Chemical Bonding

Ionic compounds form when metals and nonmetals react
The attraction between positive and negative ions is called an ionic bond
The ionic compounds form because the potential energy of the system decreases
Consider the example of sodium chloride
The energy change when NaCl forms can be calculated using the ionization energy (IE) of sodium, the electron affinity (EA) of chlorine, and the lattice energy of NaCl
Starting from 1 mole of gas phase atoms:
Na(g)  Na+(g) + e- +495.4 kJ (IE of sodium)
Cl(g) + e-  Cl-(g) -348.8 kJ (EA of chlorine)
Na+(g)+Cl-(g)NaCl(s) -787.0 kJ (-lattice energy)
Net: -640.4 kJ
It turns out that for any ionic compound, the chief stabilizing influence is the lattice energy
The size of the lattice energy depends on ion size and charge
The lattice energy increases with charge because the ions attract each other more strongly
Example: KCl (709 kJ) vs CaO (3401 kJ)
Smaller ions have larger lattice energies because they get closer together
Example: NaCl (778 kJ) vs KCl (709 kJ) and LiF (1033 kJ) vs LiCl (845 kJ)
The lattice energy can be calculated using a Born-Haber cycle
Noble gas configurations are very stable and can be useful in predicting ion charges
Consider the case of sodium:
Na(g)  Na+(g)+e- IE= 466 kJ/mol
Na+(g) Na2+(g)+e- IE=4563 kJ/mol
Na 1s22s22p63s1
Na+ 1s22s22p6 (noble gas core)
Na2+ 1s22s22p5
Formation of Na+ is relatively inexpensive
Na2+ doesn’t (ordinarily) form because breaking into the noble gas core costs a to much energy
All noble gases (except He) have 8 valence electrons
This is called an octet of electrons
Most of the representative elements tend to gain or lose electrons until they have achieved the configuration of the nearest noble gas
For example: Na and K lose electrons to achieve an octet of electrons while Cl and O gain electron to achieve an octet of electrons
The octet rule works best for ionic compounds of Group IA and IIA metals from Period 3 down and for the anions of the nonmetals
It fails for Li and Be because they achieve the He (1s2) electron configuration
It also doesn’t work for hydrogen which can form H- (electron configuration: 1s2) when it reacts with very reactive metals
The octet rule doesn’t work well for transition metals and post transition metals
For these cations:
The first electrons lost by an atom or ion are always those from the outer shell (with the largest value of n)
Within a given shell: the f (subshell) is emptied before the d, which is emptied before the p, which is emptied before the s
Consider the case of iron:
Neutral: Fe [Ar]3d64s2
Loss of 4s electrons: Fe2+ [Ar]3d6
Loss of a 3d electron: Fe3+ [Ar]3d5
Many transition elements form multiple cations (like iron)
Often, one of the cations has a charge of +2
The relative stability of the ions formed is difficult to predict
Lewis symbols provide a convenient way to keep track of valence electrons
In this notation the symbol of the element is surrounded by dots (or similar symbols) that represent the atom’s valence electrons
All the elements in a group have a similar Lewis symbol because they have the same number of valence electrons
Ions are treated in a similar fashion
Many substances comprised only of nonmetals occur as molecules
Molecules involve electron sharing
Covalent bonds are characterized by their bond distance, or average distance between the nuclei, and the bond energy, or amount of energy released when the bond forms
Lewis symbols can be used to represent the covalent or electron pair bond
Both hydrogens are considered to have two electrons
For simplicity, electron pair bonds are usually represented by a dash
Example: hydrogen molecule is represented as H-H
Formulas drawn with Lewis symbols are called Lewis formulas or Lewis structures
The term structural formula is also used because it shows how the atoms in the molecule are attached to each other
Many molecules obey the octet rule:
When atoms form covalent bonds, they tend to share sufficient electrons so as to achieve an outer shell having eight electrons
In most of their covalently bonded compounds, the number of covalent bonds formed by carbon, nitrogen, and oxygen are four, three, and two, respectively
One shared pair of electrons is called a single bond
Double and triple bonds are also common:
Organic compounds will frequently be used as examples later in the text
In general, organic compounds are held together with covalent bonds
The simplest hydrocarbons are the alkanes with the general formula CnH2n+2
The first three alkanes are methane, ethane, and propane
In condensed form they are written:
methane: CH4
ethane: CH3CH3
propane: CH3CH2CH3
Things get more complicated starting with alkanes containing four carbons
Hydrocarbons that contain one double bond have the general formula CnH2n and are called alkenes
Hydrocarbons that contain one triple bond have the general formula CnH2n-2 and are called alkynes
Most organic compounds contain elements in addition to carbon and hydrogen
These are considered to be hydrocarbon derivatives
Using the symbol “R” to represent any hydrocarbon fragment (such as CH3-, or CH3CH2-) important families include:
Ball and stick models are common
When two identical atoms form a covalent bond each atom has an equal share of the bond’s electron pair
When different kinds of atoms combine, one nuclei usually attracts the electrons in the bond more strongly
The magnitude of the polarity is expressed in terms of the dipole moment
Dipole moments are frequently reported in units of Debye (D)
The dipole moments and bond lengths for some diatomic molecules are:
Electronegativity is the term used to describe the relative attraction of an atom for the electrons in a bond
The element with the larger electronegativity will carry the partial negative charg
The difference in electronegativity provides an estimate for the degree of polarity of the bond
There is no sharp dividing line between ionic and covalent bonding: ionic bonding and nonpolar covalent bonding represent the extremes
A bond is mostly ionic when the electronegativity difference between the two atoms is large
The degree of polarity, or ionic character, varies continuously with the electronegativity difference
In general, electronegativity increases bottom to top in a group and left to right in a period
Metal reactivity refers to the tendency of the metal to undergo oxidation
The lower the electronegativity the easier a metal is to oxidize
For nonmetals, reactivity is usually gauged by the ability to act as an oxidizing agent
In general, the oxidizing ability of nonmetals increases from left to right in a period and bottom to top in a group
This makes fluorine, found in the upper right of the periodic table, the strongest oxidizing agent
Single displacement reactions may be predicted from nonmetal reactivity
Consider the halogens (Group VIIA): a halogen as an element will oxidize the anion of any halogen below it
F2 will oxidize Cl-, Br-, and I-
Example: F2 + 2Cl-  2F- + Cl2
Cl2 will oxidize Br- and I-
Example: Cl2 + 2Br-  2Cl- + Br2
Br2 will oxidize I-
Example: Br2 + 2I-  2Br- + I2
Lewis structures are useful because they give a simple way to describe the structure of molecules
Not all structures obey the octet rule
Most nonmetals beyond Period 2 form structures with more than eight electrons
Examples: PCl5 and SF6
In some compounds the central atom has less than eight electrons
Common examples include compounds of beryllium and boron
Examples: BeCl2 and BCl3
Lewis structures describe how atoms share electrons in chemical bonds
The bond length and bond energy are related to the number of electron pairs shared between to atoms
For bonds between the same elements the bond length and bond energy depend on the bond order
The bond order is the number of pairs of electrons shared between two atoms
A single bond has bond order of 1; a double bond a bond order of 2; and a triple bond a bond order of 3
The bond order is a measure of the amount of electron density in a bond
More electron density gives a stronger bond
Consider the average bond lengths and bond energies for carbon-carbon bonds:
Bond lengths and bond energies are obtained from experiment
The preferred Lewis structure is the one that best fits the experimental data
The preferred Lewis structure for sulfuric acid violates the octet rule:
Structure I obeys the octet rule, but is not consistent with experiment
Structure II violates the octet rule, but is consistent with experiment
Structure II is the preferred Lewis structure
Formal charge is the apparent charge on an atom
The formal charge on a atom is calculated by subtracting the number of valence electrons assigned to it in a Lewis structure from the number of valence electrons in an isolated atom
Consider the sulfur atoms in the two structures for sulfuric acid:
Structure I: formal charge on S = 6 - (4 + 0) = +2
Structure II: formal charge on S = 6 - (6 + 0) = 0
When several Lewis structures are possible, those with the smallest formal charges are the most stable and preferred
Note that the formal charges for all atoms in a Lewis structure sum to the charge on the species
Some molecules and ions are not well represented by a single Lewis structure
Consider the case of the formate ion
Experiment gives a single carbon-oxygen bond length
A combination of structures is needed to describe this ion
These are called resonance structures and the ion is said to be a resonance hybrid of the contributing structures
Two resonance structures are required for the formate ion because two equivalent carbon-oxygen double bonds can be formed
Note that three resonance structures would be required to represent SO3
The total energy of a resonance hybrid is lower in energy than any one of its resonance structures
This energy lowering is called the resonance energy
Consider the formation of the ammonium ion from ammonia and a hydrogen ion in solution
The nitrogen donates both of the electrons when forming the bond to H+
This is called a coordinate covalent bond
The concept of a coordinate bond can be useful when trying to understand what happens to atoms in reactions
For example, addition compounds involve coordinate covalent bonds and can result when two small molecules “join”

The Quantum Mechanical Atom

By the late 1800’s it was clear that classical physics was incapable of describing atoms and molecules
Experiments showed that electrons acted like tiny charged particles in some experiments and waves in others
The physics that describes objects with wave/particle duality is called quantum mechanics or quantum theory
Energy can be transferred between things as light or radiation
Radiation carries energy through space as waves or oscillations moving outward from a disturbance
Electromagnetic waves (radiation) may be characterized by their “height” or amplitude and the number that occur per second or frequency (v)
The units of frequency are the hertz (Hz)
The minimum and maximum amplitude of electromagnetic radiation are evenly spaced
The peak-to-peak distance is called the wavelength
The product of frequency and wavelength give the speed of light (c)
Electromagnetic radiation comes in a broad range of frequencies called the electromagnetic spectrum
The electromagnetic spectrum is divided into regions according to the wavelengths of radiation
What we call light is a small slice of the electromagnetic spectrum with wavelengths between about 400 and 700 nm
This is called the visible region because we can “see” these wavelengths of the electromagnetic spectrum
Gamma rays, X rays, and ultraviolet radiation have wavelengths shorter than the visible region
Microwaves, infrared radiation, and radio waves have wavelengths longer than visible light
The way a substance absorbs electromagnetic radiation can be used to characterize it
For example, each substance absorbs a uniquely different set of infrared frequencies
A plot of wavelengths absorbed versus the absorption is called an infrared absorption spectrum
It can be used to identify a substance
The oscillating magnetic and electric fields of an electromagnetic wave interact with particles that it passes
A charged particle can pick up energy at the expense of the radiation source
The energy transfer is not describe correctly by classical physics
In 1900 the German scientist Max Planck proposed that the electromagnetic radiation could be viewed as a stream of tiny energy packets or quanta we now call photons
Photons travel at the speed of light
Planck proposed, and Einstein confirmed, that the energy of a photon is proportional to its frequency
This means that both electrons and electromagnetic radiation can be represented as either waves or particles
The visible spectrum is a continuous spectrum because it contains a continuous distribution of light of all colors
Excited atoms can emit light
The atomic spectrum or emission spectrum is a series of individual lines called a line spectrum
Atomic spectra are unique for each element
In general, the line spectrum of an element is rather complicated
The line spectrum of hydrogen, with a single electron, is the simplest
The Rydberg equation can be used to calculated all the spectral lines of hydrogen
n1 and n2 are positive integers
The Rydberg constant, RH, is an empirical constant with a value of 109,678 cm-1
Atomic line spectra tells us that when an excited atom loses energy, not just any arbitrary amount can be lost
This is possible if the electron is restricted to certain energy levels
The energy of the electron is said to be quantized
The first theoretical model that successfully accounted for the Rydberg equation was proposed in 1913 by Niels Bohr
Bohr proposed that the electrons moved around the nucleus is fixed paths or orbits much like the planets move around the sun
The orbits, labeled with the integer n, have energy
This equation allows the calculation of the energy of any orbit
The lowest energy state of an atom is called the ground state (an electron with n = 1 for a hydrogen atom)
An electron that “escapes” from the nucleus has infinity for its quantum number and zero energy
Bohr’s (theoretical) equation explains the (empirical) Rydberg equation
The combination of constants, b/hc, has a value which differs from the experimentally derived value of RH by only 0.05%
Bohr’s efforts to develop a general theory of electronic structure was doomed by the wave/particle duality of electrons
De Broglie suggested that the wavelength of a particle of mass m moving at speed v is
This relation provides the link between the description as a particle and as a wave
Heavy objects have very “short” wavelengths so their matter waves and the wave properties go unnoticed
Tiny particles with small masses have “long” wavelengths so their wave properties are an important part of their behavior
Waves combine in two ways
The constructive and destructive interference is called diffraction
Electrons produce similar patterns
There are two types of waves: traveling and standing
A standing wave is produced when a guitar string is plucked: the center of the string vibrates, but the ends remain fixed
Points of zero wave amplitude are called nodes
For guitar strings the only waves are those for which a half-wavelength is repeated exactly a whole number of times
For a strength of length L with n an integer this can be written
These results can be used to show how quantum theory unites the wave and particle description of a bound electron
Consider the classical particle model of the “bead on a wire”
If the electron (particle) has mass m and speed v
The kinetic energy of the moving electron is
The De Broglie relation connects models (a) and (b)
The electron energy is quantized because it depends on the integer n
The lowest energy allowed is for n=1 or E=h2/8mL2 (the energy cannot be zero)
Electrons trapped on a wire have some residual kinetic energy, just like electrons trapped in atoms
The wave that corresponds to the electron is called a wave function
The amplitude of the wave function at a given point can be related to the probability of finding the electron there
According to quantum mechanics there are regions of the wire where the electrons will not be found
Regions of zero wave function amplitude are called nodes
It is generally true that the more nodes an electron has, the higher its energy
Erwin Schrödinger was the first to successfully apply the concept of the wave nature of matter to electronic structure
He developed an equation that can be solved to give wave functions and energy levels for electrons trapped in them
Wave functions for electrons in atoms are called orbitals
Orbitals are characterized by a set of three quantum numbers:
n = principle quantum number. All orbitals with the save principle quantum number are in the same shell. Allowed values: the set of positive integers.
l = secondary quantum number which divides the orbitals in a shell into smaller groups called subshells. Allowed values: from 0 to (n – 1).
ml = magnetic quantum number which divides the subshells into individual orbitals. Allowed values: integers from –l to +l.
The approximate energies of the subshells in an atom with more than one electron:
Electrons behave like tiny magnets
Electrons within atoms interact with a magnet field in one of two ways:
Electron spin is important in determining electronic structure
According to the Pauli exclusion principle no two electrons in the same atom can have identical values for all four quantum numbers
Thus two electron can occupy the same orbital only if they have opposite spin and are said to be paired
A substance with more spin in one direction is said to contain unpaired electrons
Substances with unpaired electrons are slightly attracted to a magnet and are called paramagnetic
Substances in which all electrons are paired are called diamagnetic
The distribution of electrons among the orbitals of an atom is called the electronic structure or electronic configuration
To indicate the ground state electron configuration we can:
List the subshells that contain electrons and indicate their electron population with a superscript.
Represent each orbital with a circle and use arrows to indicate the spin of each electron.
Electron configurations must be consistent with the Pauli principle, aufbau principle, and Hund’s rule
Example: N 1s22s22p3, Na 1s22s22p63s1
Electron configurations explain the structure of the periodic table
There are few important exceptions to the “expected” electronic figurations of commonly encountered elements
Following the rules for Cr, Cu, Ag, and Au using noble gas notation:
Apparently, half-filled and filled subshells are particularly stable
Similar irregularities occur among the lanthanide and actinide elements
The position of an electrons must be described with probabilities
Heisenberg’s uncertainty principle says that it is impossible to measure with complete precision the velocity and position of a particle simultaneously

These limitations are not important for large objects but are very important for small particles like electrons
Quantum mechanics requires that we talk about the probability of finding an electron in a particular region of space
This probability is often represented as an electron cloud about the nucleus
The probability varies with distance from the nucleus
This type of plot shows that electron density varies from place to place
Electron density variations define the shape, size, and orientation of orbitals
p orbitals are quite different from s orbitals
They posses a nodial plane which includes the nucleus and separates the “lobes” of high probability
Recall that there are three different orbitals in each p subshell
The shape and orientation of d orbitals are more complicated than for p orbitals
Shape and directional properties of the five d orbitals in a d subshell.
The f orbitals are even more complex than the d orbital
The amount of positive charge “felt” by outer electrons in atoms other than hydrogen is called the effective nuclear charge
It is lower than the atomic number because of shielding
The effective nuclear charge felt by outer electrons is determined primarily by the difference between the charge on the nucleus and the charge on the core
Effective nuclear charge controls a number of properties
Atomic size increases top to bottom in a group because of increasing n and gets smaller left to right in a groups because the effective nuclear charge increases
Variation in atomic and ionic radii. Values in picometers (10-12 m)
The size trends in ions can be summarized:
Positive ions are always smaller than the atoms they are formed
Negative ions always larger than the atoms from which they are formed
Ionization energy (IE) is the energy required to remove an electron from an isolated, gaseous atom
Successive ionizations are possible until no electrons remain
The trends in IE are the opposite of the trends in atomic size
The electron affinity (EA) is the potential energy change associated with the addition of an electron to a gaseous atom or ion in its ground state
The addition of one electron to a neutral atom is exothermic for nearly all atoms
The addition of more electrons requires energy
Consider the addition of electrons to oxygen:
The results for first electron affinities can be generalized
In general:
EA increases from left to right in a period
EA increases bottom to top in a group

Energy and Chemical Change

Energy is the ability to do work and supply heat
Work is motion against an opposing force
Kinetic energy is the energy an object has because of its motion
For an object of mass m with velocity v
The law of conservation of energy states that energy cannot be created or destroyed
This can be applied to the collision of two particles with only kinetic energy
Potential energy (PE) is the energy of position or internal arrangement
KE can be converted into PE and vice versa
Work is required to pull the negatively charged electron away from the positively charged nucleus
The gain and loss of PE can be summarized
Pushing or pulling an object against an opposing force requires energy. The objects PE will rise.
When the opposing force is not resisted, the object’s PE falls
The SI unit of energy is the joule (J)
A 2 kg object moving at 1 meter per second has 1 J of kinetic energy
You may also encounter the calorie (cal)
The dietary Calorie (note capital), Cal, is actually 1 kilocalorie
When a cold and hot object come into contact, they eventually reach thermal equilibrium (the same temperature)
The energy that is transferred as heat comes from the object’s internal energy
The energy associated with the motion of the object’s molecules is referred to as its molecular kinetic energy
The internal energy is often given the symbol E or U
We are interested in the change in E:
The internal energy change is positive if the system absorbs energy from the surroundings and negative if it releases energy to its surroundings
The temperature of an object is related to the average kinetic energy of its atoms and molecules
Heat is a transfer of energy due to a temperature difference
Isolated warm (left) and cold (right) objects
Thermal contact is made: thermal energy is transferred from left to right
Thermal equilibrium: the same average KE for molecules in both objects
The energy of an object depends only on its current condition
The current condition is called the state
Internal energy is a state function because it is a measure of energy
An important property of state functions is that they are independent from the mechanism or method by which a change occurred
The object we are interested in is called the system
Everything outside the system is called the surroundings
A boundary separates the system from the surroundings
The system and surroundings together are called the universe
Systems are classified according to what can cross its boundary
Open systems can gain or lose mass and energy across their boundaries
Closed systems can absorb or release energy, but not mass, across their boundaries
Isolated systems cannot exchange energy or matter with their surroundings
Consider heat flowing between the system and surroundings
The sign of the heat change is used to say whether it was gained or lost
When heat is gained by an object, it is written as a positive number
When heat is lost by an object, it is written as a negative number
A spontaneous change is one that continues on its own
Heat flows spontaneously from a warmer to colder object
The heat directly gained or lost by an object is directly proportional to the temperature change it undergoes
The object’s specific heat (C) relates the heat (q) to the objects temperature change
The heat capacity is the amount of heat needed to raise the object’s temperature by one degree Celsius and has the units J/°C
C is an extensive property that can be determined from experiment, and is proportional to the sample mass
The specific heat capacity (s) is an intensive property, and is unique for each substance
For example
Example: The temperature of 251 g of water is changed from 25.0 to 30.0 °C. How much heat was transferred to the water?
ANALYSIS: Connect heat to the temperature change.
SOLUTION:
Note: Heat was absorbed because q is positive
Chemical bonds are the net attractive force between nuclei and electrons in compounds
Breaking a chemical bond requires energy
Making a chemical bond releases energy
The potential energy that resides in chemical bonds is called chemical energy
Chemical reactions generally involve both making and breaking chemical bonds
The net gain or loss of energy is often in the form of heat
Any reaction where heat is a product is called exothermic
Reactions that consume energy are called endothermic
Reactions can release heat by replacing “weak” bonds with “strong” ones
The amount of heat absorbed or released by a chemical reaction is called the heat of reaction
A calorimeter can be used to measure the heat of reaction
Calorimeters are usually designed to measure heats of reaction under conditions of constant volume or constant pressure
Pressure is the amount of force acting on a unit area:
Atmospheric pressure is the pressure exerted by the mixture of gases in the atmosphere
At sea level the atmospheric pressure is about 14.7 lb/in²
Other common pressure units are the atmosphere (atm) and bar:
14.696 lb/in² = 1.0000 atm = 1.0133 bar
qv and qp are used to show heats measured at constant volume or pressure, respectfully
In reactions where gases are produce or consumed qv and qp can be very different
If the volume change is , work (w) is
Note that the work of expansion is negative
Work and heat are alternate ways to transfer energy
Their sum is the change in internal energy the system undergoes
This is a statement of the first law of thermodynamics, which says that energy cannot be created or destroyed
Heat and work are not state functions because they depend on the path between the final and initial state
The heat produced by a combustion reaction is called the heat of combustion
The heats are measured in closed containers because the reactions consume and produce gases
The instrument used to measure these heats is called a bomb calorimeter
The reaction is run at constant volume so that
Heats of reactions in solution are usually run in open containers at constant pressure
They may transfer heat and expansion work
The heat change measured at constant pressure is the enthalpy, H
Enthalpy is also a state function
is negative for an exothermic process
is positive for an endothermic process
The the difference in the values of the internal energy and enthalpy change can be large for reactions that consume or release gases
The amount of heat that a reaction produces or absorbs depends on the number of moles of reactant that react
A set of standard states have been defined for reporting heats of reactions
Standard thermodynamic states are: 1 bar pressure for all gases and 1 M concentration for aqueous solutions
A temperature of 25 °C (298 K) is often specified as well
The standard heat of reaction is the value of the enthalpy change occurring under standard conditions involving the actual number of moles specified the the equation coefficients
An enthalpy change for standard conditions is denoted
For example, the thermochemical equation for the production of ammonia from it elements at standard conditions is:
The physical states are important
The law of conservation of energy requires
Enthalpy is a state function
An enthalpy diagram is a graphical representation of alternate paths between initial and final states
Remember to include the physical states of reactants and products in thermochemical equations.
Enthalpy changes for reactions can be calculated by algebraic summation
This is called Hess’s Law: The value of the enthalpy change for any reaction that can be written in steps equals the sum of the values of the enthalpy change of each of the individual steps.
Enthalpy changes for a huge number of reactions may be calculate using only a few simple rules
Rules for Manipulating Thermochemical Equations:
When an equation is reversed the sign of the enthalpy change must also be reversed.
Formulas canceled from both sides of an equation must be for substances in identical physical states.
If all the coefficients of an equation are multiplied or divided by the same factor, the value of the enthalpy change must likewise be multiplied or divided by that factor.
An enormous database of thermochemical equations have been compiled:
The standard heat of combustion is the amount of heat released when 1 mol of a fuel completely burns in pure oxygen gas with all products brought to 25 °C and 1 bar
Standard heats of combustion are always negative and produce water in liquid form
The standard enthalpy of formation of a substance is the amount of heat absorbed when 1 mole of the substance if formed at 25 °C and 1 bar from its elements in their standard states
The standard enthalpy of formation for elements in their standard states are zero
These are the values most commonly used to calculated standard enthalpy changes for reactions
Standard enthalpies of formation are given in Table 7.2 and Appendix C
Hess’s law can be restated in terms of standard enthalpies of formation:
Example: Calculate the enthalpy of reaction for 2NO(g)+O2(g)2NO2(g)
ANALYSIS: Use Hess’s law and Table 7.2
SOLUTION:

Oxidation-Reduction Reactions

Reactions that involve the transfer of electrons are called oxidation-reduction or redox reactions
Oxidation is the loss of electrons by a reactant
Reduction is the gain of electrons by a reactant
Oxidation and reduction always occur together
The total number of electrons lost by one substance is the same as the total number of electrons gained by the other
For a redox reaction to occur, something must accept the electrons that are lost by another substance
The substance that accepts the electrons is called the oxidizing agent
The substance that lost the electrons is called the reduction agent
Note that the oxidizing agent is reduced and the reducing agent is oxidized
For example:
2 Na + Cl2  2 NaCl
Na is the reducing agent because it lost electrons and was oxidized
Cl2 is the oxidizing agent because it gained electrons and was reduced
Oxidation numbers provide a way to keep track of electron transfers :
The oxidation number of any free element is zero.
The oxidation number of any simple, monoatomic ion is equal to the charge on the ion.
The sum of all oxidation numbers of the atoms in a molecule or polyatomic ion must equal the charge on the particle.
In its compounds, fluorine has an oxidation number of –1.
In its compounds, hydrogen has an oxidation number of +1.
In its compounds, oxygen has an oxidation number of –2.
If there is a conflict between two rules apply the rule with the lower number and ignore the conflicting rule
In binary ionic compounds with metals, the nonmetals have oxidation numbers equal to the charges on their anions
Example: What is the oxidation number of Fe in Fe2O3?
ANALYSIS: This binary compound is ionic. Apply rule 3 and 6
Fe: 2x
O: 3(-2) = -6
0 = 2x + (-6) or x = +3 = ox. number of Fe
Note that fractional values of oxidation numbers are allowed
In terms of oxidation numbers:
Oxidation is an increase in oxidation number
Reduction is a decrease in oxidation number
This provides a simple way to follow redox reactions
Many redox reactions take place in aqueous solution
A procedure called the ion-electron method provides a way to balance these equations
The oxidation and reduction are divided into equations called half-reactions
The half-reactions are balanced separately, then combined into the fully balanced net ionic equation
Both mass and charge must be balanced
Charge is balanced by adding electrons to the side of the equation that is more positive or less negative
Example: Balance the following skeleton equation
Many reactions occur in either acidic or basic solutions
The Ion-Electron Method in Acidic Solution:
Divide the equation into two half-reactions.
Balance atoms other than H and O.
Balance O by adding water.
Balance H by adding hydrogen ion.
Balance net charge by adding electrons.
Make electron gain and loss equal: add half-reactions.
Cancel anything that’s the same on both sides of the equation.
The simplest way to balance reactions in basic solution is to first balance them as if they were in acidic solution, then “convert” to basic solution:
Additional Steps for Basic Solutions
Example: Balance the following in basic solution:
Metals more active than hydrogen (H2) dissolve in oxidizing acids
Some examples:
More active metals will displace a less active metal from its compound
This often occurs in solution and is called a single replacement reaction
An activity series arranges metals according to their ease of oxidation
They can be used to predict reactions
Activity Series for Some Metals and Hydrogen
A given element will be displaced from its compounds by any element below it in the table
Oxygen reacts with many substances
The products depends, in part, on how much oxygen is available
Combustion of hydrocarbons
Organic compounds containing O also produce carbon dioxide and water
Organic compounds containing S produce sulfur dioxide
Many metals corrode or tarnish when exposed to oxygen
Most nonmetals react with oxygen directly
Redox reactions are more complicated than most metathesis reactions
In general, it is not possible to balance a redox reaction by inspection
This is especially true when acid or bases are involved in the reaction
Once balanced, they can be used for stoichiometric calculations
Redox titrations are common because they often involve dramatic color changes
Mole-to-mole ratios are usually involved
Example: A 0.3000 g sample of tin ore was dissolved in acid solution converting all the tin to tin(II). In a titration, 8.08 mL of 0.0500 M KMnO4 was required to oxidize the tin(II) to tin(IV). What was the percentage tin in the original sample?
ANALYSIS: This is a redox titration in acidic solution.
SOLUTION:
Form skeleton equation and use the ion-electron method to produce a balanced equation
Use the balanced equation to define equivalence relations and determine the mass of Sn in the original sample
Convert to percentage

Reactions Between Ions in Aqueous Solution

A solution is a homogeneous mixture in which the two or more components mix freely
The solvent is taken as the component present in the largest amount
A solute is any substance dissolved in the solvent
For example, the percentage concentration is the number of grams of solute per 100 g of solution
The relative amounts of solute and solvent are often given without specifying the actual quantities
There is usually a limit to the amount of solute that can dissolve in a given amount of solvent
For example, 36.0 g NaCl is able to dissolve in 100 g of water at 20°C
A solution is said to be saturated when no more solute can be dissolved at the current temperature
The solubility of a solute is the number of grams of solute that can dissolve in 100 grams of solvent at a given temperature
Solubilities of some common substances
Solubility usually increases with temperature
Supersaturated solutions contain more solute than required for saturation at a given temperature
They can be formed, for example, by careful cooling of saturated solutions
Supersaturated solutions are unstable and often result in the formation of a precipitate
A precipitate is the solid substance that separates from solution
Precipitates can also form from reactions
Reactions that produce a precipitate are called precipitation reactions
Many ionic compounds dissolve in water
Solutes that produce ions in solution are called electrolytes because their solutions can conduct electricity
An ionic compounds dissociates as it dissolves in water
Most solutions of molecular compounds do not conduct electricity and are called nonelectrolytes
The dissociation of ionic compounds may be described with chemical equations
The hydrated ions, with the symbol (aq), have been written separately
Since physical states are often omitted, you might encounter the equation as:
Ionic compounds often react when their aqueous solutions combine
This reaction may be represented with a molecular, ionic, or net ionic equation:
Molecular:
Ionic:
Net Ionic:
The most compact notation is the net ionic equation which eliminates all the non-reacting spectator ions from the equation
Criteria for balanced ionic and net ionic equations:
Material balance – the same number of each type of atom on each side of the arrow
Electrical balance – the net electrical charge on the left side of the arrow must equal the net electrical charge on the right side of the arrow
In the reaction of Pb(NO3)2 with KI the cations and anions changed partners
This is an example of a metathesis or double replacement reaction
Solubility rules allows the prediction of when a precipitation reaction will occur
For many ionic compounds the solubility rules correctly predict whether the ionic compound is soluble or insoluble
Solubility rules for ionic compounds in water:
Soluble Compounds
Insoluble compounds
A knowledge of these rules will allow you to predict a large number of precipitation reactions
Acids and bases are another important class of compounds
Acids and bases affect the color of certain natural dye substances
They are called acid-base indicators because they indicate the presence of acids or bases with their color
The first comprehensive theory of acids, bases, and electrical conductivity appeared in 1884 in the Ph.D. thesis of Savante Arrhenius
He proposed that acids form hydrogen ions and bases released hydroxide ions in solution
The characteristic reaction between acids and bases is neutralization
HCl(aq) + NaOH(aq)  NaCl(aq) + H2O(l)
In general, the reaction of an acid and a base produces water and a salt
We can state the Arrhenius definition of acids and bases in updated form
In general, acids are molecular compounds that react with water to produce ions
This is called ionization:
It is common to encounter the hydrogen ion (H+) instead of the hydronium ion
The previous ionization is also written as
Monoprotic acids are capable of furnishing only one hydrogen ion per molecule
Acids that can furnish more than one hydrogen ion per molecule are called polyprotic acids
Some nonmetal oxides react with water to produce acids
They are called acidic anhydrides (anhydride means without water)
Soluble metal oxides are base anhydrides
Examples include:
Ammonia gas ionizes in water producing hydroxide ions
It is an example of a molecular base
Many molecules that contain nitrogen can act as a base
Binary compounds of many nonmetals and hydrogen are acidic
In water solution these are referred to as binary acids
They are named by adding the prefix hydro- and the suffix –ic to the stem of the nonmetal name, followed by the word acid
Acids that contain hydrogen, oxygen, plus another element are called oxoacids
They are named according to the number of oxygen atoms in the molecule and do not take the prefix hydro-
When there are two oxoacids, the one with the larger number of oxygens takes the suffix –ic and the one with the fewer oxygen atoms takes the suffix –ous
The halogen can occur with up to four different oxoacids
The oxoacid with the most oxygens has the prefix per- the one with the least has the prefix hypo-
Anions are produced when oxoacids are neutralized
There is a simple relationship between the name of the polyatomic ion and the parent acid
–ic acids give –ate ions
-ous acids give –ite ions
In naming polyatomic anions, the prefixes per- and hypo- carry over from the parent acid
Polyprotic acids can be neutralized
An acidic salt contains an anion that is capable of furnishing additional hydrogen ions
The number of hydrogens that can still be neutralized is also indicated
Naming bases is much less complicated
Ionic compounds containing metal ions are named like any other ionic compound
Molecular bases are specified by giving the name of the molecule
Acids and bases can be classified as strong or weak and so as strong or weak electrolytes
Strong acids are strong electrolytes
The most common strong acids are:
Strong bases are the soluble metal hydroxides
These include:
Most acids are not completely ionized in water
They are classified as weak electrolytes
Weak acids and bases are in dynamic equilibrium in solution
Consider the case of acetic acid:
Neutralization of a strong acid with strong base gives a salt and water:
This net ionic equation applies only to strong acids and bases
The neutralization of a weak acid with a strong base involves a strong and weak electrolyte
Consider the neutralization of acetic acid with NaOH:
Note that in ionic equations the formulas of weak electrolytes are written in “molecular” form
The situation is similar when a strong acid reacts with a strong base
For ammonia and HCl the net ionic equation is:
Note that water only appears as a product if the hydronium ion is used
Both strong and weak acids react with insoluble hydroxides and oxides
The driving force is the formation of water
Magnesium hydroxide has a low solubility in water, but reacts with strong acid
The net ionic equation is:
Magnesium hydroxide is written as a solid because it is insoluble
A number of metal oxides also dissolve in acids
For example, iron(III) oxide reacts with hydrochloric acid:
Some reactions with acids or bases produce a gas
The reactions are driven to completion because the gas escapes and is unavailable for back reaction
(CO2 and SO2 are produced by the decomposition of H2CO3 and H2SO3, respectfully)
Solutions are characterized by their concentration
The molar concentration or molarity (M) is defined as
The molarity of a solution gives an equivalence relation between the moles of solute and volume of solution
Solutions provide a convenient way to combine reactants in many chemical reactions
Example: How many grams of AgNO3 are needed to prepare 250 mL of 0.0125 M AgNO3 solution?
ANALYSIS: Find moles, then mass of solute.
SOLUTION:
Solutions of high concentration can be diluted to make solutions of lower concentration
Conservation of solute mass requires:
Where dil labels the diluted and concd the concentrated solution
Stoichiometry problems often require working with volumes and molarity
Example: How many mL of 0.124 M NaOH are required to react completely with 15.4 mL of 0.108 M H2SO4?
2 NaOH + H2SO4  Na2SO4 + 2H2O
ANALYSIS: Use the mole-to-mole ratio to convert.
SOLUTION:
Limiting reagent problems are also common
Example: How many moles of BaSO4 will form if 20.0 mL of 0.600 M BaCl2 is mixed with 30.0 mL of 0.500 M MgSO4?
BaCl2 + MgSO4  BaSO4 + MgCl2
ANALYSIS: This is a limiting reagent problem.
SOLUTION:
Titration is a technique used to make quantitative measurements of the amounts of solutions
The end-point is often determined visually
Paths for working stoichiometry problems may be summarized with a flowchart:

The Mole

Atomic mass provides a means to count atoms by measuring the mass of a sample
The periodic table on the inside cover of the text gives atomic masses of the elements
The mass of an atom is called its atomic mass
When using atomic masses, retain a sufficient number of significant figures so the atomic mass data contributes only slightly to the uncertainty of the result
The molecular mass allows counting of molecules by mass
The molecular mass is the sum of atomic masses of the atoms in the compounds formula
For example the molar mass of water, H2O, is twice the mass of hydrogen (1.008) plus the mass of oxygen (15.999) = 18.015
Strictly speaking, ionic compounds do not have a “molecular mass” because they don’t contain molecules
The mass of the formula unit is called the formula mass
Formula masses are calculated the same way as molecular masses
For example the formula mass of calcium oxide, CaO, is the mass of calcium (40.08) plus the mass of oxygen (15.999) = 56.08
One mole of a substance contains the same number of formula units as the number of atoms in exactly 12 g of carbon-12
One mole of a substance has a mass in grams numerically equal to its formula mass
The mass of one mole of a substance is also called its molar mass
One mole of any substance contains the same number of formula units
This number is called Avogadro’s number or constant
Counting formula units by moles is no different than counting eggs by the dozen (12 eggs) or pens by the gross (144 pens)
Avogadro’s number is huge because atoms and molecules are so small: a huge number of them are needed to make a lab-sized sample
Avogadro’s number links moles and atoms, or moles and molecules and provides an easy way to link mass and atoms or molecules
Using water (molar mass 18.015) as an example:
1 mole H2O  6.022 x 1023 molecules H2O
1 mole H2O  18.015 g H2O
18.015 g H2O  6.022 x 1023 molecules H2O
Within chemical compounds, moles of atoms always combine in the same ratio as the individual atoms themselves so:
1 mole H2O  2 mole H
1 mole H2O  1 mole O
Stoichiometry is the study of the mass relationships in chemical compounds and reactions
A common use for stoichiometry is to relate the masses of reactants needed to make a compound
These calculations can be solved using the factor-label method and equivalence relations relating molecular masses and/or formula masses
Example: How many grams of iron are in a 15.0 g sample of iron(III) oxide?
ANALYSIS: 15.0 g Fe2O3  ? g Fe
LINKS: 1 mol Fe2O3  2 mol Fe
1 mol Fe2O3  159.7 g Fe2O3
1 mol Fe  55.85 g Fe
SOLUTION:
The usual form for describing the relative masses of the elements in a compound is a list of percentages by mass
This is called the percentage composition or percentage composition by mass
The percentage by mass is the number of grams of the element in 100 g of the compound and can be calculated using:
Example: A sample was analyzed and found to contain 0.1417 g nitrogen and 0.4045 g oxygen. What is the percentage composition of this compound?
ANALYSIS: Find sample mass and calculate %
LINKS: whole sample = 0.5462 g
SOLUTION:
Hydrogen peroxide consists of molecules with the formula H2O2
This is called the molecular formula
The simplest formula for hydrogen peroxide is HO and is called the empirical formula
It is possible to calculate the empirical formula for a compound from mass data
The goal is to produce the simplest whole number mole ratio between atoms
Example: A 2.012 g sample of a compound contains 0.522 g of nitrogen and 1.490 g of oxygen. Calculate its empirical formula
ANALYSIS: We need the simplest whole number mole ratio between nitrogen and oxygen
SOLUTION:
Empirical formulas may also be calculated indirectly
When a compound made only from carbon, hydrogen, and oxygen burns completely in pure oxygen only carbon dioxide and water are produced
This is called combustion
Empirical formulas may be calculated from the analysis of combustion information
Example: The combustion of a 5.217 g sample of a compound of C, H, and O gave 7.406 g CO2 and 4.512 g of H2O. Calculate the empirical formula of the compound.
ANALYSIS: This is a multi-step problem. The mass of oxygen is obtained by difference:
g O = 5.217 g sample – ( g C + g H )
The masses of the elements may then by used to calculate the empirical formula of the compound
SOLUTION:
The formula for ionic compounds is the same as the empirical formula
For molecules, the molecular formula and empirical are usually different
If the experimental molecular mass is available, the empirical formula can be converted into the molecular
The molecular formula will be a common multiplier times all the coefficients in the empirical formula
Example: The empirical formula of hydrazine is NH2, and its molecular mass is 32.0. What is its molecular formula?
ANALYSIS: The molecular mass (32.0) is some simple multiple of the mass calculated from the empirical formula (16.03)
SOLUTION:
The coefficients of a balanced chemical equation provide the mole-to-mole ratios for the substances involved in the reaction
Whenever a problem asks you to convert between different substances, the calculation usually involves a mole-to-mole relationship
How to detect unbalanced equations will be covered shortly
Example: If 0.575 mole of CO2 is produced by the combustion of propane, C3H8, how many moles of oxygen are consumed? The balanced equation is:
C3H8 + 5 O2  3 CO2 + 4 H2O
ANALYSIS: Relating two compounds usually requires a mole-to-mole ratio
SOLUTION:
In many problems you will also need to perform one or more mole-to-mass conversions
These types of stoichiometry problems are summarized with the flowchart:
Example: How many grams of Al2O3 are produced when 41.5 g Al react?
2Al(s) + Fe2O3(s)  Al2O3(s) + 2 Fe(l)
ANALYSIS:
41.5 g Al  ? g Al2O3
SOLUTION:
Chemical equations provide quantitative descriptions of chemical reactions
Conservation of mass is the basis for balancing equations
To balance an equation:
Write the unbalanced equation
Adjust the coefficients to get equal numbers of each kind of atom on both sides of the arrow
Guidelines for Balancing Equations:
Balance elements other than H and O first
Balance as a group any polyatomic ions that appears unchanged on both sides of the arrow
Balance separately those elements that appear somewhere by themselves
As a general rule you should use the smallest whole-number coefficients when writing balanced chemical equations
All reactions eventually use up a reactant and stop
The reactant that is consumed first is called the limiting reactant because it limits the amount of product that can form
Any reagent that is not completely consumed during the reactions is said to be in excess and is called an excess reactant
The computed amount of product is always based on the limiting reagent
Example: How many grams of NO can form when 30.0 g NH3 and 40.0 g O2 react according to:
4 NH3 + 5 O2  4 NO + 6 H2O
ANALYSIS: This is a limiting reactant problem
SOLUTION:
The amount of product isolated from a chemical reactions is almost always less than the calculated, or maximum, amount
The actual yield is the amount of the desired product isolated
The theoretical yield is the amount that would be recovered if no loss occurred (the calculated, maximum amount)
The percentage yield is the actual yield as a percentage of the theoretical yield
When working with percentage yield:
Remember they involve a measured (actual yield) and calculated (theoretical yield) quantity
The calculation may be done in either grams or moles
The result can never be a number larger than 100%

Measurement

Observations can be qualitative or quantitative
Qualitative observations are non-numerical, they ask “what”
Quantitative observations are numerical, they ask “how much”
Quantitative observations are also called measurements
Measurements:
Always involve a comparison
Require units
Involve numbers that are inexact (numbers in mathematics are exact)
Include uncertainty due to the inherent physical limitations of the observer and the instruments used (to make the measurement)
Uncertainty is also called error
Chemists use SI units for measurements
All SI units are based on a set of seven measured base units:
Derived units involve a combination of base units, including:
Base units are frequently to large or small for a measurement
Decimal multipliers are used to adjust the size of base units, including
You may encounter non-SI metric system units, including:
English and Metric units are related using conversion factors
To measure volumes in the laboratory, one might use one of these:
Mass is determined by weighing the object using a balance
Temperature is measured in degrees Celsius or Fahrenheit using a thermometer
The difference between a measurement and the “true” value we are attempting to measure is called the error
Errors are due to limitations inherent in the measurement procedure
In science, all digits in a measurement up to and including the first estimated digit are recorded
These digits are called significant digits or significant figures
The number of significant digits in a measurement may be increased by using a more precise instrument
Errors arise from a number of sources including:
Reading scales incorrectly
Using the measuring device incorrectly
Due to thermal expansion or contraction (temperature changes)
Errors can often be detected by making repeated measurements
The central value can be estimated by reporting the average or mean
Accuracy and precision are terms used to describe a collection of repeated measurements
An accurate measurement is close to the true or correct value
A precise measurement is close to the average of a series of repeated measurements
When calibrated instruments are used properly, the greater the number of significant figures, the greater is the degree of precision for a given measurement
Nonzero digits in a measured number are always significant
Zeros must be considered more carefully:
Zeros between significant digits are significant
Zeros to the right of the decimal point are always counted as significant
Zeros to the left of the first nonzero digit are never counted as significant
Zeros at the end of a number without a decimal point are assumed not to be significant
Confusion can be avoided by representing measurement in scientific or exponential notation
Scientific notation is reviewed on the web site at www.wiley.com/college/brady
When measurements are expressed in scientific notation to the correct number of significant digits, the number of digits written is the same regardless of the units used to express the measurement
Measurements limit the precision of the results calculated from them
Rules for combining measurements depend on the type of operation performed:
Multiplication and division
The number of significant figures in the answer should not be greater than the number of significant figures in the least precise measurement.
Addition and Subtraction
The answer should have the same number of decimal places as the quantity with the fewest number of decimal places
The factor-label method, or dimensional analysis, can be used to help perform the correct arithmetic to solve a problem
This involves treating a numerical problem as one involving a conversion from one kind of units to another
This is done using one or more conversion factors to change the units of the given quantity to the units of the answer
A conversion factor is a fraction formed from a valid relationship or equality between units
Conversion factors are used to switch from one system of measure to another
Example: Convert 72.0 in. to cm using the equality 1 in. = 2.54 cm (exactly).
Density (d) is an intensive property defined as the ratio of an objects mass (m) to volume (v), d = m/v
Each pure substance has its own characteristic density
At room temperature:
Most substances expand when heated
This means density depends on temperature
For water:
Density relates a samples mass and volume
Blood has a density of 1.05 g/cm3
We can say that 1.05 g blood is equivalent to 1.00 cm3
Conversion factors can be constructed from this equivalence, which could be used in the factor-label method
The numerical value for the density of a substance depends on the units used for mass and volume
The specific gravity is defined as the ratio of the density of the substance to the density of water :
The specific gravity of a substance:
Is less than one for substances less dense than water
Is greater than one for substances more dense than water
Is independent of units
In order to rely on measured properties of substances, reliable measurements must be made
The accuracy and precision of measured results allow us to estimate their reliability
To trust conclusions drawn from measurements, the measurements must be accurate and of sufficient precision
This is a key consideration when designing experiments