy (see Figure 11.3).

Reaction rates are measured in terms of the rate of reactant disappearance or product appearance. Rate laws take the form of rate = k[A]x[B]y and must be determined from experimental data. The rate orders usually do not match the stoichiometric coefficients. The rate order of a reaction is the sum of all individual rate orders in the rate law. Zero-order reactions have a constant rate that does not depend on the concentration of reactant; their rates can be affected only by changing the temperature or by adding a catalyst. A concentration vs. time curve of a zero-order reaction is a straight line; the slope of such a line is equal to –k.

First-order reactions have a nonconstant rate that depends on the concentration of reactant. A concentration vs. time curve of a first-order reaction is nonlinear, and the slope of a ln [A] vs. time plot is –k for a first-order reaction. Second-order reactions have a nonconstant rate that depends on the concentration of reactant. A concentration vs. time curve of a second-order reaction is nonlinear, and the slope of a

vs. time plot is k for a second-order reaction.

Equilibrium

Reversible reactions eventually reach a state in which energy is minimized and entropy is maximized. Chemical equilibria are dynamic—the reactions are still occurring, just at a constant rate. In equilibrium, the concentrations of reactants and products remain constant because the rate of the forward reaction equals the rate of the reverse reaction.

The law of mass action gives the expression for the equilibrium constant, Keq. The reaction quotient, Q, has the same form but can be calculated at any concentrations of reactants and products. Q is a calculated value that relates the reactant and product concentrations at any given time during a reaction. In contrast, Keq is the ratio of products to reactants at equilibrium, with each species raised to its stoichiometric coefficient. Pure solids and liquids do not appear in the law of mass action; only gases and aqueous species do.

Comparison of Q to Keq provides information about where the reaction is with respect to its equilibrium state. If Q < Keq, ∆G < 0 and the reaction proceeds in the forward direction. If Q = Keq, ∆G = 0 and the reaction is in dynamic equilibrium. If Q > Keq, ∆G > 0 and the reaction proceeds in the reverse direction.

Equilibrium calculations are broadly applicable to many areas of chemistry but are often formulaic in their application. The magnitude of Keq determines the balance of a reaction and whether the amount that has reacted can be treated as negligible when compared to other concentrations. If Keq > 1, the products are present in greater concentration at equilibrium. If Keq < 1, the reactants are present in greater concentration at equilibrium.

Le Châtelier’s Principle states that when a chemical system experiences a stress, it will react so as to restore equilibrium. Three main types of stresses can be applied to a system: changes in concentration, changes in pressure and volume, and changes in temperature. Increasing the concentration of reactants or decreasing the concentration of products will shift the reaction to the right. By the same logic, decreasing the concentration of reactants or increasing the concentration of products will shift the reaction to the left. Increasing pressure on a gaseous system (decreasing its volume) will shift the reaction toward the side with fewer moles of gas and vice versa. Increasing the temperature of an endothermic reaction or decreasing the temperature of an exothermic reaction will shift the reaction to the right and vice versa.

Reactions may have both kinetic and thermodynamic products that can be regulated by temperature and the presence of a catalyst. Kinetic products are higher in free energy than thermodynamic products and can form at lower temperatures. Kinetic products are sometimes termed “fast” products because they can form more quickly under such conditions. Thermodynamic products are more stable and lower in free energy than kinetic products. Despite proceeding more slowly than the kinetic pathway, the thermodynamic pathway is more spontaneous (more negative ΔG). (See Figure 11.4.)

Figure 11.4. Kinetic and Thermodynamic Control of a Reaction

Thermochemistry

Systems are classified based on what is or is not exchanged with the surroundings. Isolated systems exchange neither matter nor energy with the environment. Closed systems can exchange energy but not matter with the environment. Open systems can exchange both energy and matter with the environment.

Processes can be characterized based on a single constant property. Isothermal processes occur at constant temperature. Adiabatic processes exchange no heat with the environment. Isobaric processes occur at constant pressure. Isovolumetric processes occur at constant volume.

State functions describe the physical properties of an equilibrium state. They are pathway independent and include pressure, density, temperature, volume, enthalpy, internal energy, Gibbs free energy, and entropy. Standard conditions are defined as 298 K, 1 atm, and 1 M concentrations. The standard state of an element is its most prevalent form under standard conditions; standard enthalpy, standard entropy, and standard free energy are all calculated under standard conditions.

Phase changes exist at characteristic temperatures and pressures. Fusion (melting) and freezing (crystallization or solidification) occur at the boundary between the solid and the liquid phases. Vaporization (evaporation or boiling) and condensation occur at the boundary between the liquid and the gas phases. Sublimation and deposition occur at the boundary between the solid and gas phases. At temperatures above the critical point, liquid and gas phases are no longer distinguishable. At the triple point, all three phases of matter exist in equilibrium. Phase diagrams (see Figure 11.5) graph the phases and phase equilibria as a function of temperature and pressure.

Figure 11.5. Phase Diagram for a Single Compound

Temperature is a scaled measure of the average kinetic energy of a substance. Heat is the transfer of energy that results from temperature differences between two substances. The total heat of a system undergoing heating, cooling, or phase changes is the sum of all energy changes.

Enthalpy (ΔH) is a measure of the potential energy of a system found in intermolecular attractions and chemical bonds. Hess’s law states that the total change in potential energy of a system is equal to the changes of potential energies of the individual steps of the process. Enthalpy can also be calculated using heats of formation, heats of combustion, or bond dissociation energies. Entropy (ΔS), which is often thought of as disorder, is actually a measure of the degree to which energy has been spread throughout a system or between a system and its surroundings. Entropy is a ratio of heat transferred per mole per unit kelvin. Entropy is maximized at equilibrium.

Gibbs free energy (G) is derived from both enthalpy and entropy values for a system. The change in Gibbs free energy determines whether a process is or is not spontaneous (see Table 11.2). At ΔG < 0, a reaction proceeds in the forward direction (is spontaneous). At ΔG = 0, a reaction is in dynamic equilibrium. At ΔG > 0, a reaction proceeds in the reverse direction (is nonspontaneous). ΔG depends on temperature. Temperature-dependent processes change between spontaneous and nonspontaneous depending on the temperature. ΔG determines whether or not a reaction is spontaneous.

Table 11.2. The Effects of Enthalpy, Entropy, and Temperature on the Spontaneity of Reactions

Enthalpy (ΔH) Entropy (ΔS) Outcome

+ + Spontaneous at high temperatures

+ − Nonspontaneous at all temperatures

− + Spontaneous at all temperatures

− − Spontaneous at low temperatures

The Gas Phase

Gases are the least dense phase of matter. They are fluids and therefore conform to the shapes of their containers. However, gases are easily compressible. Gas systems are described by the variables temperature (T), pressure (P), volume (V), and number of moles (n). Important pressure equivalencies include 1 atm = 760 mmHg ≡ 760 torr = 101.325 kPa.

Standard temperature and pressure (STP) is 273 K (0 °C) and 1 atm. Equations for ideal gases assume negligible mass and volume of gas molecules. Regardless of the identity of the gas, equimolar amounts of two gases occupy the same volume at the same temperature and pressure. At STP, 1 mole of an ideal gas occupies 22.4 L.

The ideal gas law describes the relationship between the four variables of the gas state for an ideal gas (PV = nRT).

Avogadro’s principle is a special case of the ideal gas law for which the pressure and temperature are held constant; it shows a direct relationship between the number of moles of gas and volume.

Boyle’s law is a special case of the ideal gas law for which temperature and number of moles are held constant; it shows an inverse relationship between pressure and volume (P1V1 = P2V2).

Charles’s law is a special case of the ideal gas law for which pressure and number of moles are held constant; it shows a direct relationship between temperature and volume

Gay-Lussac’s law is a special case of the ideal gas law for which volume and number of moles are held constant; it shows a direct relationship between temperature and pressure

Dalton’s law of partial pressures states that individual gas components of a mixture of gases exert individual pressures in proportion to their mole fractions. The total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases.

Henry’s law states that the amount of gas dissolved in solution is directly proportional to the partial pressure of that gas at the surface of a solution.

Graham’s law describes the behavior of gas diffusion or effusion, stating that gases with lower molar masses diffuse or effuse faster than gases with higher molar masses at the same temperature.

Diffusion is the spreading out of particles from high to low concentration. Effusion is the movement of gas from one compartment to another through a small opening under pressure.

The kinetic molecular theory attempts to explain the behavior of gas particles. It makes a number of assumptions about the gas particles: gas particles have negligible volume, gas particles do not have intermolecular attractions or repulsions, gas particles undergo random collisions with each other and the walls of the container, collisions between gas particles (and with the walls of the container) are elastic, and the average kinetic energy of the gas particles is directly proportional to temperature.

Real gases deviate from ideal behavior under high pressure (low volume) and low temperature conditions. At moderately high pressures, low volumes, or low temperatures, real gases occupy less volume than predicted by the ideal gas law because the particles have intermolecular attractions. At extremely high pressures, low volumes, or low temperatures, real gases occupy more volume than predicted by the ideal gas law because the particles occupy physical space. The van der Waals equation of state is used to correct the ideal gas law for intermolecular attractions (a) and molecular volume (b).

Solutions

Solutions are homogeneous mixtures composed of two or more substances. They combine to form a single phase, generally the liquid phase. Solvent particles surround solute particles via electrostatic interactions in a process called solvation or dissolution. Most dissolutions are endothermic, although the dissolution of gas into liquid is exothermic. Solubility is the maximum amount of a solute that can be dissolved in a given solvent at a given temperature; it is often expressed as molar solubility—the molarity of the solute at saturation.

Complex ions are composed of metallic ions bonded to various neutral compounds and anions, referred to as ligands. Formation of complex ions increases the solubility of otherwise insoluble ions (the opposite of the common ion effect). The process of forming a complex ion involves electron pair donors and electron pair acceptors such as in coordinate covalent bonding.

Concentration can be expressed in many ways. Percent composition by mass (mass of solute per mass of solution times 100%) is used for aqueous solutions and solid-in-solid solutions. The mole fraction (moles of solute per total moles) is used for calculating vapor pressure depression and partial pressures of gases in a system. Molarity (moles of solute per liters of solution) is the most common unit for concentration and is used for rate laws, the law of mass action, osmotic pressure, pH and pOH, and the Nernst equation. Molality (moles of solute per kilograms of solvent) is used for boiling point elevation and freezing point depression. Normality (number of equivalents per liters of solution) is the molarity of the species of interest and is used for acid-base and oxidation-reduction reactions.

Saturated solutions are in equilibrium at that particular temperature. The solubility product constant (Ksp) is simply the equilibrium constant for a dissociation reaction. Comparison of the ion product (IP) to Ksp determines the level of saturation and behavior of the solution. When IP < Ksp, the solution is unsaturated; if more solute is added, that solute will dissolve. When IP = Ksp, the solution is saturated (at equilibrium); if more solute is added, that solute will not dissolve unless another change occurs to the system (change in temperature or amount of solvent, for instance). When IP > Ksp, the solution is supersaturated, and disruptions of the solution will lead to precipitation.

Formation of a complex ion in solution greatly increases solubility. The formation or stability constant (Kf) is the equilibrium constant for complex formation. Its value is usually much greater than Ksp. The formation of a complex increases the solubility of other salts containing the same ions because the complex uses up the products of those dissolution reactions, shifting the equilibrium to the right (the opposite of the common ion effect). The common ion effect decreases the solubility of a compound in a solution that already contains one of the ions in the compound. The presence of that ion in solution shifts the dissolution reaction to the left, decreasing dissociation.

Colligative properties are physical properties of solutions that depend on the concentration of dissolved particles but not on their chemical identity. Vapor pressure depression follows Raoult’s law (see Figure 11.6). The presence of other solutes decreases the evaporation rate of a solvent without affecting its condensation rate, thus decreasing its vapor pressure. Vapor pressure depression also explains boiling point elevation—as the vapor pressure decreases, the temperature (energy) required to boil the liquid must be raised.

Figure 11.6. Molecular Basis of Raoult’s Law

Freezing point depression and boiling point elevation are shifts in the phase equilibria dependent on the molality of the solution. Osmotic pressure is primarily dependent on the molarity of the solution. For solutes that dissociate, the van’t Hoff factor (i) is used in freezing point depression, boiling point elevation, and osmotic pressure calculations.

Acids and Bases

Arrhenius acids dissociate to produce excess of hydrogen ions in solution. Arrhenius bases dissociate to produce an excess of hydroxide ions in solution. Brønsted-Lowry acids are species that can donate hydrogen ions. Brønsted-Lowry bases are species that can accept hydrogen ions. Lewis acids are electron-pair acceptors. Lewis bases are electron-pair donors. All Arrhenius acids and bases are Brønsted-Lowry acids and bases, respectively; all Brønsted-Lowry acids and bases are Lewis acids and bases, respectively. However, the converse of these statements is not necessarily true.

Amphoteric species are those that can behave as either an acid or a base. Amphiprotic species are amphoteric species that specifically behave as a Brønsted-Lowry acid or base. Water is a classic example of an amphoteric, amphiprotic species—it can accept a hydrogen ion to become a hydronium ion, or it can donate a hydrogen ion to become a hydroxide ion. Conjugate species of polyvalent acids and bases can also behave as amphoteric and amphiprotic species.

The water dissociation constant, Kw, is 10−14 at 298 K. Like other equilibrium constants, Kw is affected only by changes in temperature. pH and pOH can be calculated using the concentrations of H3O+ and OH− ions, respectively. In aqueous solutions, pH + pOH = 14 at 298 K. Strong acids and bases completely dissociate in solution. Weak acids and bases do not completely dissociate in solution and have corresponding dissociation constants (Ka and Kb, respectively).

In the Brønsted-Lowry definition, acids have conjugate bases that are formed when the acid is deprotonated. Bases have conjugate acids that are formed when the base is protonated. Strong acids and bases have very weak (inert) conjugates, and weak acids and bases have weak conjugates. Neutralization reactions form salts and (sometimes) water.

An equivalent is defined as 1 mole of the species of interest. In acid-base chemistry, normality is the concentration of acid or base equivalents in solution. Polyvalent acids and bases are those that can donate or accept multiple electrons.

Titrations are used to determine the concentration of a known reactant in a solution. The titrant has a known concentration and is added slowly to the titrand to reach the equivalence point. The titrand has an unknown concentration but a known volume. The half-equivalence point is the midpoint of the buffering region, in which half of the titrant has been protonated (or deprotonated); thus, [HA] = [A−] and a buffer is formed.

Figure 11.7Titrations and Equivalence Points

The equivalence point is indicated by the steepest slope in a titration curve (see Figure 11.7). It is reached when the number of acid equivalents in the original solution equals the number of base equivalents added, or vice versa. Strong acid and strong base titrations have equivalence points at pH = 7. Weak acid and strong base titrations have equivalence points at pH > 7. Weak base and strong acid titrations have equivalence points at pH < 7. Weak acid and weak base titrations can have equivalence points above or below 7, depending on the relative strength of the acid and base.

Indicators are weak acids or bases that display different colors in protonated and deprotonated forms. The indicator chosen for a titration should have a pKa close to the pH of the expected equivalence point. The endpoint of a titration is when the indicator reaches its final color. Multiple buffering regions and equivalence points are observed in polyvalent titrations (see Figure 11.7).

Buffer solutions consist of a mixture of a weak acid and its conjugate salt or a weak base and its conjugate salt; they resist large fluctuations in pH. Buffering capacity refers to the ability of a buffer to resist changes in pH; maximal buffering capacity is seen within 1 pH point of the pKa of the acid in the buffer solution. The Henderson-Hasselbalch equation quantifies the relationship between pH and pKa for weak acids and between pOH and pKb for weak bases. When a solution is optimally buffered, pH = pKa and pOH = pKb.

Oxidation-Reduction Reactions

Oxidation is a loss of electrons, and reduction is a gain of electrons; the two are paired together in what is known as an oxidation-reduction (redox) reaction. An oxidizing agent facilitates the oxidation of another compound and is reduced itself in the process; a reducing agent facilitates the reduction of another compound and is itself oxidized in the process. Common oxidizing agents almost all contain oxygen or a similarly electronegative element. Common reducing agents often contain metal ions or hydrides (H–).

To assign oxidation numbers, one must know the common oxidation states of the representative elements. Any free element or diatomic species has an oxidation number of zero. The oxidation number of a monatomic ion is equal to the charge of the ion.

When in compounds, Group IA metals have an oxidation number of +1; Group IIA metals have an oxidation number of +2. When in compounds, Group VIIA elements have an oxidation number of –1 (unless combined with an element with higher electronegativity). The oxidation state of hydrogen is +1 unless it is paired with a less electronegative element, in which case the oxidation state of hydrogen is –1. The oxidation state of oxygen is usually –2, except in peroxides (when its charge is –1) or in compounds with more electronegative elements. The sum of the oxidation numbers of all the atoms present in a compound is equal to the overall charge of that compound.

A complete ionic equation accounts for all of the ions present in a reaction. To write a complete ionic reaction, split all aqueous compounds into their relevant ions, but keep all solid salts intact. Net ionic equations ignore spectator ions to focus on only the species that actually participate in the reaction. To obtain a net ionic reaction, subtract the ions appearing on both sides of the reaction, which are called spectator ions. For reactions that contain no aqueous salts, the net ionic equation is generally the same as the overall balanced reaction. For double-displacement (metathesis) reactions that do not form a solid salt, there is no net ionic reaction because all ions remain in solution and do not change oxidation number.

Disproportionation (dismutation) reactions are a type of redox reaction in which one element is both oxidized and reduced, forming at least two molecules containing the element with different oxidation states. Oxidation-reduction titrations are similar in methodology to acid-base titrations. These titrations follow the transfer of charge. Indicators used in such titrations change color when certain voltages of solutions are achieved. Potentiometric titration is a form of redox titration in which a voltmeter or an external cell measures the electromotive force (emf) of a solution. No indicator is used, and the equivalence point is determined by a sharp voltage change.

Electrochemistry

An electrochemical cell describes any cell in which oxidation-reduction reactions take place. Certain characteristics are shared among all types of electrochemical cells. Electrodes are strips of metal or other conductive materials placed into an electrolyte solution. The anode, which attracts anions, is always the site of oxidation. The cathode, which attracts cations, is always the site of reduction. Electrons flow from the anode to the cathode, while current flows from the cathode to the anode.

Cell diagrams are shorthand notation that represent the reactions taking place in an electrochemical cell. They are written from anode to cathode with electrolytes (the solution) in between. A vertical line represents a phase boundary, and a double vertical line represents a salt bridge or other physical boundary.

Galvanic (voltaic) cells house spontaneous reactions (ΔG < 0) with a positive electromotive force. Electrolytic cells house nonspontaneous reactions (ΔG > 0) with a negative electromotive force. These nonspontaneous cells can be used to create useful products through electrolysis. Concentration cells are a specialized form of a galvanic cell in which both electrodes are made of the same material. Rather than a potential difference causing the movement of charge, the concentration gradient between the two solutions causes the movement of charge.

The charge on an electrode depends on the type of electrochemical cell one is studying. For galvanic cells, the anode is negatively charged and the cathode is positively charged. For electrolytic cells, the anode is positively charged and the cathode is negatively charged.

Rechargeable batteries are electrochemical cells that can experience both charging (electrolytic) and discharging (galvanic) states (see Figure 11.8). Rechargeable batteries are often ranked by energy density—the amount of energy a cell can produce relative to the mass of battery material.

Figure 11.8. Lead-Acid Battery

A reduction potential quantifies the tendency for a species to gain electrons and be reduced. The higher the reduction potential, the more a given species wants to be reduced. Standard reduction potentials (E°red) are calculated by comparison to the standard hydrogen electrode (SHE) under the standard conditions of 298 K, 1 atm pressure, and 1 M concentrations. The standard hydrogen electrode has a standard reduction potential of 0 V.

Standard electromotive force (E°cell) is the difference in standard reduction potential between the two half-cells. For galvanic cells, the difference of the reduction potentials of the two half-reactions is positive; for electrolytic cells, the difference of the reduction potentials of the two half-reactions is negative.

Electromotive force and change in free energy always have opposite signs.

When E°cell is positive, ΔG° is negative. This is the case in galvanic cells.

When E°cell is negative, ΔG° is positive. This is the case in electrolytic cells.

When E°cell is 0, ΔG° is 0. This is the case in concentration cells.

The Nernst equation describes the relationship between the concentration of species in a solution under nonstandard conditions and the electromotive force. The equilibrium constant (Keq) is the ratio of the products’ concentrations at equilibrium over the reactants’ concentrations, raised to their stoichiometric coefficients. There exists a relationship between the equilibrium constant (Keq) and E°cell.

When Keq is greater than 1, E°cell is positive.

When Keq is less than 1, E°cell is negative.

When Keq is equal to 1, E°cell is 0.

🎯 11.4 Preparing for the MCAT: General Chemistry