Download Chemistry Unit Summaries - Oak Park Unified School District

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 = mcT. 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 – TS. 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 –TS. 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.