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Chemistry Unit Summaries The unified atomic mass scale (u) is 1/12 the mass of a C-12 atom. The average atomic mass of an element is calculated Measurement in Chemistry using the formula: 100mav = %1m1 + %2m2 ... Science knowledge is advanced by observing patterns The two kinds of pure substances are elements and (laws) and constructing explanations (theories), which are compounds. Elements are identified by a chemical symbol. supported by repeatable experimental evidence. Compounds are composed of two or more elements joined Measurements are made using the metric system, where the chemically and identified by a chemical formula, which shows the standard units are called SI units, which are based on the meter, composition. Molecular compounds have a defined size, whereas kilogram, and second as the basic units of length, mass, and crystalline compounds are unbounded, where their formula time, respectively. The SI temperature scale is the Kelvin scale, shows the ratio of atoms in the compound. although the Celsius scale is frequently used in chemistry. The Mixtures are composed of multiple pure substances in an metric system employs a set of prefixes to indicate decimal object or container and have variable compositions. They can be fractions or multiples of the base units; k (10-3), c (10-2), m (10-3), homogeneous or heterogeneous. Homogeneous mixtures are (10-6) and n (10-9). also called solutions and are uniform throughout. All measured quantities are inexact to some extent. The Radioactivity precision of a measurement indicates how closely different There are four kinds of radioactive decay: emission of alpha measurements of a quantity agree with one another. The particles ( or 42He), beta particle ( or 0-1e), positron particle accuracy of a measurement indicates how well a measurement (, 01e), and gamma radiation (00). agrees with the accepted value. Significant figures indicate the In nuclear equations, reactant and product nuclei are level of certainty in a measurement. Significant figures in a represented by AZX, which is its nuclear symbol. In a balanced measured quantity include one estimated digit; the last digit of equation the sum of reactant A and Z values equal the sum of the measurement. Calculations involving measured quantities are product A and Z values. reported with the appropriate number of significant figures. In Modes of decay can be predicted by comparing the number multiplication and division, the number of significant figures is of neutrons with the average (A – Z). In general, neutron-rich used. In addition and subtraction, the position of the least nuclei emit beta particles; neutron-poor nuclei emit positron accurate significant figure is used. Relative difference between particles; and nuclei above Z = 83 emit alpha particles. an experiment value (E) and a true value (T) is % difference: Nuclear transmutations, induced conversions of one nucleus % = 100|E – T|/T. Relative spread of N number of trials is % into another, can be brought about by bombarding nuclei with deviation: % = 100|trial – mean|/N(mean). either charged particles or neutrons. Mass and volume measure amount of matter. Density The decay rate (radioactivity) is proportional to the number relates mass to volume, d = m/V. Chemical processes involve of radioactive atoms, rate = kNt. The time for half of the interaction of particles, which are measured in moles. The radioactive atoms to decay is constant, t½ = (ln2)/k. The time number of particles in a mole is called Avogadro's number, which interval t for No number of radioactive atoms to reduce to Nt is is 6.02 x 1023. This number is based on using periodic table determined by the formula, kt = ln(No/Nt). masses to be equal to mass of a formula unit labeled in grams. Electron Structure—Bohr Model Molar mass (MM) is the sum of atomic masses in the chemical The electronic structure of an atom describes the energies formula. For example, the mass of one H2O molecule is 18.0 u, and arrangement of electrons around the atom. Much of what is so the molar mass of H2O is 18.0 g. known about the electronic structure of atoms was obtained by In the dimensional analysis technique, we keep track of units observing atomic spectra, which is the radiant energy emitted or as we carry measurements through calculations. The given units absorbed by matter. are multiplied by a series of conversion factors, which are ratios Equations for radiant energy, Ephoton = hf and speed of light, of equivalent quantities. After canceling out units algebraically, c = f are combined in Ephoton = hc/ = 2 x 10-25 J•m/. what remain are the target units. Bohr analyzed the wavelengths of light emitted by hydrogen Atomic Nature of Matter atoms and proposed a model that explains its atomic spectrum. Atoms are the basic building blocks of matter; they are the In this model the energy of the hydrogen atom depends on the smallest units of an element that can combine with other value of its quantum number n, where En = -2.18 x 1018 J/n2. The elements. Atoms are composed of even smaller subatomic value of n is a positive integer (1, 2, 3 . . .). As n increases, the particles. Experiments led to the discovery and characterization energy of the electron increases until it reaches a value of 0 J, of subatomic particles. Thomson experimented with cathode rays where n equals infinity and the electron leaves the atom or in magnetic and electric fields, which led to the discovery of the ionizes. The lowest energy state where n = 1 is called the ground electron and its charge-to-mass ratio. Millikan worked with oilstate. Other values of n correspond to excited states. Light is drops in a vacuum to determine the charge of the electron. emitted when the electron drops from a higher energy state to a Rutherford observed the scattering of particles by gold metal lower energy state and light is absorbed when electrons are foil and concluded that atoms have a dense, positive nucleus. excited from a lower energy state to a higher one. The energy of The atom's nucleus contains protons and neutrons, whereas light emitted or absorbed equals the difference in energy electrons move in the space around the nucleus. The charges of between two states, Ephoton = En-final – En-initial = 2.00 x 10-25 J•m/. subatomic particles in terms of the charge of an electron are: Summary 2 electron -1, proton +1 and neutron 0. Masses in terms of the Quantum Mechanical Model mass of a proton are: proton and neutron 1, and electron In the quantum mechanical model each electron has a 0.00055. precisely known energy, but according to the Heisenberg Elements are classified by their atomic number or Z value, Uncertainty Principle, the location of the electron cannot be which equals the number of protons. The mass number or A determined exactly; rather, the 90 % probability of it being at a value is the sum of protons and neutrons. Atoms of the same particular point in space is given by its orbital. An orbital is element that differ in mass number are called isotopes. In a neutral atom, the number of protons equals the number described by a combination of four quantum numbers. The of electrons. An anion is formed when electrons exceed protons. principal quantum number n is indicated by the integers 1, 2 . . . This quantum number relates to the radius and energy of the A cation is formed when protons exceed electrons. Summary 1 orbital. The sublevel quantum number l is indicated by the letters s, p, d, and f, which correspond to l = 0, 1, 2, and 3 respectively. The l quantum number defines the shape of the orbital. For a given value of n, l can have integer values from 0 to (n – 1). The orbital quantum number ml relates to the orientation of the orbital in space. For a given value of l, ml can have integral values ranging from –l to +l. The spin quantum number ms defines the orientation of the electron's magnetic field and has two possible values +½ and –½. The Pauli Exclusion Principle states that no two electrons in an atom can have the same spin in the same orbital. This principle limits the number of electrons that occupy any one atomic orbital to two. Electron Arrangements in Atoms and Ions Energy increases as n increases (1 < 2 < 3, etc.) and within the same value of n, energy increases as the sublevel progresses from letters s p d f. Orbitals within the same sublevel are degenerate, meaning they have the same energy. The energies of s and p sublevels are less than the energy of the next higher s sublevel, whereas the energies of d and f sublevels are greater than the next higher s sublevel. This restricts the outermost occupied sublevels for any atom to s and p. Electrons that occupy the outermost sublevels are involved in chemical bonding and are called valence electrons. Non-valence electrons are called core electrons. The periodic table is partitioned into different types of elements based on their electron arrangement. Elements with the same valence energy level form a row or period. Elements with the same number of valence electrons form a column or group. The elements in which an s or p sublevel is being filled are called the main-group elements, which include group 1— alkali metals, group 2—alkaline earth metals, group 17— halogens and group 18—noble gases. Transition metals are where the d-sublevel is filling. The 4f and 5f sublevel filling regions are called lanthanide and actinide respectively. Electron configurations show how electrons are distributed among the atom's sublevels. In ground state configurations electrons occupy the lowest sublevel available until its capacity is reached. Additional electrons fill the next lowest sublevel until its filled, etc. Excited state configurations have gaps. Orbital diagrams show how the electrons fill the specific orbitals, where arrows are used to represent electrons; () for ms = +½ and () for ms = –½. When electrons occupy a sublevel with more than one degenerate orbital, Hund's Rule applies. The rule states that the lowest energy is attained by maximizing the number of electrons with the same electron spin. Transition metals in columns 6 and 11 have a half-filled s sublevel in order to have a Half-filled or fully occupied d sublevel, which is more stable than other arrangements. The electron arrangement for monatomic ions is the same as the element with the same number of electrons. Elements within three squares on the periodic table of a noble gas form ions with the same electron arrangement as the noble gas and are isoelectronic. Transition metals form ions by losing all s level electrons first. Elements with unpaired electrons have reinforcing magnetic fields, which makes the atom paramagnetic. If all of the electrons are paired, then the atom is diamagnetic. Periodic Properties—Main Groups Core electrons are very effective at screening the outer electrons from the full charge of the nucleus, whereas electrons in the valence shell do not screen each other very effectively. As a result, the effective nuclear charge (Zeff) experienced by valence electrons increases as we move left to right across the main-group elements because the number of protons in the nucleus increases, without a corresponding increase in core electrons. The increase in Zeff is less pronounced with transition metals because the added electrons enter the core and cancel the added protons. As a result of the Zeff and the added energy levels, atomic radii increase as we go down a group and decrease as we proceed left to right across a period of main group elements. Cations are smaller than their parent atoms; anions are larger than their parent atoms, but group and period trends are the same as atomic radius. For an isoelectronic series the radius decreases with increasing nuclear charge. Ionization energy is the energy needed to remove an electron from a gaseous atom; forming a cation. Successive ionization energies show a sharp increase after all the valence electrons have been removed, because of the much higher effective nuclear charge experienced by the core electrons. For the main group elements, the first ionization energy trend is generally opposite the atomic radii trend, with smaller atoms having higher first ionization energies, except for columns 13 (where a higher energy p orbital electron is removed rather than an s orbital electron, therefore requiring less energy to ionize) and column 16 (where an electron is removed from a fully occupied orbital, which is at higher energy state than an electron from a half-filled orbital). Electron affinity measures the energy change when adding an electron to a gaseous atom; forming an anion. A negative electron affinity means that the anion is stable; a positive electron affinity means that the anion is not stable relative to the separate atom and electron. In general, electron affinities become more negative from left to right across the main groups except for column 2 (adding an electron to a p orbital), column 15 (adding an electron to a half-filled orbital) and column 18 (adding an electron to the next higher energy level). Summary 3 Bonding Bonds are classified into three broad groups: ionic bonds are the result of electrostatic (Coulomb's) forces between cations and anions; covalent bonds form when electrons are shared between non-metal atoms; and metallic bonds, which bind metal cations with mutually shared valence electrons. Bonds involve the interaction of valence electrons, which are represented by electron-dot or Lewis-dot symbols. The tendencies of atoms to gain, lose, or share their valence electrons often follow the octet rule, which can be viewed as an attempt by atoms to achieve a noble gas electron configuration. The strength of the electrostatic attraction between ions is measured by the lattice energy, which increases with ionic charge (Q) and decreases with distance between ions (r), E Q1Q2/r. Electronegativity measures the ability of an atom to attract electrons in a covalent bond. Electronegativity generally increases from left to right in the periodic table and decreases down a column. The difference in atoms' electronegativities is used to determine the polarity of a covalent bond; the greater the difference, the more polar the bond. A polar molecule has a positive side (+) and a negative side (–). The separation of charge produces a dipole, the magnitude of which is given by the dipole moment. Polar bonds are stronger and shorter than nonpolar bonds. Bond strength and length is also affected by the number of shared electrons. Sharing of one pair of electrons produces a single bond; whereas the sharing of two or three pairs of electrons produces double or triple bonds, respectively. Multiple bonds are stronger and shorter than single bonds. The procedures used for naming two-element, binary, molecular compounds follow the rules below. 1. The lower electronegative element is written first in the formula and named as an element. 2. The name of the second element is given an –ide ending. 3. Prefixes are used to indicate the number of atoms of each element; mono is not used with the first. Lewis Structures Electron distribution in molecules is shown with Lewis structures, which indicate how many valence electrons are involved in forming bonds and how many remain as unshared electron pairs. If we know which atoms are connected to one another, we can draw Lewis structures for molecules and ions by a simple procedure, where eight electrons are placed around each atom. When there are too few valence electrons, then it will be necessary to add double or triple bonds. When there are too many valence electrons (and the central atom has at least third energy level electrons), then it will be necessary to place additional electrons (up to 10 or 12) around the central atom; forming an expanded octet. When the total number of valence electrons is an odd number, then it will be necessary to place seven electrons around the atom with the odd number of valence electrons; usually nitrogen. When there are multiple valid Lewis structures for a molecule or ion, we can determine which is most likely by assigning a formal charge to each atom, which is the sum of half the bonding electrons and all the unshared electrons. Most acceptable Lewis structures will have low formal charges with any negative formal charge on the more electronegative atom. VSEPR Model The valence-shell electron-pair repulsion (VSEPR) model rationalizes molecular geometries based on the repulsions between electron domains, which are regions about a central atom where electrons are likely to be found. Pairs of electrons, bonding and non-bonding, create domains around an atom, which are as far apart as possible from each other. Electron domains from non-bonding pairs exert slightly greater repulsions, which leads to smaller bond angles than idealized values between bonding atoms. The arrangement of electron domains around a central atom is called the electron domain geometry; the arrangement of atoms is called the molecular geometry. Certain molecular shapes have cancelling bond dipoles, producing a nonpolar molecule, which is one whose dipole moment is zero. In other shapes the bond dipoles do not cancel and the molecule is polar (a nonzero dipole moment). In general non-bonding pairs of electrons around the central atom produce polar molecules. Valence-Bond Theory Valence-bond theory is an extension of Lewis's notion of electron-pair bonds. In valence-bond theory, covalent bonds are formed when atomic orbitals on neighboring atoms overlap. The bonding electrons occupy the overlap region and are attracted to both nuclei simultaneously, which bonds the atoms together. To extend valence-bond theory to polyatomic molecules, s, p, and sometimes d orbitals are blended to form hybrid orbitals, which overlap with orbitals on another atom to make a bond. Hybrid orbitals also hold non-bonding pairs of electrons. A particular mode of hybridization can be associated with each of the five common electron-domain geometries (linear = sp; trigonal planar = sp2; tetrahedral = sp3; trigonal bipyramidal = sp3d; and octahedral = sp3d2). Covalent bonds formed between hybridized electrons are called sigma () bonds, where the electron density lies along the line connecting the atoms. Bonds that form between nonhybridized p orbitals are called pi () bonds. A double bond consists of one bond and one bond and a triple bond consists of one and two bonds. Sometimes a bond can be placed in more than one location. In such situations, we describe the molecule by using two or more resonance structures. The molecule is envisioned as a blend of these multiple resonance structures and the bonds are delocalized; that is, spread among several atoms. The bond order value represents the actual bond strength and is sum of the bond plus a share of the bond(s). Hydrocarbons Carbon molecules (except CO, CO2) are called organic. Hydrocarbons are organic molecules that contain mostly carbon and hydrogen. The four groups of hydrocarbons are alkanes, alkenes, alkynes, and aromatic. The naming of hydrocarbons is based on the longest continuous chain of carbon atoms in the structure. The locations of alkyl groups, which branch off the chain, are specified by numbering along the carbon chain. Ring structures have the prefix cyclo. The names of alkenes and alkynes are based on the longest continuous chain of carbon atoms that contains the multiple bond, and the location of the multiple bond is specified by a numerical prefix. The chemistry of an organic compound is dominated by the presence of the functional group. For example, alcohols contain a hydroxyl group (–OH), which makes the molecule water soluble and acids contain both a hydroxyl and carbonyl group (=O), which weakens the bond between O and H and allows the proton (H+) to separate from the rest of the molecule, thus acting as an acid. Amines contain nitrogen with a lone pair of electrons (:N), which can attract a proton, thus acting as a base. Isomers are substances that possess the same molecular formula, but differ in the arrangements of atoms. In structural isomers the bonding arrangements differ. Different isomers are given different names. Alkenes exhibit not only structural isomerism but geometric isomerism (cis-trans) as well. In geometric isomers the bonds are the same, but the molecules have different geometries. Geometric isomerism is possible in alkenes because rotation about the C=C bond is restricted. Summary 4 Gas State Gases at room temperatures tend to be molecular with low molar mass. Air is a mixture composed mainly of N2 and O2. Some liquids and solids can also exist in the gaseous state, where they are known as vapor. Gases' volume can change because they are compressible and they mix in all proportions because their component molecules are far apart. The gas state is characterized by four variables: pressure (P), volume (V), temperature (T), and quantity (n). Volume is measured in liters, temperature in kelvins, and quantity of gas in moles. Pressure is the force per unit area. In chemistry, pressure is measured in atmospheres (atm), torr (named after Torricelli), millimeter of mercury (mm Hg) and kilopascals (kPa). 1 atm = 101 kPa = 760 torr = 760 mm Hg. A barometer is used to measure atmospheric pressure and a manometer is used to measure the pressure of enclosed gases. The ideal-gas law equation is PV = nRT, where V is in L, n is in moles and T is in K. The term R is the gas constant, which is 0.0821 when P is in atm or 8.31 when P is in kPa. The conditions of 273 K and 1 atm are known as the standard temperature and pressure and abbreviated as STP, where the molar volume of all gases is 22.4 L/mol. Additional equations using molar mass (MM) are MM = mRT/PV and MM = dRT/P. In gas mixtures the total pressure (Ptot) is the sum of the partial pressures (PA) that gas A would exert if it were present alone under the same conditions: Ptot = PA + PB ... The pressure of gas A is proportional to its mole fraction (XA): PA = XAPtot. In calculating the quantity of a gas collected over water, correction must be made for the partial pressure of water vapor. The kinetic-molecular theory accounts for the properties of an ideal gas in terms of a set of statements about the nature of gases: molecules are in continuous, chaotic motion; the volume of gas molecules is negligible compared to the volume of their container; the gas molecules have no attraction for one another; their collisions are elastic; and the molecule's kinetic energy is proportional to the absolute temperature: K = 3/2RT. Molecules of a gas do not all have the same kinetic energy at a given instant. Their speeds are distributed over a wide range; the distribution varies with the molar mass of the gas and with temperature. The root-mean-square speed, u = (3RT/MM)½. Effusion (rate of escape through a tiny hole into a vacuum) and diffusion (rate of spreading) are related to molar mass by Graham's law: rA/rB = (MMB/MMA)½. Departures from ideal behavior increase in magnitude as pressure increases and as temperature decreases. Real gases depart from ideal behavior because the molecules possess finite volume (making Vreal > Videal) and because the molecules experience attractive forces for one another (making Preal < Pideal). The van der Waals equation is an equation that modifies the ideal-gas law equation to account for molecular volume and intermolecular forces. Phase Change Substances that are gases or liquids at room temperature are usually composed of molecules. In gases the intermolecular attractive forces are negligible compared to the kinetic energies of the molecules; thus, the molecules are widely separated and undergo constant, chaotic motion. In liquids the intermolecular forces are strong enough to keep the molecules in close proximity; nevertheless, the molecules are free to move with respect to one another. In solids the inter-particle attractive forces are strong enough to restrain molecular motion and to force the particles to occupy specific locations in a threedimensional arrangement, crystal lattice. Three types of intermolecular forces exist between neutral molecules: dipole-dipole forces, London dispersion forces, and hydrogen bonding. London dispersion forces operate between all molecules as a result of temporary polarization due to an uneven electron distribution. Dispersion forces increase in strength with increasing molecular mass, although molecular shape is also an important factor. Dipole-dipole forces exist between polar molecules, where the negative pole of one molecule is attracted to the positive pole of a neighbor. The strength of dipole-dipole forces is proportional to polarity. Hydrogen bonding occurs in compounds containing N, O or F bonded to H. Hydrogen bonds are stronger than dipole-dipole or dispersion forces, but operate on the same principle of Coulomb interactions between opposite charged regions. (For your information. The stronger the intermolecular force, the greater is the viscosity, or resistance to flow, of a liquid. The surface tension of a liquid also increases as intermolecular forces increase in strength. Surface tension is a measure of the tendency of a liquid to maintain a minimum surface area. The adhesion of a liquid to the walls of a narrow tube and the cohesion of the liquid account for capillary action and the formation of a meniscus at the surface of a liquid.) A substance may exist in more than one state of matter, or phase. Phase changes are transformations from one state to another. Changes of a solid to liquid, melting, solid to gas, sublimation, and liquid to gas, vaporization, absorb energy. The reverse processes release energy. A gas cannot be liquefied by application of pressure if the temperature is above its critical temperature. The pressure required to liquefy a gas at its critical temperature is called the critical pressure. The vapor pressure is the partial pressure of the vapor when it is in dynamic equilibrium with the liquid. At equilibrium the rate of evaporation, transfer of molecules from the liquid to the vapor, equals the rate of condensation, transfer from the vapor to the liquid. The higher the vapor pressure of a liquid, the more readily it evaporates and the more volatile it is. Vapor pressure increases nonlinearly with temperature. Boiling occurs when the vapor pressure equals the atmospheric pressure. The normal boiling point occurs at 1 atm pressure. The equilibria between the solid, liquid, and gas phases of a substance as a function of temperature and pressure are displayed on a phase diagram. Equilibria between any two phases are indicated by a line. The line through the melting point usually slopes slightly to the right as pressure increases, because the solid is usually more dense than the liquid. The melting point at 1 atm is the normal melting point. The point on the diagram at which all three phases coexist in equilibrium is called the triple point. Crystalline Solids In a crystalline solid, particles are arranged in a regularly repeating pattern. An amorphous solid or glass is one whose particles show no such order. The properties of solids depend both on the type of particles and on the attractive forces between them. Molecular solids, which consist of atoms or molecules held together by intermolecular forces, are soft and low melting. Covalent network solids, which consist of atoms held together by covalent bonds that extend throughout the solid, are hard and high melting. Ionic solids are hard and brittle and have high melting points. Metallic solids, which consist of metal cations held together by a sea of electrons, exhibit a wide range of properties. Solubility Solutions form when one substance disperses uniformly throughout another. The dissolving medium of the solution (usually in the greater amount) is called the solvent. The substance dissolved in a solvent (usually the smaller amount) is called the solute. The attractive interaction of solvent molecules with solute is called solvation. When the solvent is water, the interaction is called hydration. The dissolution of ionic substances in water is promoted by hydration of the separated ions by the polar water molecules. The overall change in energy upon solution formation may be either positive (endothermic) or negative (exothermic), depending on the amount of energy needed to break the solute and solvent bonds compared to the amount of energy released when forming solute-solvent bonds. The equilibrium between a saturated solution and undissolved solute is dynamic; the process of dissolution and the reverse process, crystallization, occur simultaneously. In a solution in equilibrium with undissolved solute, the two processes occur at equal rates, giving a saturated solution. The amount of solute needed to form a saturated solution at any particular temperature is the solubility of that solute at that temperature. The solubility of one substance in another depends on the tendency of systems to become more random, by becoming more dispersed in space, and on the relative intermolecular solute-solute and solvent-solvent energies compared with solute-solvent interactions. Temperature can affect solubility, where solubility decreases with increased temperature for exothermic dissolution and increases with increased temperature for endothermic dissolution. Polar and ionic solutes tend to dissolve in polar solvents such as water and alcohol, and nonpolar solutes tend to dissolve in nonpolar solvents ("like dissolves like"). Liquids that mix in all proportions are miscible; those that do not dissolve significantly in one another are immiscible. Hydrogen-bonding interactions between solute and solvent often play an important role in determining solubility; for example, ethanol and water, whose molecules form hydrogen bonds with each other, are miscible. The solubilities of gases in a liquid are generally proportional to the pressure of the gas over the solution, as expressed by Henry's law, where solubility Mg = kPg. The solubilities of most solid solutes in water increase as the temperature increases. In contrast, the solubilities of gases in water generally decrease with increasing temperature. Concentrations of solutions can be expressed quantitatively by several different measures, including mole fraction: Xsolute = molsolute/moltotal molarity: M = molsolute/Vsolution(L) molality: m = molsolute/msolvent(kg) Conversions between concentration units is possible if molar mass of solute and solvent are known and/or the density of the solution is known. Colligative Properties A physical property of a solution that depends on the concentration of solute particles present, regardless of the nature of the solute, is a colligative property. Colligative properties include vapor-pressure lowering, freezing-point lowering, boiling-point elevation, and osmotic pressure. The presence of solute particles reduces the number of solvent particles on the surface of a solution, which lowers the rate of evaporation, therefore the vapor pressure of a solution is lower than that of the pure solvent, Pvap = XsolventPosolvent. A solution containing a nonvolatile solute (ideal solution) possesses a higher boiling point than the pure solvent. The molal boiling-point constant, Kb, represents the increase in boiling point for a 1 m solution of solute particles as compared with the pure solvent. Similarly, the molal freezing-point constant, Kf, measures the lowering of the freezing point of a solution for a 1 m solution of solute particles. The temperature changes are given by the equations Tb = Kbm and Tf = Kfm. When NaCI dissolves in water, two moles of solute particles are formed for each mole of dissolved salt. The boiling point or freezing point is thus elevated or depressed, respectively, approximately twice as much as that of a nonelectrolyte solution of the same concentration. The multiplier is called the van't Hoff factor i. Similar considerations apply to other strong electrolytes. Osmosis is the movement of solvent molecules through a semipermeable membrane from a less concentrated to a more concentrated solution. This net movement of solvent generates an osmotic pressure which can be measured in units of gas pressure, such as atm. The osmotic pressure of a solution as compared with pure solvent is proportional to the solution molarity: = MRT. Summary 5 Chemical Reactions One of the important concepts of stoichiometry is the law of conservation of mass, which states that the total mass of the products of a chemical reaction is the same as the total mass of the reactants. Likewise, the same numbers of atoms of each type are present before and after a chemical reaction. A balanced chemical equation shows equal numbers of atoms of each element on each side of the equation (but not number of molecules). Equations are balanced by placing coefficients in front of the chemical formulas for the reactants and products of a reaction, not by changing the subscripts in chemical formulas. Among the reaction types described in this unit are (1) combination reactions, in which two reactants combine to form one product; (2) decomposition reactions, in which a single reactant forms two or more products; (3) combustion reactions in oxygen, in which a hydrocarbon or related compound reacts with O2 to form CO2 and H2O. The coefficients in a balanced equation give the relative numbers of moles of reactants and products. To calculate the grams of a product from the grams of a reactant, first convert grams of reactant to moles of reactant, then use the coefficients to convert the number of moles of reactant to moles of product, and finally convert moles of product to grams of product. A limiting reactant is completely consumed in a reaction. When it is used up, the reaction stops, thus limiting the quantities of products formed. The theoretical yield is the quantity of product calculated to form when all of the limiting reagent reacts. The actual yield is always less than the theoretical yield. The percent yield compares the actual and theoretical yields. Gravimetric Analysis The empirical formula can be determined from its percent composition by calculating the relative number of moles of each atom in 100 g of the substance. Similarly, the empirical formula can be determined from the mass of each element in the compound, or if it is a combustion reaction, from the mass of CO2 and H2O produced. If the substance is molecular in nature, its molecular formula can be determined from the empirical formula if the molecular mass is also known. Summary 6 Volumetric Analysis Solutions of known molarity can be formed either by adding a measured mass of solute and diluting it to a known volume or by the dilution of a more concentrated solution of known concentration (a stock solution). Adding solvent to the solution (the process of dilution) decreases the concentration of the solute without changing the number of moles of solute in the solution, thus (Mstock)(Vstock) = (Mstandard)(Vstandard). In titration, a measured volume of solution of known concentration (the standard solution) is added to a solution of unknown concentration in order to determine the moles of unknown (MstandardVstandard = molstandard). The point in the titration at which stoichiometrically equivalent quantities of reactants (standard and unknown) are brought together is called the equivalence point. An indicator can be used to show the end point of the titration, which coincides closely with the equivalence point. Once moles of unknown are calculated, then the molar mass (given moles and mass) or molarity (given moles and volume) can be determined. Precipitation Reactions Metals tend to lose their valence electrons, becoming positively charged ions (cations). Nonmetals tend to gain additional electrons to complete their valence shell, forming negatively charged ions (anions). Molecules that carry a net charge are called polyatomic ions. In naming an ionic compound, the cation is named first and then the anion. Cations formed from metal atoms have the same name as the metal. If the metal can form cations of differing charges, the charge is given using Roman numerals. Monatomic anions have names ending in -ide. Polyatomic anions containing oxygen and another element (oxyanions) have names ending in -ate or –ite, where the –ite ending is used for the species with fewer oxygens compare to the –ate species. The chemical formulas used for ionic compounds are empirical formulas, where the total positive charge of the cations equals the total negative charge of the anions. Solubility rules are used to determine if an ionic compound is soluble in water. In general alkali metal and ammonium cations and nitrate and acetate anions form soluble salts. Most Cl-, Br- and I- compounds are soluble except with Ag+, Pb2+ and Hg22. Most SO42- compounds are soluble except Sr2+, Ba2+, Pb2+ and Hg22+. Most OH- and S2- compounds are insoluble except with alkali metal ions, ammonium, Sr2+ and Br2+. Otherwise, you can assume that an ionic compound is insoluble. Precipitation reactions are those in which an insoluble product, called a precipitate, forms when two soluble salts are mixed. The net ionic equation shows only those ions that react to form the precipitate. Small anions or polar molecules (ligands) can form coordination complexes with cations. Chemists take advantage of the high solubility of coordination complexes to dissolve an otherwise insoluble precipitate, by adding the ligand to a solution containing the precipitate. Acid-Base Reactions Properties of acidic solutions are due to H+(aq) ions. Seven anions (Cl-, Br-, I-, NO3-, ClO4-, ClO3- and SO42-) when attached to H+ form strong acid molecules. When strong acids are dissolved, they ionize 100 % into H+ and anion forming a strong electrolyte. Naming acids depend on the anion ending. If the anion ends in -ide, the acid is named with the prefix hydro- and suffic –ic acid. If the anion ends in –ate, the acid ends in –ic ate (without the prefix), and when the anion ends in –ite, the acid ends in –ous acid. Properties of basic solutions are due to OH-(aq) ions. Strong bases are the hydroxides and oxides of the alkali metals and the heavier alkaline earth metals (Ca2+, Sr2+ and Ba2+). Strong acid-strong base reactions are called neutralization reaction where H+(aq) + OH-(aq) combine to form H2O, with the counterions forming salt. Oxidation-Reduction Reactions Oxidation is the loss of electrons by an atom, whereas reduction is the gain of electrons by an atom. Oxidation numbers are assigned to atoms by using specific rules; neutral atoms and compounds have a total oxidation value of 0. Monatomic or polyatomic ions have a total oxidation value equal to the ionic charge. Some atoms in a compound always have the same oxidation number and are called standards: alkali metal ions have oxidation number +1, alkaline earth metal ions are +2, aluminum ions are +3 and fluorine atoms/ions are -1. Oxygen is usually -2, but can also be -1 in peroxides. Hydrogen is usually +1, but can be -1 in hydrides. A non-standard atom in a compound can be assigned an oxidation number by applying standards and the total oxidation value for the compound. The oxidation of an atom results in an increase in its oxidation number, whereas reduction is accompanied by a decrease in oxidation number. In every oxidation-reduction (redox) reaction one atom is oxidized (oxidation number increases) and one atom is reduced (oxidation number decreases). The substance that contains the oxidized atom is the reducing agent because it causes the reduction of some other atom. Similarly, the atom that is reduced is the oxidizing agent. Many redox reaction involve metal atoms and ions. Reactive metals tend to lose their valence electrons (oxidation) to a less reactive metal or nonmetal. The ability of a substance to take an electron (reduction) is listed on the Standard Reduction Potential Chart, which orders the species from strongest oxidizing agent to weakest. A similar chart listing metals only is called a Activity Series, where the most reactive metals (strongest reducing agent) are listed on top. Summary 7 Oxidation-Reduction Reactions A redox reaction can be balanced by dividing the reaction into two half-reactions, one for oxidation and one for reduction. Each half-reaction is balanced separately. First the non-oxygen and non-hydrogen atoms are balanced, then oxygen is balanced by adding H2O, then hydrogen is balanced by adding H+, and finally charge is balanced by adding electrons, e-. In oxidation half-reactions the electrons are on the product side of the reaction and in reduction half-reactions the electrons are on the reactant side of the reaction. The two half-reactions are brought together with proper coefficients to balance the electrons on each side of the equation. This process assumed the reaction occurred in an acid environment. When the reaction occurs in base, OH- ions are added to both sides of the equation for each H+ ion. OH- and H+ combine to form water. Standard Reduction Potentials Chart A voltaic cell generates a cell potential or voltage (E) that moves the electrons from the anode to the cathode through the external circuit. E is measured in volts (1 V = 1 J/C). The cell potential under standard conditions is called the standard cell potential, and is denoted Eo. The standard conditions are 1 M for ions, 1 atm for gas partial pressure and 25oC temperature. A standard reduction potential Eored can be assigned for an individual half-reaction by comparing the potential of the halfreaction to the reduction of H+: 2 H+(aq) + 2 e- H2(g), where Eored = 0 V. Standard oxidation potential is the negative of the standard reduction potential. The standard cell potential of a redox reaction is the sum of the reduction and oxidation potentials: Eo = Eored + Eoox. E is positive for a spontaneous reaction. Eored measures the tendency of an oxidizing agent to acquire electrons (the more positive the value for Eored the greater the strength as a reducing agent). Eoox measures the oxidizing strength of a substance, which is its tendency to lose electrons. Fluorine (F2) has the most positive Eored and is the strongest oxidizing agent. Li+ has the most negative Eored (most postive Eoox) and is the strongest reducing agent. E for a redox reaction varies with temperature and with the concentrations of reactants and products. The Nernst equation relates E under nonstandard conditions: E = Eo – (RT/nF)lnQ, where R = 8.31 J/mol•K, T = 298 K, n = moles of electrons and F = 96,500 C/mol and Q = products/reactants (where ions are measured in mol/L, gases are measured in atm, and liquids and solids are not included). Voltaic (Galvanic) Cell A voltaic (or galvanic) cell uses a spontaneous redox reaction to generate electricity (battery). In a voltaic cell the oxidation and reduction half-reactions occur in separate compartments. Each compartment has a solid surface called an electrode, where the half-reaction occurs. The electrode where oxidation occurs is called the anode; reduction occurs at the cathode. The electrons released at the anode flow through an external circuit (where they do electrical work) to the cathode. Electrical neutrality in the solution is maintained by the migration of cations to the cathode and anions to the anode through a salt bridge or porous barrier. Electrolytic Cell An electrolysis reaction, which is carried out in an electrolytic cell, employs an external source of electricity (battery or generator) to drive a nonspontaneous redox reaction. The negative terminal of the external source is connected to the cathode of the cell in order to drive electrons onto the electrode and induce reduction. The positive terminal is attached to the anode to pull electrons off of the electrode and induce oxidation. The current-carrying medium within an electrolytic cell may be either a molten salt, where the cation is reduced and the anion is oxidized, or an electrolyte solution, where either the electrolyte ions or water undergoes oxidation and reduction. The electrodes in an electrolytic cell can be inert, which is necessary when ions, gases or water react, or reactive, which is important in electroplating. The quantity of substance oxidized or reduced during electrolysis can be calculated by considering the number of electrons involved in the redox reaction and the amount of electrical charge that passes into the cell. The total charge Q equals current I measured in Coulombs/second (C/s) x time t measured in seconds: Q = It. Summary 8 Change in Enthalpy (H) Chemical reactions typically involve breaking some bonds between reactant atoms and forming new bonds. Breaking bonds absorbs energy, therefore the chemical system gains bond energy and the surroundings lose energy, typically in the form of heat. In contrast, forming bonds releases energy; resulting in lose of energy by the chemical system and a gain in energy by the surroundings (also in the form of heat). When energy required to break bonds is greater than the energy released to form new bonds, then products are at a higher energy state than reactants (making the product bonds weaker than the reactant bonds) and energy of the system increases (+H), which is described as endothermic because the surroundings typically lose heat energy and cool down. Alternatively, when energy required to break bonds is less than the energy released to form new bonds, then products are at a lower energy state than reactants (making the product bonds stronger than the reactant bonds) and energy of the system decreases, –H, which is described as exothermic because the surroundings typically gain heat energy and warm up. The change in enthalpy, H, is listed to the right of a balanced chemical equation. H can be treated in the same way as a coefficient when using dimensional analysis. The amount of heat transferred between the system and the surroundings is measured experimentally by calorimetry. A calorimeter measures the temperature change accompanying a process. The temperature change of a calorimeter depends on its heat capacity, the amount of heat required to raise its temperature by 1 K. The heat capacity for one mole of a pure substance is called its molar heat capacity; the term specific heat is used for one gram of the substance. Water has a very high specific heat, c = 4.18 J/g•K. The exchange of heat, q, with the surroundings is the product of the surrounding medium's specific heat (c), mass (m), and change in temperature (T), such that q = mcT. If a Bomb calorimeter is used, then the bomb constant (C) is in the equation: q = (C + mc)T. Bond energy, BE, measures the energy needed to break a covalent bond in a diatomic, gaseous molecule. The bond energy is approximately the same for any gaseous molecule. Change in enthalpy is estimated by adding the bond energies of all bonds that are broken and subtracting the bond energies of all bonds formed: H = BEreact – BEprod. Change in Entropy (S) All chemical systems have an inherent amount of disorder because of the complexity of the atomic arrangement within molecules, the spacing of molecules with respect to each other; and the overall motion of the system. Increases in complexity, spacing and overall motion result in increased disorder as measured by change in entropy, S. A positive S for physical changes can be predicted based on whether the molecules spread out. Evaporation, diffusion and effusion have +S values. Dissolving is more complicated because spreading out solute and solvent increases disorder, but formation of hydration bonds between solute and solvent decreases disorder, therefore it is impossible to predict the sign for S (although most dissolving is +S). All chemical reactions that result in more moles of gas products compared to reactants have a +S. Thermodynamic Data The standard enthalpy of formation, Hfo, of a substance is the enthalpy change for the reaction in which one mole of substance is formed from its constituent elements under standard conditions of 1 atm pressure and 25oC (298 K). For any element in its most stable state under standard conditions, Hfo = 0 kJ/mol. Most compounds have negative values of Hfo. Large negative Hfo indicate a strong bond and stable compound. The standard entropy So is based H+ having So = 0 kJ/mol•K (although the AP exam often lists the values in J/mol•K). The thermodynamic data chart lists the Hfo and So for common substances. Hfo applies to situations involving more than one mole, where Hfo is multiplied by the number of moles, and involving decomposition, where H = -Hfo. An important use of Hfo and So is for calculating H and S for a wide variety of reactions under laboratory conditions, where H Ho = Hfoprod – Hforeact and S So = Soprod – Soreact. H depends only on the initial and final states of the system. Thus, the enthalpy change of a process is the same whether the process is carried out in one step or in a series of steps. Hess's law states that if a reaction is carried out in a series of steps, H for the reaction will be equal to the sum of the enthalpy changes for the steps. We can therefore calculate H for any process, as long as we can write the process as a series of steps for which H is known. Change in Free Energy (G) The Gibbs free energy (or just free energy) G combines enthalpy and entropy. For processes that occur at constant temperature, G = H – TS. The sign of G relates to the spontaneity of the process. When G is negative, the process is spontaneous. When G is positive, the process is nonspontaneous (the reverse process is spontaneous). At equilibrium the process is reversible and G = 0 kJ/mol. The values of H and S generally do not vary much with temperature. As a consequence, the dependence of G with temperature is governed mainly by the value of T in the expression G = H –TS. The threshold temperature, T = H/S, is when a reaction goes from spontaneous nonspontaneous. This only occurs when H and S are both positive or both negative. When are both positive, the reaction is spontaneous at all temperatures above the threshold. When they are both negative, the reaction is spontaneous at all temperatures below the threshold. When H and S have opposite signs, then the reaction is spontaneous at all temperatures (-H and +S) or nonspontaneous (+H and –S). Summary 9 Reaction Rate Chemical kinetics is the area of chemistry that studies the rates of chemical reactions and the factors that affect them, namely, concentration, temperature, and catalysts. Reaction rates are usually expressed as changes in concentration per unit time: Typically, for reactions in solution, rates are given in units of molarity per second, M/s. For most reactions, a plot of molarity versus time shows that the rate slows down as the reaction proceeds. The instantaneous rate is the slope of a line drawn tangent to the concentration-versustime curve at a specific time. Rates can be written in terms of products, which are positive rates, or in terms of reactants, which are negative rates. The coefficients in the balanced equation are proportional to the various rates for the same reaction. The quantitative relationship between rate and initial concentration is expressed by a rate law, which has the form: rate = k[A]m[B]n, where A and B are reactants k is called the rate constant, and the exponents m and n are called reaction orders. The sum of the reaction orders gives the overall reaction order. Reaction orders must be determined experimentally. The unit of the rate constant depend on the overall reaction order. The unit for k is Mxt-1, where x = 1 – overall order. Rate laws can be used to determine the concentrations of reactants or products at any time during a reaction. In a zeroorder reaction, rate = k and kt = [A]o – [A]t, where [A]o is the initial concentration of A, [A]t is the concentration of A at time t, and k is the rate constant. A graph of [A] vs. t yields a straight line. In a first-order reaction, rate = k[A]t and kt = In([A]o/[A]t),. Thus, for a first-order reaction, a graph of In[A] vs. t yields a straight line of slope -k. In a second-order reaction, rate = k[A]2, and kt = 1/[A]t – 1/[A]o. In this case a graph of 1/[A]t vs. t yields a straight line. The half-life of a reaction t½ is the time required for the concentration of a reactant to drop to one-half of its original value. For a first-order reaction, t½ = ln2/k (same formula as radioactive decay half-life). Collision Model The collision model, which assumes that reactions occur as a result of collisions between molecules, helps explain why the rate constant increases with increasing temperature. At higher temperature, reactant molecules have more kinetic energy and their collisions are more energetic. The minimum energy required for a reaction to occur is called the activation energy Ea. A collision with energy Ea or greater can cause the atoms of the colliding molecules to reach the activated complex, which is the highest energy arrangement in the pathway from reactants to products. Even if a collision is energetic enough, it may not lead to reaction; the reactants must also have correct orientation for a collision to be effective. Because the kinetic energy depends on temperature, the rate constant is dependent on temperature. The two point equation is ln(k1/k2) = (Ea/R)(1/T2 – 1/T1), where R = 8.31 J/mol•K. The slope of lnk versus 1/T equals -Ea/R. Reaction Mechanism Many reactions occur by a multistep mechanism, involving two or more elementary reactions, or steps. A reaction mechanism details the individual steps that occur in the course of a reaction. Each of these steps has 1 or 2 reactants and low activation energy. The rate law for each step corresponds exactly to the number of reactant molecules, so that reactant coefficients become exponents in the rate law. An intermediate is produced in one elementary step and is consumed in a later elementary step and therefore does not appear in the overall equation for the reaction. When a mechanism has several elementary steps, the overall rate is limited by the slowest elementary step, called the rate-determining step. A catalyst is a substance that increases the rate of a reaction without undergoing a net chemical change itself. It does so by providing a different mechanism for the reaction, one that has lower activation energy. A homogeneous catalyst is one that is in the same phase as the reactants. It is consumed in the slow step and reappears in a later step. As a result, it is not included in the overall reaction, but is included in the rate law. A heterogeneous catalyst has a different phase from the reactants and is written above the reaction arrow. Summary 10 The Equilibrium State A chemical reaction can achieve a state in which the forward and reverse reactions are occurring at the same rate. This condition is called equilibrium and it results in the coexistence of the reactants and products of the reaction. The composition of an equilibrium mixture does not change with time. A historically important equilibrium is called the Haber process, where nitrogen gas and hydrogen gas are in equilibrium with ammonia gas: N2(g) + 3 H2(g) 2 NH3(g). This equilibrium is typical in that reactants and products are confined in the same container in the same state, and Ea is relatively small (catalyzed in this instance). The mathematical relationship between the concentrations of the reactants and products of an equilibrium system is given by the law of mass action. For the Haber process, the equilibrium expression Kc = [NH3]2/[N2][H2]3. The equilibrium expression depends only on the stoichiometry of the reaction as long as it is a gas. For equilibrium, which include solids and liquids—heterogeneous equilibrium, liquids and solids are left out of the equilibrium expressions because their concentrations are constant. For a system at equilibrium at a given temperature, Kc is a constant called the equilibrium constant, where the reactant and product concentrations are measured in mol/L and written with square brackets. When the equilibrium system consists of gases, it is often convenient to express the concentrations of reactants and products in terms of gas pressures. For the Haber process, Kp = (PNH3)2/(PN2)(PH2)3, where the partial pressures of reactants and products are measured in atm. The mathematical relationship between Kc and Kp is Kp = Kc x (RT)n(gas), where n(gas) equals the moles of gas products minus the moles of gas reactants. Whether Kc or Kp, the constant is usually expressed without units. The value of the equilibrium constant changes with temperature. A large value of Kc (greater than 1) indicates that the equilibrium mixture contains more products than reactants. Starting from standard conditions (1 mol/L or 1 atm), an equilibrium mixture will proceed to the right, that is to say is spontaneous in the forward direction. Spontaneous reactions at standard conditions have –Go (although G = 0) and +Eo, therefore as a generalization, we can say that when K > 1, Go < 0 and Eo > 0. Conversely when 0 < K < 1, Go > 0 and Eo < 0. Equations relating Go and Eo to K are: Go = -RTlnK and Eo = (RT/nF)lnK, where R = 8.31 J/mol•K, T = 298 K, n = moles eand F = 96,500 C/mol e-. The equilibrium expression and the equilibrium constant of the reverse reaction are the reciprocals of those of the forward reaction. When the coefficients of an equilibrium reaction are multiplied by a factor, then the equilibrium constant is raised to a power equal to that factor. If a reaction is the sum of two or more reactions, its equilibrium constant will be the product of the equilibrium constants for the individual reactions. Problems involving equilibrium reactions fall into five general categories. (1) To determine the direction a reaction will proceed to reach equilibrium: the reaction quotient Q is found by substituting initial reactant and product partial pressures or concentrations into the equilibrium expression. If the system is at equilibrium, Q = K. If Q K, however, the system is not at equilibrium. When Q < K, the reaction will move toward equilibrium by forming more products (the forward reaction); when Q > K, the reaction will proceed from right to left. (2) To determine K given the equilibrium concentrations of all species, the equilibrium expression is used to calculate the value of the equilibrium constant. (3) To determine K given the initial concentration of all species and the equilibrium concentration of one species, the equilibrium concentration of the remaining species are determined because the changes in the concentrations of reactants and products on the way to achieving equilibrium are governed by the stoichiometry of the reaction. An "ICE" box diagram is often useful to organize the data. The equilibrium values are substituted into the expression and solved for K. (4) To determine an equilibrium concentration given the other equilibrium concentrations and K, the equilibrium expression is used to calculate the unknown concentration. (5) To determine all equilibrium concentrations given the initial concentrations and K, "nx" is used to represent the change in concentration to reach equilibrium for each species, where n equals the coefficient for that species. An "ICE" box diagram is often useful to organize the data. The equilibrium values are expressed in terms of x and substituted into the equilibrium expression, which is set equal to K. Solving for x and substituting x back into the expression for each species gives the equilibrium concentrations. Le Chatelier's Principle Le Chatelier's principle states that if a system at equilibrium is disturbed, the equilibrium will shift to minimize the disturbing influence. By this principle, if a reactant or product is added to a system at equilibrium, the equilibrium will shift to consume the added substance. If a reactant or product is removed from the system at equilibrium, the equilibrium will shift to replace the removed substance. The enthalpy change for a reaction indicates how a change in temperature affects the equilibrium: An increase in temperature favors the endothermic direction, whereas a decrease in temperature favors the exothermic direction. In the case of changing temperature, K is also changed. When the equilibrium shifts to the right due to a temperature change, K increases. When the equilibrium shifts to the left, K decreases. Changing the volume of a reaction vessel can affect the equilibrium position. If the volume of the system is reduced, the equilibrium will shift in the direction that decreased the number of gas molecules. An increase in volume favors the production of more gas molecules. If there is no difference in the number of gas products compared to reactants, then the system is unresponsive. An added inert gas has no effect on the system. Catalysts affect the speed at which equilibrium is reached but do not affect the equilibrium position or K. Summary 11 Acids and Bases The Brønsted-Lowry (B-L) concept of acids and bases is more general than the Arrhenius concept and emphasizes the transfer of a proton (H+) from an acid to a base. (The H+ ion is strongly bound to water and forms the hydronium ion, H3O+). A B-L acid donates a proton to another substance; a B-L base. Substances such as H2O and HCO3- that can donate or accept a proton are called amphiprotic. A B-L base is formed when a proton is removed from a B-L acid. Together, an acid and its corresponding base are called a conjugate acid-base pair. The strengths of an acid-base pairs are related: The stronger an acid, the weaker its conjugate base; the weaker an acid, the stronger its conjugate base. In every acid-base reaction, the position of the equilibrium favors the transfer of the proton from the stronger acid to the stronger base. The Lewis concept of acids and bases emphasizes the shared electron pair rather than the proton. A Lewis acid is an electron-pair acceptor and a Lewis base is an electron-pair donor. The Lewis concept is more general than the BrønstedLowry concept because it can apply to cases in which the acid is some substance other than H+. The Lewis concept helps to explain why many hydrated metal cations form acidic aqueous solutions, in fact all coordination complex formations can be described as a Lewis acid-base reaction. Water ionizes to a slight degree, forming H+(aq) + OH-(aq). The extent of this autoionization is expressed by the ion-product constant for water: Kw = [H+][OH-] = 1.0 x 10-14 (25°C). This relationship describes both pure water and aqueous solutions. The Kw expression indicates that the product of [H+] and [OH-] is a constant. Thus, as [H+] increases, [OH-] decreases. In acid solutions [H+] > [OH-] and in basic solutions [OH-] > [H+]. The concentration of H+(aq) is expressed as pH = -log[H+]. At 25°C the pH of a neutral solution is 7.00, whereas the pH of an acidic solution is below 7.00, and the pH of a basic solution is above 7.00. The pH notation is also used to represent the negative log of other small quantities, as in pOH and pKw. Weak acids are weak electrolytes; only a fraction of the molecules exist in solution in ionized form. The extent of ionization is expressed by the acid-dissociation constant, Ka, for the equilibrium HA(aq) H+ + A-, which can also be written HA(aq) + H2O(I) H3O+ + A-. The larger the value of Ka, the stronger the acid. The concentration of a weak acid and its Ka value can be used to calculate the pH of a solution. Polyprotic acids, such as H2SO3, have more than one ionizable proton. These acids have acid-dissociation constants that decrease in magnitude in the order Ka1 > Ka2 > Ka3. Because nearly all the H+(aq) in a polyprotic acid solution comes from the first dissociation step, the pH can usually be estimated by considering only Ka1. Weak bases include NH3, amines, and weak acid anions. The base-dissociation constant Kb, is used for the equilibriums: B(aq) + H2O(l) HB+ + OH- or A- + H2O(l) HA(aq) + OH-. The relationship between the strengths of an acid and its conjugate base is expressed quantitatively by the equation Ka x Kb = Kw, where Ka and Kb are dissociation constants for the acid-base conjugate pair. The acid-base properties of salts can be ascribed to the behavior of their respective cations and anions. The reaction of ions with water, with a resultant change in pH, is called hydrolysis. The cations of the alkali metals and the heavier alkaline earth metals and the anions of strong acids do not undergo hydrolysis. They are always spectator ions in acid-base chemistry. Acid character requires the presence of a highly polar H–X bond. Acidity is also favored when the H–X bond is weak and when the X- ion is very stable. For oxyacids with the same number of OH groups and the same number of O atoms, acid strength increases with increasing electronegativity of the central atom. For oxyacids with the same central atom, acid strength increases as the number of oxygen atoms attached to the central atom increases. The structures of carboxylic acids, which are organic acids containing the COOH group, also helps us to understand their acidity. Buffered solutions (buffers) are formed from a mixture of a weak acid (or base) and its conjugate base (or acid). Addition of small amounts of a strong acid or a strong base to a buffered solution causes only small changes in pH because the buffer reacts with the added acid or base. (Reactions involving strong acids or strong bases go to completion and therefore do not act as buffers.) Buffered solutions are usually prepared from a weak acid (or base) and a salt of the conjugate base (or acid), or by partially neutralizing a weak acid (or base). The pH after strong acid or base is added is determined by using stoichiometry to calculate the moles of acid (HA) and conjugate base (A-) or moles of base (B) and conjugate acid (HB+) that exist after the strong acid or base are added, and then use the equations: [H+] = Ka(nHA/nA-) or [OH-] = Kb(nB/nHB+). Acid-Base Titration The plot of the pH of an acid (or base) as a function of the volume of added base (or acid) is called a pH titration curve. Titration curves aid in selecting a proper pH indicator for an acidbase titration. The titration curve of a strong acid-strong base titration exhibits a large change in pH in the immediate vicinity of the equivalence point; at pH equals 7. For weak acid-strong base or weak base-strong acid titrations, the pH change in the vicinity of the equivalence point is smaller. Furthermore, the pH at the equivalence point is greater than 7 for a weak acid-strong base titration; it is based on the pH of the pure conjugate base, where [OH] = (Kb[A-])½. For a weak base-strong acid titration, the pH at the equivalence point is less than 7; it is based on the pH of the pure conjugate acid, where [H+] = (Ka[HB+])½. It is possible to calculate the pH at any point beyond equivalence for all titrations and before equivalence for strong acid-strong base titrations by determining the concentration of excess H+ or OH-. Since the region prior to equivalence for a weak acid-strong base or weak base-strong acid titrations is buffered, the buffer equations above are used. Solubility-Product Constant, Ksp The equilibrium between a solid compound and its ions in solution provides an example of heterogeneous equilibrium. The solubility-product constant (or simply the solubility product), Ksp, is an equilibrium constant that expresses quantitatively the extent to which the compound dissolves. Ksp can be used to calculate the solubility of an ionic compound, and the solubility can be used to calculate Ksp. "ICE" box diagrams are used to develop an equation that relates solubility with Ksp. Alternatively, general formulas are used, where s equals solubility. When the precipitate has the form MX, then Ksp = s2; for MX2 or M2X, then Ksp = 4s3; and for MX3 or M3X, then Ksp = 27s4. Comparison of the ion product Q with the value of Ksp can be used to judge whether a precipitate will form when solutions are mixed or whether a slightly soluble salt will dissolve under various conditions. Precipitates form when Q > Ksp. Factors that Affect Solubility Several experimental factors, including temperature, affect the solubility of ionic compounds in water. The solubility of a slightly soluble ionic compound is decreased by the presence of a second solute that furnishes a common ion, this is called the common-ion effect. The solubility of most compounds increases as the solution is made more acidic (add H+). Salts containing Cl-, Br-, I- or SO42- are unaffected by addition of H+. The solubility of metal salts is also affected by the presence of polar molecules or anions that react with metal ions to form stable complex ions. The extent to which such complex formation occurs is expressed quantitatively by the formation constant for the complex ion Kf. Some insoluble metal oxides and hydroxides are soluble in strong acid or strong base. This is called amphoterism.