CHEM 101: TEST 2 - Ch.4, Ch. 5

Note that a forward-and-backward double arrow (⇌) is used in the dissociation equation to indicate that the reaction takes place simultaneously in both directions. That is, dissociation is a dynamic process in which an equilibrium is established between the forward and reverse reactions. Dissociation of acetic acid takes place in the forward direction, while recombination of H+ and CH3CO2− ions takes place in the reverse direction. The size of the equilibrium arrow indicates whether the equilibrium reaction forms mostly products or mostly reactants. Ultimately, the concentrations of the reactants and products reach constant values and no longer change with time. We'll learn much more about chemical equilibria in Chapter 15.

A chemical equilibrium, as we'll see in Chapter 15, is the state in which a reaction takes place in both forward and backward directions so that the concentrations of products and reactants remain constant over time.

A compound is soluble if it meets either (or both) of the following criteria:

A compound is soluble if it contains one of the following cations: Li+, Na+, K+, Rb+, Cs+ (group 1A cations) NH+4 (ammonium ion) That is, essentially all ionic compounds containing an alkali metal cation or ammonium cation are soluble in water and will not precipitate, regardless of the anions present. A compound is soluble if it contains one of the following anions: Cl−, Br−, I− (halide) except: Ag+, Hg2+2 and Pb2+ halides NO−3 (nitrate), ClO−4 (perchlorate), CH3CO−2 (acetate), and SO2−4 (sulfate) except: Sr2+, Ba2+, Hg2+2 and Pb2+ sulfates That is, most ionic compounds containing a halide, nitrate, perchlorate, acetate, or sulfate anion are soluble in water and will not precipitate regardless of the cations present. The exceptions that will precipitate are silver(I), mercury(I) and lead(II) halides and strontium, barium, mercury(I), and lead(II) sulfates. On the other hand, a compound that does not contain one of the cations or anions listed above is not soluble. Thus, carbonates (CO32−) sulfides (S2−) phosphates (PO43−) and hydroxides (OH−) are generally not soluble unless they contain an alkali metal or ammonium cation. The main exceptions are the sulfides and hydroxides of Ca2+, Sr2+ and Ba2+.

The success of the Bohr model was that it was able to explain the line spectrum observed for hydrogen. Each orbit has its own radius, referred to as n, which is directly related to energy. As the radius increases, the energy also increases. Thus, n=2 has greater energy than n=1 and n=3 has greater energy than n=2, and so on. In Bohr's model, there is no change in energy when an electron moves within its orbit, but when an electron falls into a lower orbit, it emits a photon whose energy equals the difference in the energies of the two orbits (Figure 5.10).

ΔE=Efinal−Einitial=hv

When an acid and a base are mixed in the right stoichiometric proportions, both acidic and basic properties disappear because of a neutralization reaction that produces water and an ionic salt. The anion of the salt (A−) comes from the acid, and the cation of the salt (M+) comes from the base: HA(aq) acid + MOH(aq) base --> H2O(l) water + MA(aq) salt

Because salts are generally strong electrolytes in aqueous solution, we can write the neutralization reaction of a strong acid with a strong base as an ionic equation: H+(aq)+A−(aq)+M+(aq)+OH−(aq)→H2O(l)+M+(aq)+A−(aq) Canceling the ions that appear on both sides of the ionic equation, A− and M+ gives the net ionic equation, which describes the reaction of any strong acid with any strong base in water. Net Ionic Equation orH+(aq)+OH−(aq)→H2O(l)H3O+(aq)+OH−(aq)→2 H2O(l) For the reaction of a weak acid with a strong base, a similar neutralization occurs, but we must write the molecular formula of the acid rather than simply H+(aq) because the dissociation of the acid in water is incomplete. Instead, the acid exists primarily as the neutral molecule. In the reaction of the weak acid HF with the strong base KOH, for example, we write the net ionic equation as HF(aq)+OH−(aq)→H2O(l)+F−(aq)

Higher frequencies and shorter wavelengths correspond to higher-energy radiation, while lower frequencies and longer wavelengths correspond to lower energy.

Blue light (λ≈450 nm) for instance, has a shorter wavelength and is more energetic than red light (λ≈650 nm). Similarly, an X ray (λ≈1 nm) has a shorter wavelength and is more energetic than an FM radio wave (λ≈1010 nm, or 10 m). If the frequency (or energy) of the photon striking a metal is below a minimum value, no electron is ejected. Above the threshold level, however, sufficient energy is transferred from the photon to an electron to overcome the attractive forces holding the electron to the metal (Figure 5.7). The amount of energy necessary to eject an electron is called the work function (Φ) of the metal and is lowest for the group 1A and group 2A elements. That is, elements on the left side of the periodic table hold their electrons less tightly than other metals and lose them more readily (Table 5.1). The greater the frequency, the greater the number of electrons ejected. Greater even for higher intensity light than lower intensity.

Redox reactions take place with every element in the periodic table except helium and neon and occur in a vast number of processes throughout nature, biology, and industry. Here are just a few examples:

Combustion. Combustion is the burning of a fuel by oxidation with oxygen in air. Gasoline, fuel oil, natural gas, wood, paper, and other organic substances of carbon and hydrogen are the most common fuels. Even some metals, such as magnesium and calcium, will burn in air. CH4(g)Methane(Natural gas)+2 O2(g)→CO2(g)+2 H2O(l) Bleaching. Bleaching uses redox reactions to decolorize or lighten colored materials. Dark hair is bleached to turn it blond, clothes are bleached to remove stains, wood pulp is bleached to make white paper, and so on. The exact oxidizing agent used depends on the situation—hydrogen peroxide (H2O2) is used for hair, sodium hypochlorite (NaOCl) is used for clothes, and ozone or chlorine dioxide is used for wood pulp—but the principle is always the same. In all cases, colored impurities are destroyed by reaction with a strong oxidizing agent. Batteries. Although they come in many types and sizes, all types of batteries are powered by redox reactions. In a typical redox reaction carried out in the laboratory— say, the reaction of zinc metal with Ag+ to yield Zn2+ and silver metal—the reactants are simply mixed in a flask and electrons are transferred by direct contact between them. In a battery, however, the two reactants are kept in separate compartments and the electrons are transferred through a wire running between them. The inexpensive alkaline battery commonly used in flashlights and other small household items uses a thin steel can containing zinc powder and a paste of potassium hydroxide as one reactant, separated by paper from a paste of powdered carbon and manganese dioxide as the other reactant. A graphite rod with a metal cap sticks into the MnO2 to provide electrical contact. When the can and the graphite rod are connected by a wire, zinc sends electrons flowing through the wire toward the MnO2 in a redox reaction. The resultant electrical current can be used to light a bulb or power a small electronic device. The reaction is Zn(s)+2 MnO2(s)→ZnO(s)+Mn2O3(s) Metallurgy. Metallurgy, the extraction and purification of metals from their ores, makes use of numerous redox processes. Metallic zinc is prepared by reduction of ZnO with coke, a form of carbon: ZnO(s)+C(s)→Zn(s)+CO(g) Corrosion. Corrosion is the deterioration of a metal by oxidation, such as the rusting of iron in moist air. The economic consequences of rusting are enormous: It has been estimated that up to one-fourth of the iron produced in the United States is used to replace bridges, buildings, and other structures that have been destroyed by corrosion. (The raised dot in the formula Fe2O3⋅H2O for rust indicates that one water molecule is associated with each Fe2O3 in an unspecified way.) 4 Fe(s)+3 O2(g)−→H2O2 Fe2O3Rust⋅H2O(s) Respiration. The term respiration refers to the processes of breathing and using oxygen for the many biological redox reactions that provide the energy needed by living organisms. The energy is released from food molecules slowly and in complex, multi-step pathways, but the overall result of respiration is similar to that of a combustion reaction. For example, the simple sugar glucose (C6H12O6) reacts with O2 to give CO2 and H2O according to the following equation: C6H12O6Glucose(a carbohydrate)+6 O2→6 CO2+6 H2O+energy

Since we cannot observe visible light traveling as a wave with our eyes, you may be wondering how we know that radiant energy has wave properties. Scientists have performed experiments testing for the presence of physical phenomena exhibited by waves, such as diffraction and interference.

Diffraction is the bending of a light wave around an object, as shown in Figure 5.4a. Interference occurs when two or more waves superpose to form a new wave, as shown in Figure 5.4b. Constructive interference occurs when two waves of the same frequency are in phase with the crests and troughs aligned. The sum of the amplitudes of both waves at each point gives a new wave with the same frequency but larger amplitude. Destructive interference occurs when two waves of the same frequency are out of phase. The crest from one wave is aligned with the trough from the other wave. The sum of the amplitude of each wave at each point gives a new wave with zero amplitude.

Flow Diagram for Acid Base Titration

For the balanced equation: NaOH + HCl --> NaCl + H2O Given volume of NaOH use the molarity of NaOH as a conversion factor to find moles of NaOH, then use the coefficients in the balanced equation to find mole ratios to find moles of HCl, and then divide by the volume of HCl to find the molarity of HCl.

Using molarity as a conversion factor between moles and volume in stoichiometry calculations.

For the balanced equation: aA + bB --> cC + dD Given Volume of solution A Use molarity as a conversion factor to find moles of A Use coefficients in the balanced equation to find the A: B mole ratio to find moles of B needed Use molarity as a conversion factor to find the volume of solution pf B

In the early 1800s, Thomas Young (1773-1829) demonstrated that light consists of waves in an experiment known as the "double-slit" experiment (Figure 5.5).

If light waves of a single wavelength are in phase and directed at a plate with two parallel slits, an interference pattern is observed on a detector on the other side. When light waves pass through the two slits, they are diffracted; the diffracted waves interfere constructively to produce bright bands and destructively to produce dark bands at the detector. The wave properties of light cause the observed interference pattern of bright and dark bands. We will see in Section 5.4 that particles such as high-speed electrons also exhibit wave properties in a similar double-slit experiment.

As noted earlier in this section, the energy levels of different orbitals in a hydrogen atom depend only on the principal quantum number n, but the energy levels of orbitals in multielectron atoms depend on both n and l.

In other words, the orbitals in a given shell all have the same energy for hydrogen but have slightly different energies for other atoms, depending on their subshell. In fact, there is even some crossover of energies between one shell and another. A 3d orbital in some multielectron atoms has a higher energy than a 4s orbital, for instance.

Many common chemical reactions that take place in aqueous solution fall into one of three general categories: precipitation reactions, acid-base neutralization reactions, and oxidation-reduction reactions.

In precipitation reactions, soluble ionic reactants (strong electrolytes) yield an insoluble solid product called a precipitate, which falls out of the solution, thereby removing some of the dissolved ions. Most precipitations take place when the anions and cations of two ionic compounds change partners. In acid-base neutralization reactions, an acid reacts with a base to yield water plus an ionic compound called a salt. Acids are compounds that produce H+ ions when dissolved in water, and bases are compounds that produce OH− ions when dissolved in water. Thus, a neutralization reaction removes H+ and OH− ions from solution, just as a precipitation reaction removes metal and nonmetal ions. In oxidation-reduction reactions, or redox reactions, one or more electrons are transferred between reaction partners (atoms, molecules, or ions). As a result of this electron transfer, the charges on atoms in the various reactants change.

Molarity can be used as a conversion factor to relate a solution's volume to the number of moles of solute. If we know the molarity and volume of a solution, we can calculate the number of moles of solute. If we know the number of moles of solute and the molarity of the solution, we can find the solution's volume.

Molarity = Moles of solute/Volume of solution(L) Moles of solute = Molarity x Volume of solution Volume of solution = Moles of solution/Molarity

Thus, the most useful means of expressing a solution's concentration is molarity (M), the number of moles of a substance, or solute, dissolved in enough solvent to make 1 liter of solution.

Molarity(M)=Moles of solute/Liters of solution Note that it's the final volume of the solution that's important, not the starting volume of the solvent used. The final volume of the solution might be a bit larger than the volume of the solvent because of the additional volume of the solute. In practice, a solution of known molarity is prepared by weighing an appropriate amount of solute and placing it in a container called a volumetric flask, as shown in Figure 4.1. Enough solvent is added to dissolve the solute, and further solvent is added until an accurately calibrated final volume is reached. The solution is then gently mixed to reach a uniform concentration.

The main thing to remember when diluting a concentrated solution is that the number of moles of solute is constant; only the volume of the solution is changed by adding more solvent. Because the number of moles of solute can be calculated by multiplying molarity times volume, we can set up the following equation:

Moles of solute (constant) = Molarity x Volume = M1V1 = M2V2 where Mi is the initial molarity, Vi is the initial volume, Mf is the final molarity, and Vf is the final volume after dilution. Rearranging this equation into a more useful form shows that the molar concentration after dilution (Mf) can be found by multiplying the initial concentration (Mi) by the ratio of initial and final volumes (Vi/Vf) M2=M1xV1/V2

Substances such as NaCl or KBr, which dissolve in water to produce conducting solutions of ions, are called electrolytes. Substances such as sucrose or ethyl alcohol, which do not produce ions in aqueous solution, are nonelectrolytes.

Most electrolytes are ionic compounds, but some are molecular. Hydrogen chloride, for instance, is a gaseous molecular compound when pure but dissociates, or splits apart, to give H+ and Cl− ions when it dissolves in water.

Note that pure water is a nonelectrolyte because it does not dissociate appreciably into H+ and OH− ions.

Strong Electrolytes HCl, HBr, HI HClO4 HNO3 H2SO4 KBr NaCl NaOH, KOH Other soluble ionic compounds Weak Electrolytes CH3CO2H HF HCN Nonelectrolytes H2O CH3OH C2H5OH C12H22O11 Most compounds of carbon *organic*

Electromagnetic energy traveling through a vacuum behaves in some ways like ocean waves traveling through water. Like ocean waves, electromagnetic energy is characterized by a frequency, a wavelength, and an amplitude. If you could stand in one place and look at a sideways, cutaway view of an ocean wave moving through the water, you would see a regular rise-and-fall pattern like that in Figure 5.3. *Know Image*

The frequency (v, Greek nu) of a wave is simply the number of wave peaks that pass by a given point per unit time, usually expressed in units of reciprocal seconds, or hertz (Hz; 1 Hz=1 s−1). The wavelength (λ, Greek lambda) of the wave is the distance from one wave peak to the next, and the amplitude of the wave is the height of the wave, measured from the center line between peak and trough. Physically, what we perceive as the intensity of electromagnetic energy is proportional to the square of the wave amplitude. A faint beam and a blinding glare of light may have the same wavelength and frequency, but they differ greatly in amplitude.

In summary, within any given shell, a lower value of the angular-momentum quantum number l corresponds to a higher Zeff and to a lower energy for the electron.

The idea that electrons in different orbitals are shielded differently and feel different values of Zeff is a very useful one to which we'll return on several occasions to explain various chemical phenomena. Orbital type: ns np nd nf <-- Attraction to nucleus, Zeff --> Energy

Most acids are oxoacids; that is, they contain oxygen in addition to hydrogen and other elements. When dissolved in water, an oxoacid yields one or more H+ ions and an oxoanion like one of those listed in Table 4.4 and discussed previously in Section 2.13. Oxoanions are polyatomic anions in which an atom of a given element is combined with different numbers of oxygen atoms.

The names of oxoacids are related to the names of the corresponding oxoanions, with the -ite or -ate ending of the anion name replaced by -ous acid or -ic acid, respectively. In other words, the acid with fewer oxygens has an -ous ending, and the acid with more oxygens has an -ic ending. In addition to the oxoacids, there are a small number of other common acids, such as HCl, that do not contain oxygen. For such compounds, the prefix hydro- and the suffix -ic acid are used for the aqueous solution.

The volume to be diluted is withdrawn using a calibrated tube called a pipet, placed in an empty volumetric flask of the chosen volume, and diluted to the calibration mark on the flask.

The one common exception to this order of steps is when diluting a strong acid such as H2SO4 where a large amount of heat is released. In such instances, it is much safer to add the acid slowly to the water rather than adding water to the acid.

That white light actually consists of a spectrum of many colors of light is made evident when a narrow beam of white light is passed through a glass prism to produce a "rainbow" of colors (Figure 5.8a).

This happens because the different wavelengths contained in white light travel through the glass at different speeds. The prism separates the white light into its component colors, ranging from red at the long-wavelength end of the spectrum (780 nm) to violet at the short-wavelength end (380 nm). This separation into colors also occurs when light travels through water droplets in the air, forming a rainbow, or through oriented ice crystals in clouds, causing a parhelion, or sundog (Figure 5.8b).

You might notice that most of the ions that impart solubility to compounds are singly charged—either singly positive (Li+, Na+, K+, Rb+, Cs+, NH4+) or singly negative (Cl−, Br−, I−, NO3−, ClO4−, CH3CO2−). Very few doubly charged ions or triply charged ions form soluble compounds.

This solubility behavior arises because of the relatively strong ionic bonds in compounds containing ions with multiple charges. The greater the strength of the ionic bonds holding ions together in a crystal, the more difficult it is to break those bonds apart during the solution process.

Multiplying the wavelength of a wave in meters (m) by its frequency in reciprocal seconds (s−1) gives the speed of the wave in meters per second (m/s). The rate of travel of all electromagnetic energy in a vacuum is a constant value, commonly called the speed of light and abbreviated c. Its numerical value is defined as exactly 2.997 924 58×108 m/s, usually rounded off to 3.00×108 m/s:

Wavelength×Frequency=Speedλ(m)×v(s−1)=c(m/s) which can be rewritten as λ=c/v or v=c/λ This equation says that frequency and wavelength are inversely related: Electromagnetic energy with a longer wavelength has a lower frequency, and energy with a shorter wavelength has a higher frequency. Worked Example 5.1 demonstrates how to convert between the wavelength and frequency of electromagnetic radiation.

De Broglie suggested that a similar equation might be applied to moving particles like electrons by replacing the speed of light, c, by the speed of the particle, v. The resultant de Broglie equation allows calculation of a "wavelength" of an electron or of any other particle or object of mass m moving at velocity v:

de Broglie equation λ=h/mv We know that electrons are tiny particles with a mass of 9.11×10−31 kg. If electrons behave as particles, they would also produce a pattern of two strips after passing through a barrier with two slits (Figure 5.11a). However, when a beam of electrons is directed at two slits, an interference pattern of bright and dark bands appears on the detector and resembles the interference pattern obtained with light waves (Figure 5.11b). Recall from Section 5.1 that when a light ray was directed at a double slit, an interference pattern was observed as a result of constructive and destructive interference of diffracted light waves. The image produced from directing a beam of electrons at a double slit is shown in Figure 5.11c. Observations from the double-slit experiment support the theory that subatomic particles such as electrons exhibit wave properties.

We all know that both sugar (sucrose) and table salt (NaCl) dissolve in water. The solutions that result, though, are quite different. When sucrose, a molecular substance, dissolves in water, the resulting solution contains neutral sucrose molecules surrounded by water. When NaCl, an ionic substance, dissolves in water, the solution contains separate Na+ and Cl− ions surrounded by water. Because of the presence of the charged ions, the NaCl solution conducts an electric current, but the sucrose solution does not.

A molecule is a unit of matter that results when two or more nonmetal atoms are joined by covalent bonds in which electrons are shared. An ionic substance is formed when a metal and nonmetal atom form an ionic bond in which electrons are transferred from the metal to the nonmetal to form ions. The electrical conductivity of an aqueous NaCl solution is easy to demonstrate using a battery, a light bulb, and several pieces of wire, connected as shown in Figure 4.3. When the wires are dipped into an aqueous NaCl solution, the positively charged Na+ ions move through the solution toward the wire connected to the negatively charged terminal of the battery, and the negatively charged Cl− ions move toward the wire connected to the positively charged terminal of the battery. The resulting movement of electrical charges allows a current to flow, so the bulb lights. When the wires are dipped into an aqueous sucrose solution, however, there are no ions to carry the current, so the bulb remains dark.

Solubility Table for Ionic Compounds in Water

Soluble Li, Na, K, Rb, Cs NH4 Cl, Br, I except Ag, Hg2, Pb NO3 ClO4 CH3CO2 SO4 except Sr, Ba, Hg2, Pb Insoluble Compounds CO3 except carbonates of group 1A cations, NH4 S except sulfides of group 1A cations, NH4, Ca, Sr, Ba PO4 except phosphates of group 1A cations, NH4 OH except hydroxides of group 1A cations, NH4, Ca, Sr, Ba

All the parts are now in place to provide an electronic description for every element. Knowing the relative energies of the various orbitals, we can predict for each element which orbitals are occupied by electrons—the element's electron configuration.

A set of three rules called the aufbau principle, from the German word for "building up," guides the filling order of orbitals. In general, each successive electron added to an atom occupies the lowest-energy orbital available. The resultant lowest-energy configuration is called the ground-state electron configuration of the atom. Often, several orbitals will have the same energy level—for example, the three p orbitals or the five d orbitals in a given subshell. Orbitals that have the same energy level are said to be degenerate. Rules of the Aufbau Principle: Lower-energy orbitals fill before higher-energy orbitals. 1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p An orbital can hold only two electrons, which must have opposite spins. If two or more degenerate orbitals are available, one electron goes into each until all are half-full, a statement called Hund's rule (If two or more orbitals with the same energy are available, one electron goes in each until all are half full. The value of the spin quantum number of electrons in the half-filled orbitals will be the same.)

We saw in Section 4.9 that the concentration of an acid or base solution can be determined by titration. A measured volume of the acid or base solution of unknown concentration is placed in a flask, and a base or acid solution of known concentration is slowly added from a buret. By measuring the volume of the added solution necessary for a complete reaction, as signaled by the color change of an indicator, the unknown concentration can be calculated. Remember . . . The reaction used for a titration must go to completion and have a yield of 100%

A similar procedure can be carried out to determine the concentration of many oxidizing or reducing agents using a redox titration. All that's necessary is that the substance whose concentration you want to determine undergo an oxidation or reduction reaction in 100% yield and that there be some means, such as a color change, to indicate when the reaction is complete. The color change might be due to one of the substances undergoing reaction or to some added indicator. Let's imagine that we have a potassium permanganate solution whose concentration we want to find. Aqueous KMnO4 reacts with oxalic acid, H2C2O4, in acidic solution according to the following net ionic equation (K+ is a spectator ion): 5 H2C2O4(aq)+2 MnO4−(aq)+6 H+(aq)→10 CO2(g)+2 Mn2+(aq)+8 H2O(l) The reaction goes to completion with 100% yield and is accompanied by a sharp color change when the intense purple color of the MnO4− ion disappears. The strategy used is outlined in Figure 4.9. As with acid—base titrations, the general idea is to measure a known amount of one substance—in this case, H2C2O4—and use mole ratios from the balanced equation to find the number of moles of the second substance—in this case, KMnO4—necessary for complete reaction. With the molar amount of KMnO4 thus known, titration gives the volume of solution containing that amount. Dividing the number of moles by the volume gives the concentration.

To understand how the answer slowly emerged, it's necessary to look first at the nature of visible light and other forms of radiant energy. Spectroscopy, the study of the interaction of radiant energy with matter, has provided immense insight into atomic structure.

Although they appear quite different to our senses, visible light, infrared radiation, microwaves, radio waves, and X rays are all different forms of electromagnetic radiation or radiant energy. Collectively, they make up the electromagnetic spectrum, shown in Figure 5.2. *Make sure to know the little picture with the wavelengths and frequencies...*

The rules for assigning oxidation numbers are as follows:

An atom in its elemental state has an oxidation number of 0. An atom in a monatomic ion has an oxidation number identical to its charge. Review Section 2.13 to see the charges on some common ions. An atom in a polyatomic ion or in a molecular compound usually has the same oxidation number it would have if it were a monatomic ion. - In general, the farther left an element is in the periodic table, the more probable that it will be cationlike. Metals, therefore, usually have positive oxidation numbers. The farther right an element is in the periodic table, the more probable that it will be anionlike. Nonmetals, such as O, N, and the halogens, usually have negative oxidation numbers. ----Hydrogen can be either +1 or −1. When bonded to a metal, such as Na or Ca, hydrogen has an oxidation number of −1 When bonded to a nonmetal, such as C, N, O, or Cl, hydrogen has an oxidation number of +1. ----Oxygen usually has an oxidation number of −2 The major exception is in compounds called peroxides, which contain either the O22− ion or an O—O covalent bond in a molecule. Both oxygen atoms in a peroxide have an oxidation number of −1. ----Halogens usually have an oxidation number of −1. The major exception is in compounds of chlorine, bromine, or iodine in which the halogen atom is bonded to oxygen. In such cases, the oxygen has an oxidation number of −2, and the halogen has a positive oxidation number. In Cl2O, for instance, the O atom has an oxidation number of −2, and each Cl atom has an oxidation number of +1. The sum of the oxidation numbers is 0 for a neutral compound and is equal to the net charge for a polyatomic ion. This rule is particularly useful for finding the oxidation number of an atom in difficult cases. The general idea is to assign oxidation numbers to the "easy" atoms first and then find the oxidation number of the "difficult" atom by subtraction.

s Orbitals

As described in Section 5.6, wave functions (ψ), or orbitals, are solutions to the wave equation and predict the allowed energy states of the electron. The square of the wave function (ψ2) is the probability of finding an electron in a given region of space. Figure 5.13a represents ψ2 using dots in an electron density plot for a 1s orbital. The higher concentration of dots near the nucleus corresponds to a greater probability of finding the electron. Note that all s orbitals are spherical, meaning the probability of finding an electron in an s orbital depends only on the distance from the nucleus and not on the direction. The value of electron density (ψ2) for a 1s orbital is greatest near the nucleus and drops off as the distance (r) from the nucleus increases (Figure 5.13b). Although the electron density is greatest close to the nucleus, the radial distribution plot (Figure 5.13c) more accurately represents the probability of finding the electron in a thin shell at any given distance (r) from the nucleus. The radial probability function is the electron density (ψ2) times the surface area of a sphere with radius (r). At the nucleus, the surface area of the sphere is zero because r=0 and surface area=4πr2. As r increases, the radial probability function increases because the increase in surface area of the sphere outweighs the decrease in electron density. At even larger values of r, the radial probability function decreases due to the exponential decrease of electron density, which now outweighs the increase in surface area. As shown in Figure 5.13b, the value of ψ2 for an s orbital is greatest near the nucleus and then drops off rapidly as the distance from the nucleus increases, although it never goes all the way to zero, even at a large distance. As a result, there is no definite boundary to the atom and no definite size. For purposes like that of Figure 5.15, however, we usually imagine a boundary surface enclosing the volume where an electron has a 90% chance of being found. Although all s orbitals are spherical, there are significant differences among the s orbitals in different shells. For one thing, the size of the s orbital increases in successively higher shells, implying that an electron in an outer-shell s orbital is farther from the nucleus on average than an electron in an inner-shell s orbital. For another thing, the electron distribution in an outer-shell s orbital has more than one region of high probability. As shown in Figure 5.15, a 2s orbital is essentially a sphere within a sphere and has two regions of high probability, separated by a surface of zero probability called a node. Similarly, a 3s orbital has three regions of high probability and two spherical nodes. The concept of an orbital node—a surface of zero electron probability separating regions of nonzero probability—is difficult to grasp because it raises the question "How does an electron get from one region of the orbital to another if it's not allowed to be at the node?" The question is misleading, though, because it assumes particlelike behavior for the electron rather than wavelike behavior. In fact, nodes are an intrinsic property of waves, from moving waves of water in the ocean to the stationary, or standing, wave generated by vibrating a rope or guitar string (Figure 5.16). A node simply corresponds to the zero-amplitude part of the wave. On either side of the node is a nonzero wave amplitude. Note that a wave has two phases—peaks above the zero line and troughs below—corresponding to different algebraic signs, + and −. Similarly, the different regions of 2s and 3s orbitals have different phases, + and −, as indicated in Figure 5.15 by different colors. Another way to visualize differences in the 1s, 2s, and 3s orbitals in the hydrogen atom is to examine the radial probability plots shown in Figure 5.17. The 1s orbital has a maximum in its radial probability function at a smaller r value than the maximum in the 2s orbital. This means that, on average, an electron in a 1s orbital spends more time closer to the nucleus than an electron in a 2s orbital. Similarly, the maximum in the radial probability for the 2s orbital is at a smaller r value than the maximum for the 3s orbital, meaning the electron in the 2s orbital has a greater probability of being closer to the nucleus than an electron is a 3s orbital. The radial probability plots for the s orbitals show that increasing the n level increases the size of the orbital. Larger orbitals are higher in energy than smaller orbitals because the electron has a greater probability of being further from the nucleus and it requires energy to separate a positive and negative charge. Orbital size and energy:1s<2s<3s The presence of nodes in the 2s and 3s orbitals shown in Figure 5.15 is also evident in the radial probability plots. The 2s orbital has radial probability of zero at a distance of just over 100 pm from the nucleus corresponding to a node. The 3s orbital has two nodes shown by a radial probability of zero near 100 pm and 375 pm.

Soon after the discovery that energetic atoms emit light of specific wavelengths, chemists began cataloging the line spectra of various elements. They rapidly found that each element has its own unique spectral "signature," and they began using the results to identify the elements present in minerals and other substances.

As often happens in science, experimental results are obtained before a theory to explain them is developed. The discovery of atomic line spectra was made decades before a theory of atomic structure to explain the spectra was developed. During the time period 1900-1911, scientists conducted key experiments and developed new theories that helped to solve the puzzle of line spectra. Among them were Planck's postulate of quantized energy (1900), Einstein's concept of photons and the photoelectric effect (1905), and Rutherford's nuclear model of the atom (1911). Building upon these seminal discoveries, Niels Bohr (1885-1962), a Danish physicist working in Rutherford's lab, proposed an atomic model that predicted the existence of line spectra. His model of the hydrogen atom described a small, positively charged nucleus with an electron circling around it, much as a planet orbits the Sun. Bohr postulated that the energy levels of the orbits are quantized so that only certain specific orbits corresponding to certain specific energies for the electron are available. You might think of the quantized nature of orbits in terms of an analogy: climbing stairs versus a ramp. The height of a ramp changes continuously, but stairs change height only in discrete amounts; the height reached by climbing each stair is thus quantized.

Common Acids and Bases Strong to Weak

HClO4 H2SO4 HBr HCl HNO3 H3PO4 HF HNO2 CH3COOH KOH NaOH Ba(OH)2 Ca(OH)2 NH3

Electron configurations are normally represented by listing the n quantum number and the s, p, d, or f designation of the occupied orbitals, beginning with the lowest energy one, and with the number of electrons occupying each orbital indicated as a superscript. Let's look at some examples to see how the rules of the aufbau principle are applied.

Hydrogen: Hydrogen has only one electron, which must go into the lowest-energy, 1s orbital. Thus, the ground-state electron configuration of hydrogen is 1s1. H: 1s1 Helium: Helium has two electrons, both of which fit into the lowest-energy 1s orbital. The two electrons have opposite spins. H: 1s2 Lithium and beryllium: With the 1s orbital full, the third and fourth electrons go into the next available orbital, 2s. Li: 1s2 2s1Be: 1s2 2s2 Boron through neon: In the six elements from boron through neon, electrons fill the three 2p orbitals successively. Because these three 2p orbitals have the same energy, they are degenerate and are thus filled according to Hund's rule. In carbon, for instance, the two 2p electrons occupy different orbitals, which can be arbitrarily specified as 2px,2py, or 2pz when writing the electron configuration. The same is true of nitrogen, whose three 2p electrons must be in three different orbitals. Per Hund's rule, the electrons in each of the singly occupied carbon and nitrogen 2p orbitals must have the same value of the spin quantum number—either +1/2 or −1/2 —but this is not usually noted in the written electron configuration. For clarity, we sometimes specify electron configurations using orbital-filling diagrams, in which electrons are represented by arrows. The two values of the spin quantum numbers are indicated by having the arrow point either up or down. An up-down pair indicates that an orbital is filled, while a single up (or down) arrow indicates that an orbital is half filled. Note in the diagrams for carbon and nitrogen that the degenerate 2p orbitals are half filled rather than filled, according to Hund's rule, and that the electron spin is the same in each.From oxygen through neon, the three 2p orbitals are successively filled. For fluorine and neon, it's no longer necessary to distinguish among the different 2p orbitals, so we can simply write 2p5 and 2p6. Sodium and magnesium: The 3s orbital is filled next, giving sodium and magnesium the ground-state electron configurations shown. Note that we often write the configurations in a shorthand version by giving the symbol of the noble gas in the previous row to indicate electrons in filled shells and then specifying only those electrons in partially filled shells. Aluminum through argon: The 3p orbitals are filled according to the same rules used previously for filling the 2p orbitals of boron through neon. Rather than explicitly identify which of the degenerate 3p orbitals are occupied in Si, P, and S, we'll simplify the writing by giving just the total number of electrons in the subshell. For example, we'll write 3p2 for silicon rather than 3p1x 3p1y. Elements past argon: Following the filling of the 3p subshell in argon, the first crossover in the orbital filling order is encountered. Rather than continue filling the third shell by populating the 3d orbitals, the next two electrons in potassium and calcium go into the 4s subshell. Only then does filling of the 3d subshell occur to give the first transition metal series from scandium through zinc.

Although the Bohr model was very successful in accounting for the line spectrum of hydrogen, it suffered from several limitations.

It failed to predict the spectrum of any atom other than hydrogen and only works for one-electron species such as H, He+, or Li2+. If more than one electron exists, interactions such as electron-electron repulsions must be accounted for in a more complex model. It does not give an accurate depiction of electron location. Electrons do not move in fixed, defined orbits. In fact, we can never know the precise location of an electron in the atom and can only define probabilities of an electron existing within a given volume of space. However, the fundamental idea of quantized energy levels for the electron was an important theory for which Bohr was awarded the Nobel Prize in Physics in 1922. The next several sections will expand on Bohr's ideas and further describe the modern model for electrons in an atom.

Approximately 71% of the Earth's surface is covered by water, and another 3% is covered by ice; 66% of the mass of an adult human body is water, and water is needed to sustain all living organisms.

It's therefore not surprising that a large amount of important chemistry, including all those reactions that happen in our bodies, takes place in water—that is, in aqueous solution.

Einstein explained the photoelectric effect by assuming that a beam of light behaves as if it were a stream of small particles, called photons, whose energy (E) is related to their frequency, v (or wavelength, λ) by an equation called Planck's postulate after the German physicist Max Planck (1858-1947).

Planck's postulate E=hv=hc/λ The proportionality constant h represents a fundamental physical constant that we now call Planck's constant and that has the value h=6.626×10−34 J⋅s. For example, one photon of red light with a frequency v=4.62×1014s−1(wavelength λ=649 nm) has an energy of 3.06×10−19 J. [Recall from Section 1.8 that the SI unit for energy is the joule (J), where 1J=1(kg⋅m2)/s2.] E=hv=(6.626×10−34 J⋅s)(4.62×1014 s−1)=3.06×10−19 J It's often convenient to express electromagnetic energy on a per-mole basis rather than a per-photon basis. Multiplying the per-photon energy of 3.06×10−19 J by Avogadro's number gives an energy of 184 kJ/mol.

To do that, you must know the solubility of each potential product—how much of each compound will dissolve in a given amount of solvent at a given temperature. If a substance has a high solubility in water, no precipitate will form. If a substance has a low solubility in water, it's likely to precipitate from an aqueous solution.

Solubility is a continuum with some substances having a high solubility and others having a low solubility. In this section, we will define a substance as soluble if it dissolves to give a concentration of 0.01 M or greater. Solubility can be predicted by looking at the cations and anions that make up the compound.

Compounds that dissociate to a large extent (70-100%) into ions when dissolved in water are said to be strong electrolytes, while compounds that dissociate to only a small extent are weak electrolytes.

Potassium chloride and most other ionic compounds, for instance, are largely dissociated in dilute solution and are thus strong electrolytes. Acetic acid (CH3CO2H), by contrast, dissociates only to the extent of about 1.3% in a 0.10 M solution and is a weak electrolyte. As a result, a 0.10 M solution of acetic acid is only weakly conducting, and the bulb in Figure 4.3 would only light dimly.

oxidation and reduction reactions, called half-reactions, always occur together. A redox reaction consists of two half-reactions; one oxidation half-reaction and one reduction half-reaction. Whenever one atom loses one or more electrons, another atom must gain those electrons. The substance that causes a reduction by giving up electrons—the iron atom in the reaction of Fe with O2 and the carbon atom in the reaction of C with Fe2O3—is called a reducing agent. The substance that causes an oxidation by accepting electrons—the oxygen atom in the reaction of Fe with O2 and the iron atom in the reaction of C with Fe2O3—is called an oxidizing agent. The reducing agent is itself oxidized when it gives up electrons, and the oxidizing agent is itself reduced when it accepts electrons.

Reducing agent - causes reduction, loses one or more electrons, undergoes oxidation, oxidation number of atoms increases Oxidizing agent - causes oxidation, gains one or more electrons, undergoes reduction, oxidation number of atom decreases redox reactions are common for almost every element in the periodic table except for the noble-gas elements of group 8A. In general, metals give up electrons and act as reducing agents, while reactive nonmetals such as O2 and the halogens accept electrons and act as oxidizing agents. Different metals can give up different numbers of electrons in redox reactions. Lithium, sodium, and the other group 1A elements give up only one electron and become monopositive ions with oxidation numbers of +1 Beryllium, magnesium, and the other group 2A elements, however, typically give up two electrons and become dipositive ions. The transition metals in the middle of the periodic table can give up a variable number of electrons to yield more than one kind of ion depending on the exact reaction. Titanium, for example, can react with chlorine to yield either TiCl3 or TiCl4. Because a chloride ion has a −1 oxidation number, the titanium atom in TiCl3 must have a +3 oxidation number, and the titanium atom in TiCl4 must be +4.

One important step toward developing a model of atomic structure came in 1905, when Albert Einstein (1879-1955) proposed an explanation of the photoelectric effect.

Scientists had known since the late 1800s that irradiating a clean metal surface with light causes electrons to be ejected from the metal (Figure 5.6). Furthermore, the frequency of the light used for the irradiation must be above some threshold value, which is different for every metal. Blue light (v≈6.5×1014Hz) causes metallic sodium to emit electrons, for example, but red light (v≈4.5×1014Hz) has no effect on sodium.

The analogy between matter and radiant energy developed in the early 1900s was further extended in 1924 by the French physicist Louis de Broglie (1892-1987). De Broglie suggested that if light can behave in some respects like matter, then perhaps matter can behave in some respects like light. That is, perhaps matter is wavelike as well as particlelike. In developing his theory about the wavelike behavior of matter, de Broglie focused on the inverse relationship between energy and wavelength for photons:

SinceE=hc/λthenλ=hc/E Using the famous equation E=mc2 proposed in 1905 by Einstein as part of his special theory of relativity, and substituting for E, then gives λ=hc/E=hc/mc2=h/mc

In 1777, the French chemist Antoine Lavoisier (1743-1794) proposed that all acids contain a common element: oxygen. In fact, the word oxygen is derived from a Greek phrase meaning "acid former." Lavoisier's idea had to be modified, however, when the English chemist Sir Humphrey Davy (1778-1829) showed in 1810 that muriatic acid (now called hydrochloric acid) contains only hydrogen and chlorine but no oxygen. Davy's studies thus suggested that the common element in acids is hydrogen, not oxygen.

Swedish chemist Svante Arrhenius (1859-1927) clarified the relationship between acidic behavior and the presence of hydrogen in a compound in 1887. Arrhenius proposed that an acid is a substance that dissociates in water to give hydrogen ions (H+) and a base is a substance that dissociates in water to give hydroxide ions (OH−). An acid HA(aq)→H+(aq)+A−(aq)A base MOH(aq)→M+(aq)+OH−(aq) In these equations, HA is a general formula for an acid—for example, HCl or HNO3—and MOH is a general formula for a metal hydroxide—for example, NaOH or KOH. Although convenient to use in equations, the symbol H+(aq) does not really represent the structure of the ion present in aqueous solution. As a bare hydrogen nucleus— a proton—with no electron nearby, H+ is much too reactive to exist by itself. Rather, the H+ bonds to the oxygen atom of a water molecule and forms the more stable hydronium ion, H3O+. We'll sometimes write H+(aq) for convenience, particularly when balancing equations, but will more often write H3O+(aq) to represent an aqueous acid solution.

The breakthrough in understanding atomic structure came in 1926, when the Austrian physicist Erwin Schrödinger (1887-1961) proposed what has come to be called the quantum mechanical model of the atom. The fundamental idea behind the model is that it's best to abandon the notion of an electron as a small particle moving around the nucleus in a defined path and to concentrate instead on the electron's wavelike properties. In fact, it was shown in 1927 by Werner Heisenberg (1901-1976) that it is impossible to know precisely where an electron is and what path it follows—a statement called the Heisenberg uncertainty principle.

The Heisenberg uncertainty principle can be understood by imagining what would happen if we tried to determine the position of an electron at a given moment. For us to "see" the electron, light photons of an appropriate frequency would have to interact with and bounce off the electron. But such an interaction would transfer energy from the photon to the electron, thereby increasing the energy of the electron and making it move faster. Thus, the very act of determining the electron's position would make that position change. In mathematical terms, Heisenberg's principle states that the uncertainty in the electron's position, Δx, times the uncertainty in its momentum, Δmv, is equal to or greater than the quantity h/4π: (Δx)(Δmv)≥h/4π According to this equation, we can never know both the position and the velocity of an electron (or of any other object) beyond a certain level of precision. If we know the velocity with a high degree of certainty (Δmv is small), then the position of the electron must be uncertain (Δx must be large). Conversely, if we know the position of the electron exactly (Δx is small), then we can't know its velocity (Δmv must be large). As a result, an electron will always appear as something of a blur whenever we attempt to make any physical measurements of its position and velocity.

Bases, like acids, can also be either strong or weak, depending on the extent to which they produce OH− ions in aqueous solution. Most metal hydroxides, such as NaOH and Ba(OH)2, are strong electrolytes and strong bases.

The dissociation reactions for sodium hydroxide and barium hydroxide are: NaOH(aq)−→Na+(aq)+OH−(aq)Ba(OH)2(aq)−→Ba2+(aq)+2 OH−(aq) Ammonia (NH3) is a weak electrolyte and a weak base. Ammonia is a weak base because it reacts to a small extent with water to yield NH4+ and OH− ions. In fact, aqueous solutions of ammonia are often called ammonium hydroxide, although this is really a misnomer because the concentrations of NH4+ and OH− ions are low. NH3(g)+H2O(l)⇌NH4+(aq)+OH−(aq) As with the dissociation of acetic acid, discussed in Section 4.3, the reaction of ammonia with water takes place only to a small extent (about 1%). Most of the ammonia remains unreacted, and we therefore write the reaction with a double arrow to show that a dynamic equilibrium exists between the forward and reverse reactions.

How does electron shielding lead to energy differences among orbitals within a shell?

The answer is a consequence of the difference in orbital shapes. Compare the shapes of s, p, and d orbitals. The 3s orbital is spherical in shape and has a high electron density near the nucleus, the 3p orbitals are dumbbell shaped with a node at the nucleus, and four of the 3d orbitals are shaped like a cloverleaf with a node at the nucleus. Figure 5.22 shows the radial probability plot for the 3s, 3p, and 3d orbitals. The 3s orbital has a maximum radial probability at a distance further from the nucleus than the maximum in either the 3p or 3d orbital. If on average an electron in a 3s orbital is farther from the nucleus than an electron in a 3p or 3d orbital, we might expect the 3s orbital to be highest in energy. However, the 3s orbital is actually the lowest in energy due to its ability to penetrate closer to the nucleus and into the region occupied by inner electrons. The small bump in the curve for the 3s orbital represents a significant probability of finding the electron closer to the nucleus than in the 3p or 3d orbitals. The effect is that electrons in a 3s orbital are less efficiently shielded by inner electrons than 3p or 3d electrons and experience the highest effective nuclear charge (Zeff). A higher effective nuclear charge corresponds to a lower energy for the electron. Similarly, an electron in a 3p orbital is lower in energy than an electron in a 3d orbital due to its ability to penetrate closer to the nucleus.

As we said in Section 5.6, the energy level of an orbital in a hydrogen atom, which has only one electron, is determined by its principal quantum number n. Within a shell, all hydrogen orbitals have the same energy, independent of their other quantum numbers. For example, in hydrogen the 2s and 2p orbitals have the same energy, and the 3s, 3d, and 3p orbitals have the same energy. The situation is different in multielectron atoms, however, where the energy level of a given orbital depends not only on the shell but also on the subshell. The s, p, d, and f orbitals within a given shell have slightly different energies in a multielectron atom, as shown previously in Figure 5.12. Upon inspection of Figure 5.12, we find that in n=3 for multielectron atoms the ordering of orbital energies is 3s<3p<3d.

The difference in energy between subshells in multielectron atoms results from electron- electron repulsions. In hydrogen, the only electrical interaction is the attraction of the positive nucleus for the negative electron, but in multielectron atoms there are many different interactions. Not only are there the attractions of the nucleus for each electron, there are also the repulsions between every electron and each of its neighbors. The repulsion of outer-shell electrons by inner-shell electrons is particularly important because the outer-shell electrons are pushed farther away from the nucleus and are thus held less tightly. Part of the attraction of the nucleus for an outer electron is thereby canceled, an effect we describe by saying that the outer electrons are shielded from the nucleus by the inner electrons (Figure 5.21). The nuclear charge actually felt by an electron, called the effective nuclear charge, Zeff, is often substantially lower than the actual nuclear charge Z. Effective nuclear charge Zeff=Zactual−Electron shielding

The three quantum numbers n, l, and ml discussed in Section 5.6 define the energy, shape, and spatial orientation of orbitals, but they don't quite tell the whole story. When the line spectra of many multielectron atoms are studied in detail, it turns out that some lines actually occur as very closely spaced pairs. (You can see this pairing if you look closely at the visible spectrum of sodium in Figure 5.9.) Thus, there are more energy levels than simple quantum mechanics predicts, and a fourth quantum number is required. Denoted ms, this fourth quantum number is related to a property called electron spin. In some ways, electrons behave as if they were spinning around an axis, somewhat as the Earth spins daily. This spinning charge gives rise to a tiny magnetic field and to a spin quantum number (ms), which can have either of two values, +1/2 or −1/2 (Figure 5.20). A spin of +1/2 is usually represented by an up arrow (↑⏐), and a spin of −1/2 by a down arrow (⏐↓). Note that the value of ms is independent of the other three quantum numbers, unlike the values of n, l, and ml, which are interrelated.

The importance of the spin quantum number comes when electrons occupy specific orbitals in multielectron atoms. According to the Pauli exclusion principle, proposed in 1925 by the Austrian physicist Wolfgang Pauli (1900-1958), no two electrons in an atom can have the same four quantum numbers. In other words, the set of four quantum numbers associated with an electron acts as a unique "address" for that electron in an atom, and no two electrons can have the same address. Pauli exclusion principle No two electrons in an atom can have the same four quantum numbers. What are the consequences of the Pauli exclusion principle? Electrons that occupy the same orbital have the same three quantum numbers, n, l, and ml. ml. But if they have the same values for n, l, and ml, they must have different values for the fourth quantum number, ms: either ms=+1/2 or ms=−1/2. Thus, an orbital can hold only two electrons, which must have opposite spins.

Note again that the energy of an individual photon depends only on its frequency (or wavelength), not on the intensity of the light beam. The intensity of a light beam is a measure of the number of photons in the beam, whereas frequency is a measure of the energies of those photons. A low-intensity beam of high-energy photons might easily knock a few electrons loose from a metal, but a high-intensity beam of low-energy photons might not be able to knock loose a single electron.

The main conclusion from Einstein's work was that the behavior of light and other forms of electromagnetic energy is more complex than had been formerly believed. In addition to behaving as waves, light energy can also behave as small particles. The idea might seem strange at first but becomes less so if you think of light as analogous to matter. Both are said to be quantized, meaning that both matter and electromagnetic energy occur only in discrete amounts. Just as there can be either 1 or 2 hydrogen atoms but not 1.5 or 1.8, there can be 1 or 2 photons of light but not 1.5 or 1.8. A quantum is the smallest possible unit of a quantity, just like an atom is the smallest possible quantity of an element. The quantum of energy corresponding to one photon of light is almost inconceivably small, just as the amount of matter in one atom is inconceivably small, but the idea is the same. Planck's postulate and Einstein's photons with particlelike properties were a dramatic departure from the laws of classical physics at the time and ultimately led to a revolution in the way that scientists thought about the structure of the atom.

To see why it's called the periodic table, look at the graph of atomic radius versus atomic number in Figure 5.1, which shows a periodic rise-and-fall pattern. Beginning on the left with atomic number 1 (hydrogen), the size of the atoms increases to a maximum at atomic number 3 (lithium), then decreases to a minimum, then increases again to a maximum at atomic number 11 (sodium), and then decreases in a repeating pattern. It turns out that all the maxima occur for atoms of group 1A elements—Li, Na, K, Rb, Cs, and Fr—and that the minima occur for atoms of the group 7A elements—F, Cl, Br, and I.

There's nothing unique about the periodicity of atomic radii shown in Figure 5.1. Any of several dozen other physical or chemical properties could be plotted in a similar way with similar results.

p Orbitals

The p orbitals are dumbbell-shaped rather than spherical, with their electron distribution concentrated in identical lobes on either side of the nucleus and separated by a planar node cutting through the nucleus. As a result, the probability of finding a p electron near the nucleus is zero. The two lobes of a p orbital have different phases, as indicated in Figure 5.18 by different colors. We'll see in Chapter 7 that these phases are crucial for bonding because only lobes of the same phase can interact in forming covalent chemical bonds. There are three allowable values of ml when l=1, so each shell beginning with the second has three p orbitals, which are oriented in space at 90° angles to one another along the three coordinate axes x, y, and z. The three p orbitals in the second shell, for example, are designated 2px,2py, and 2pz. As you might expect, p orbitals in the third and higher shells are larger than those in the second shell and extend farther from the nucleus. Their shape is roughly the same, however.

Why are electron configurations so important, and what do they have to do with the periodic table? The answers emerge when you look closely at Figure 5.24. Focusing only on the electrons in the outermost shell, called the valence shell, all the elements in a given group of the periodic table have similar valence-shell electron configurations (Table 5.3). The group 1A elements, for example, all have an s1 valence-shell configuration; the group 2A elements have an s2 valence-shell configuration; the group 3A elements have an s2 p1 valence-shell configuration; and so on across every group of the periodic table (except for the small number of anomalies). Furthermore, because the valence-shell electrons are outermost and least tightly held, they are the most important for determining an element's properties, thus explaining why the elements in a given group of the periodic table have similar chemical behavior.

The periodic table can be divided into four regions, or blocks, of elements according to the orbitals being filled (Figure 5.25). The group 1A and group 2A elements on the left side of the table are called the s-block elements because they result from the filling of an s orbital, the group 3A-8A elements on the right side of the table are the p-block elements because they result from the filling of p orbitals, the transition metal d-block elements in the middle of the table result from the filling of d orbitals, and the lanthanide/actinide f-block elements detached at the bottom of the table result from the filling of f orbitals. Thinking of the periodic table as outlined in Figure 5.25 provides a useful way to remember the order of orbital filling. Beginning at the top left corner of the periodic table and going across successive rows gives the correct orbital-filling order. The first row of the periodic table, for instance, contains only the two s-block elements H and He, so the first available s orbital (1s) is filled first. The second row begins with two s-block elements (Li and Be) and continues with six p-block elements (B through Ne), so the next available s orbital (2s) and then the first available p orbitals (2p) are filled. Moving similarly across the third row, the 3s and 3p orbitals are filled. The fourth row again starts with two s-block elements (K and Ca) but is then followed by 10 d-block elements (Sc through Zn) and six p-block elements (Ga through Kr). Thus, the order of orbital filling is 4s followed by the first available d orbitals (3d) followed by 4p. Continuing through successive rows of the periodic table gives the entire filling order: 1s→2s→2p→3s→3p→4s→3d→4p→5s→4d→5p→6s→4f→5d→6p→7s→5f→6d→7p

The equations we've been writing up to this point have all been molecular equations. That is, all the substances involved in the reactions have been written using their complete formulas as if they were molecules.

The physical state of a substance in a chemical reaction is often indicated with a parenthetical state abbreviation (s) for solid, (l) for liquid, (g) for gas, and (aq) for aqueous solution (Section 3.3). A Molecular Equation This equation implies that molecules are interacting. It is the case, however, that lead nitrate, potassium iodide, and potassium nitrate are strong electrolytes that dissolve in water to yield solutions of ions. Thus, it's more accurate to write the precipitation reaction as an ionic equation, in which all the ions are explicitly shown. An Ionic Equation This ionic equation shows that the NO3− and K+ ions undergo no change during the reaction. Instead, they appear on both sides of the reaction arrow and act merely as spectator ions, whose only role is to balance the charge. A Net Ionic Equation A net ionic equation gives only the species that react (the Pb2+ and I− ions in this instance) because spectator ions are canceled from both sides of the equation. Leaving the spectator ions out of a net ionic equation doesn't mean that their presence is irrelevant. If a reaction occurs by mixing a solution of Pb2+ ions with a solution of I− ions, then those solutions must also contain additional ions to balance the charge in each. That is, the Pb2+ solution must also contain an anion, and the I− solution must also contain a cation. Leaving these other ions out of the net ionic equation only implies that these ions do not undergo a chemical reaction. Any nonreactive spectator ion could serve to balance charge.

The guidelines discussed in the previous section for determining ground-state electron configurations work well but are not completely accurate. A careful look at Figure 5.24 shows that 90 electron configurations are correctly accounted for by the rules but that 21 of the predicted configurations are incorrect.

The reasons for the anomalies often have to do with the unusual stability of both half-filled and fully filled subshells. Chromium, for example, which we would predict to have the configuration 4s23d4, actually has the configuration [Ar]4s1 3d5. By moving an electron from the 4s orbital to an energetically similar 3d orbital, chromium trades one filled subshell (4s2) for two half-filled subshells (4s1 3d5), thereby allowing the two electrons to be farther apart. In the same way, copper, which we would predict to have the configuration [Ar]4s2 3d9, actually has the configuration [Ar]4s1 3d10. By transferring an electron from the 4s orbital to a 3d orbital, copper trades one filled subshell (4s2) for a different filled subshell (3d10) and gains a half-filled subshell (4s1). Most of the anomalous electron configurations shown in Figure 5.24 occur in elements with atomic numbers greater than Z=40, where the energy differences between subshells are small. In all cases, the transfer of an electron from one subshell to another lowers the total energy of the atom because of a decrease in electron—electron repulsions.

d and f Orbitals

The third and higher shells each contain five d orbitals, which differ from their s and p counterparts because they have two different shapes. Four of the five d orbitals are cloverleaf-shaped and have four lobes of maximum electron probability separated by two nodal planes through the nucleus (Figure 5.19a-d). The fifth d orbital is similar in shape to a pz orbital but has an additional donut-shaped region of electron probability centered in the xy plane (Figure 5.19e). In spite of their different shapes, all five d orbitals in a given shell have the same energy. As with p orbitals, alternating lobes of the d orbitals have different phases. You've probably noticed that both the number of nodal planes through the nucleus and the overall geometric complexity of the orbitals increases with the l quantum number of the subshell: An s orbital has one lobe and no nodal plane through the nucleus; a p orbital has two lobes and one nodal plane; and a d orbital has four lobes and two nodal planes. The seven f orbitals are more complex still, having eight lobes of maximum electron probability separated by three nodal planes through the nucleus. (Figure 5.19f shows one of the seven 4f orbitals.) Most of the elements we'll deal with in the following chapters don't use f orbitals in bonding, however, so we won't spend time on them.

A technique frequently used for determining a solution's exact molarity is called a titration.

Titration is a procedure for determining the concentration of a solution by allowing a measured volume of that solution to react with a second solution of another substance (the standard solution) whose concentration is known. By finding the volume of the standard solution that reacts with the measured volume of the first solution, the concentration of the first solution can be calculated. (It's necessary, though, that the reaction go to completion and have a yield of 100%.) To see how titration works, let's imagine that we have an HCl solution (an acid) whose concentration we want to find by allowing it to react with NaOH (a base) in an acid—base neutralization reaction. The balanced equation is NaOH(aq)+HCl(aq)→NaCl(aq)+H2O(l) We'll begin the titration by measuring out a known volume of the HCl solution and adding a small amount of an indicator, a compound that undergoes a color change during the course of the reaction. The compound phenolphthalein, for instance, is colorless in acid solution but turns red in base solution. Next, we fill a calibrated glass tube called a buret with an NaOH standard solution of known concentration and slowly add the NaOH to the HCl. When the phenolphthalein just begins to turn pink, all the HCl has completely reacted, and the solution now has a tiny amount of excess NaOH. By then reading from the buret to find the volume of the NaOH standard solution that has been added to react with the known volume of HCl solution, we can calculate the concentration of the HCl.

Although these and many thousands of other reactions appear unrelated, and many don't even take place in aqueous solution, all are oxidation—reduction (redox) reactions. Historically, the word oxidation referred to the combination of an element with oxygen to yield an oxide, and the word reduction referred to the removal of oxygen from an oxide to yield the element

Today, the words oxidation and reduction have taken on a much broader meaning. Oxidation is now defined as the loss of one or more electrons by a substance, whether element, compound, or ion, and reduction is the gain of one or more electrons by a substance. Thus, an oxidation—reduction, or redox, reaction is any process in which electrons are transferred from one substance to another. How can you tell when a redox reaction takes place? The answer is that you assign to each atom in a compound a value called an oxidation number (or oxidation state), which indicates whether the atom is neutral, electron-rich, or electron-poor. By comparing the oxidation number of an atom before and after reaction, you can tell whether the atom has gained or lost electrons. Note that oxidation numbers don't necessarily imply ionic charges; they are just a convenient device to help keep track of electrons during redox reactions.

Schrödinger's quantum mechanical model of atomic structure is framed in the form of a mathematical expression called a wave equation because it is similar in form to the equation used to describe the motion of ordinary waves in fluids. The solutions to the wave equation are called wave functions, or orbitals, and are represented by the symbol ψ (Greek psi). The best way to think about an electron's wave function is to regard it as an expression whose square, ψ2, defines the probability of finding the electron within a given volume of space around the nucleus. It is important to distinguish the difference between "orbits" in the Bohr model of the atom and "orbitals" in the quantum mechanical model. An orbit defines a specific location for the electron while the orbital is a mathematical equation. As Heisenberg showed, we can never be completely certain about an electron's position. A wave function, however, tells where the electron will most probably be found.

Wave equation→−SolveWave functionor orbital (ψ)→Probability of findingelectron in a region of space (ψ2) A wave function is characterized by three parameters called quantum numbers, represented as n, l, and ml, which describe the energy level of the orbital and the three-dimensional shape of the region in space occupied by a given electron. The principal quantum number (n) is a positive integer (n=1,2,3,4,...) on which the size and energy level of the orbital primarily depend. For hydrogen and other one-electron atoms, such as He+, the energy of an orbital depends only on n. For atoms with more than one electron, the energy level of an orbital depends both on n and on the l quantum number. As the value of n increases, the number of allowed orbitals increases and the size of those orbitals becomes larger, thus allowing an electron to be farther from the nucleus. Because it takes energy to separate a negative charge from a positive charge, this increased distance between the electron and the nucleus means that the energy of the electron in the orbital increases as the quantum number n increases. We often speak of orbitals as being grouped according to the principal quantum number n into successive layers, or shells, around the nucleus. The angular-momentum quantum number (l) defines the three-dimensional shape of the orbital. For an orbital whose principal quantum number is n, the angular-momentum quantum number l can have any integral value from 0 to n−1. Thus, within each shell, there are n different shapes for orbitals.Just as it's convenient to think of orbitals as being grouped into shells according to the principal quantum number n, we often speak of orbitals within a shell as being further grouped into subshells according to the angular-momentum quantum number l. Different subshells are usually designated by letters rather than by numbers, following the order s, p, d, f, g. (Historically, the letters s, p, d, and f arose from the use of the words sharp, principal, diffuse, and fundamental to describe various lines in atomic spectra.) After f, successive subshells are designated alphabetically: g, h, and so on. The magnetic quantum number (ml) defines the spatial orientation of the orbital with respect to a standard set of coordinate axes. For an orbital whose angular-momentum quantum number is l, the magnetic quantum number ml can have any integral value from −l to +l. Thus, within each subshell—orbitals with the same shape, or value of l —there are 2l+1 different spatial orientations for those orbitals. We'll explore this point further in the next section.

Acids that dissociate to a large extent are strong electrolytes and strong acids, whereas acids that dissociate to only a small extent are weak electrolytes and weak acids.

We've already seen in Table 4.1, for instance, that HCl, HClO4, HNO3 and H2SO4 are strong electrolytes and therefore strong acids, while CH3CO2H and HF are weak electrolytes and therefore weak acids. You might note that acetic acid actually contains four hydrogens, but only the one bonded to the oxygen atom dissociates. We will explain the effect of molecular structure on acid dissociation in Chapter 16. Different acids can have different numbers of acidic hydrogens and yield different numbers of H3O+ ions in solution. Hydrochloric acid (HCl) is said to be a monoprotic acid because it provides only one H+ ion, but sulfuric acid (H2SO4) is a diprotic acid because it can provide two H+ ions. Phosphoric acid (H3PO4) is a triprotic acid and can provide three H+ ions. With sulfuric acid, the first dissociation of an H+ is complete—all H2SO4 molecules lose one H+—but the second dissociation is incomplete, as indicated by the double arrow in the following equation: Sulfuric acid:H2SO4(aq)+H2O(l)−→HSO4−(aq)+H3O+(aq)HSO4−(aq)+H2O(l)⇌SO42−(aq)+H3O+(aq) With phosphoric acid, none of the three dissociations is complete: Phosphoric acid:H3PO4(aq)+H2O(l)⇌H2PO4−(aq)+H3O+(aq)H2PO4−(aq)+H2O(l)⇌HPO42−(aq)+H3O+(aq)HPO42−(aq)+H2O(l)⇌PO43−(aq)+H3O+(aq)

Quantization of energy in the atom arises from the fact that an electron cannot reside between orbits in the Bohr model, just like you cannot stand between steps on the stairs.

When energy is absorbed by an atom, an electron moves from a lower- to higher-energy orbit (ninitial<nfinal). Conversely, when an electron falls from a higher- to lower-energy orbit, energy is released (ninitial>nfinal). In the hydrogen atom, electrons moving from n=6,5,4,3 to n=2 result in emission of wavelengths in the visible region of the electromagnetic spectrum (Balmer series). As seen in Figure 5.10, electrons moving from n=6,5,4,3 to n=1 correspond to greater energy than the Balmer series and result in emission of photons in the ultraviolet region of the spectrum. Similarly, electronic transitions from n=6,5,4 to n=3 are lower in energy than the Balmer series and correlate to spectral lines in the infrared. Prior to Bohr's model of the atom, the combined work of Johann Balmer (1825-1898) and Johannes Rydberg (1854-1919) led to a formula describing the relation between spectral lines in hydrogen. The wavelengths of the lines in the hydrogen spectrum can be expressed by the Balmer-Rydberg equation. 1/lambda = Rinfinity [1/m2 - 1/n2] where Rinfinity = 1.097x10-2 nm-1; n level of lower energy orbit and n level of higher energy orbit for values of m and n. The Rydberg constant, R∞, has a value of 1.097×10−2nm−1, and the variables m and n in the Balmer-Rydberg equation for hydrogen represent the energy levels of the orbits in the Bohr model. The variable n corresponds to the n value of the higher-energy orbit, and the variable m corresponds to the n value of the lower-energy orbit closer to the nucleus. Notice in Figure 5.10 that as n becomes larger and approaches infinity, the energy difference between n=∞ and n=1 converges to a value of 1312 kJ/mol. That is, 1312 kJ is released when electrons come from a great distance (the "infinite" level) and add to H+ to give a mole of hydrogen atoms, each with an electron in its lowest energy state: H++e−→−−H+Energy(1312 kJ/mol) Because the energy released upon adding an electron to H+ is equal to the energy absorbed on removing an electron from a hydrogen atom, we can also say that 1312 kJ/mol is required to remove the electron from a hydrogen atom. We'll see in the next chapter that the amount of energy necessary to remove an electron from a given atom provides an important clue about that element's chemical reactivity.

It turns out that atoms give off light when heated or otherwise energetically excited, thereby providing a clue to their atomic makeup. Unlike the white light from the Sun, though, an energetically excited atom emits light not in a continuous distribution of wavelengths but only at certain specific wavelengths.

When passed first through a narrow slit and then through a prism, the light emitted by an excited atom is found to consist of only a few wavelengths rather than a full rainbow of colors, giving a series of discrete lines on an otherwise dark background—a line spectrum that is unique for each element. If hydrogen atoms are electrically excited in a discharge tube, they give off a pinkish light made of several different colors (Figure 5.9a). Other elements also produce line spectra upon excitation such as neon in signs or sodium salts in a flame (Figure 5.9b). In fact, the brilliant colors of fireworks are produced by mixtures of metal atoms that have been heated by explosive powder