Chem Chapter 8

Electron configurations and magnetic properties of ions

-

Sublevel energy splitting in multielectron atoms

- A major difference in the solutions to the Schrodinger equation for multielectron atoms compared to the solution for the hydrogen atom is the energy ordering of orbitals. In H atoms, the energy of an orbital depends only on n, the principal quantum number. For example, 3s, 3p, and 3d orbitals (which are all empty for H in its lowest energy state) all have the same energy: they are degenerate. - The orbitals within a principal level of a multielectron atom are not degenerate, meaning their energy depends on the value of l (s, p, d, f). We say that the energies of the sublevels are split. In general, the lower the value of l within a principal level ,the lower the energy (E) of the corresponding orbital: E(s orbital) < E(p orbital) < E (d orbital) < E(f orbital). - Sublevel energy splitting is the result of concepts relating to the energy of an electron in the vicinity of a nucleus: (1) Coulomb's law, (2) shielding, and (3) penetration.

Periodic trend: effective nuclear charge

- According to Coulomb's law, the attraction between a nucleus and an electron increases with increasing magnitude of nuclear charge. A higher charge in the nucleus makes it harder for an electron to be removed in the valence shell (for atoms with the same principal quantum number). Thus, as you move right across the periodic table, electrons are held more tightly (and have lower potential energy), making them more difficult to remove and making the atom smaller. - Electrons experience the positive charge of the nucleus (attractive) and the negative charges of other electrons (repulsive). - Effective nuclear charge (Zeff) = actual nuclear charge (Z) - charge screened by other electrons (S). E.g. 3+ (charge of nucleus) + 2- (charge of core electrons) = 1+. - Two types of shielding: (1) the shielding of the outermost electrons by the core electrons; (2) the shielding of the outermost electrons by each other. - Core electrons efficiently shield electrons in the outermost principal energy level from nuclear charge, but outermost electrons don't efficiently shield one another from nuclear charge. Thus, shielding caused by the outermost electrons is nearly 0, with the majority of shielding come from inner electrons. - A greater effective nuclear charge means electrons are held more tightly, the atom is smaller, and have a more positive effective nuclear charge. - As me move down a column in the periodic table, the principal quantum number (n) of the electrons in the outermost principal energy level increases, resulting in larger orbitals and therefore larger atomic radii. - As we move to the right across a row in the periodic table, the effective nuclear charge (Zeff) increases, resulting in a stronger attraction between the outermost electrons and the nucleus, making a smaller atomic radii.

Introduction

- Chemical gradient: concentration of one substance is greater on one side of a membrane than on the other side. - Ion channels: allow certain substances to flow through a membrane. - The movement of ions is the basis for the transmission of nerve signals in the brain. - All group 1A metals tend to lose one electron to form cations with a 1+ charge. - Periodic property: a property that is predictable based on an element's position within the periodic table. - Examples of periodic properties: atomic radius, ionization energy, and electron affinity.

Penetration

- Describes how one atomic orbital can overlap spatially with another, thus penetrating into a region that is close to the nucleus (and therefore less shielded from nuclear charge). - As an electron penetrates the electron cloud of the 1s orbital, it begins to experience the charge of the nucleus more fully because it's less shielded by the intervening electrons. - As the outer electron undergoes penetration into the region occupied by the inner electrons, it experiences a greater nuclear charge and therefore (according to Coulomb's law) a lower energy. - An orbital that penetrates into the region occupied by core electrons is less shielded from nuclear charge than an orbital that doesn't penetrate and will therefore have a lower energy.

Shielding

- Describes how one electron can shield another electron from the full charge of the nucleus. - Any one electron experiences both the positive charge of the nucleus (which is attractive) and the negative charges of the other electrons (which are repulsive). - Shielding: the repulsion of one electron by other electrons; protects electrons from the full effects of the nuclear charge. - An electron far from the nucleus is partially shielded by electrons in the 1s orbital (and other lower energy orbitals blow it), thereby reducing the effective net nuclear charge it experiences. - Effective nuclear charge (Zeff) = charge of nucleus + charge of lower energy electrons. - Inner electrons SHIELD the outer electrons from the full nuclear charge.

Coulomb's law

- Describes the interactions between charged particles. - States that the potential energy (E) of 2 charged particles depends on their charges (q1 and q2) and on their separation (r): E = (1/4πe0) x (q1q2/r). - E0 is a constant = 8.85 x 10^-12 C^2/J x m). - The potential energy is positive for charges of the same sign (plus x plus, minus x minus) and negative for charges of the opposite sign (plus x minus). The magnitude of the potential energy depends inversely on the separation between the charged particles. - (1) For like charges, the potential energy (E) is positive and decreases as the particles get farther apart (as r increases). Since systems tend toward lower potential energy, like charges repel each other. - (2) For opposite charges, the potential energy (E) is negative and becomes more negative as the particles get closer together (as r decreases). Therefore, opposite charges attract each other. - (3) The magnitude of the interaction between charged particles increases as the charges of the particles increases. Consequently, an electron with a charge of 1- is more strongly attracted to a nucleus of charge 2+ than of charge 1+.

Electron affinity

- Electron affinity: a measure of how easily an atom will accept an additional electron; crucial to chemical bonding; the energy change associated with the gaining of an electron by the atom in the gaseous state. - Usually, but not always, negative because an atom or ion usually releases energy when it gains an electron (similar to an exothermic reaction). I.e. the coulombic attraction between the nucleus of an atom and the incomplete electron usually results in the release of energy as the electron is gained. - Group 2A and Group 8A atoms have the least negative (typically >0) electron affinities. Group 7A has the most negative electron affinities. Group 5A atoms are also less negative than expected. - Main groups (column) of the periodic table don't exhibit any definite trend in electron affinity. Among group 1A metals, however, electron affinity becomes more positive as we move down the column. - Electron affinity generally becomes more negative as we move right across a period.

Electron configurations

- Electron configuration: shows the particular orbitals that electrons occupy for that atom. - Ground state: lowest energy state of an element. - Electrons generally occupy the lowest energy orbitals available. - Electron spin is a fundamental property of all electrons that affects the number of electrons allowed in any one orbital. Sublevel energy splitting determines the order of orbital filling within a level.

Multielectron atom electron configurations

- Electrons occupy the lowest energy orbitals (ground state) available when the atom is in its ground state, and only 2 electrons (with opposing spins) are allowed in each orbital. - The number of electrons in a neutral atom is equal to its atomic number. Electrons with parallel spins have correlated motion that minimizes their repulsion. - Aufbau principle: electrons fill the lowest available energy levels before filling higher levels (e.g., 1s before 2s); a pattern of orbital filling. - Hund's rule: when filling degenerate orbitals, electrons fill them singly first, with parallel spins; electrons occupy orbitals (of equal energy) singly first, rather than pairing in one orbital. - When 2 electrons occupy separate orbitals of equal energy, the repulsive interaction between them is lower than when they occupy the same orbital because their electrons are more spread out. - Electrons occupy orbitals so as to minimize the energy of the atom; therefore, lower energy orbitals fill before higher energy orbitals. Occurs in this order: 1s2s2p3s3p4s3d4p5s4d5p6s. - Orbitals can hold no more than 2 electrons; when 2 electrons occupy the same orbital, their spins are opposite. - When orbitals of identical energy are available, electrons first occupy these orbitals singly with parallel spins rather than in pairs. Once the orbitals are half full, then the electrons start to pair. - Inner electron configuration: e.g. writing [Ne]3s1 for Na instead of 1s22s22p63s1. - The s sublevel has 1 orbital and can hold 2 electrons. The p sublevel has 3 orbitals and can hold 6 electrons. The d sublevel has 5 orbitals and can hold 10 electrons. The f sublevel has 7 orbitals and can hold 14 electrons.

Exceptions to trends in first ionization energy

- Exceptions: B (<), O (<), Al (<), S (<), Ga (<), Se (<), Bi (<). - Group 3A atoms often have lower ionization energies than Group 2A atoms (even though they're farther to the right) because of the switch from the s to the p block. The 2p orbital penetrates into the nuclear region less than the 2s orbital, so the 2p orbitals are higher in energy, therefore making the electrons easier to remove (have lower ionization energies). Group 3A exceptions: B, Al, Ga. - Oxygen (as well as other Group 6A elements including S and Se) is another exception, and is caused by the repulsion between electrons when they occupy the same orbital.

Trends in first ionization energy

- First ionization energies are highest for noble gases and lowest for alkali metals. - Ionization energy is lower as we move down a column because electrons in the outermost principal level are increasingly farther away from the positively charged nucleus and therefore held less tightly. - Ionization energy is greater as we move right across a row because electrons the outermost principal energy level generally experience a greater effective nuclear charge. - Ionization energy is related to the atomic radii, which is influenced by how tightly electrons are held (they're held tighter in smaller atoms).

Electron configurations and magnetic properties of ions

- For anions, we add the number of electrons indicated by the magnitude of the charge of the anion. - For cations, we subtract the number of electrons indicated by the magnitude of the charge. We remove the main-group elements' electrons in the reverse order of filling. However, with transition metals, we remove the electrons in the highest n-value orbitals first, even if this doesn't correspond to the reverse order of filling, e.g. 4s is emptied before 3d. - During filling, the 4s is usually filled before the 3d, but for cations, the 4s is emptied first. Emptying the s orbital first makes the atom lower in energy. - Paramagnetic: an ion that contains unpaired electrons and is attracted to an external magnetic field. As long as the electrons in the highest n-value orbitals are unpaired, the ion is paramagnetic. - Diamagnetic: has all electrons paired. An atom or ion in which all electrons are paired isn't attracted to an external field; it is instead slightly repelled. An empty orbital also makes an atom or ion diamagnetic. - Overall, ns electrons are lost before (n - 1)d electrons for transition metals.

The transition and inner transition elements

- For the transition metals, the principal quantum number of the d orbitals that fill across each row in the transition series is equal to the row number minus one, e.g. 4s goes with 3d. This happens because the s orbital is generally lower in energy (because it penetrates more efficiently into the region occupied by the core electrons) than the d orbital of the previous principal quantum number. - Thus the 4s orbital fills before the 3d orbital, while the 4p orbital fills after the 3d orbital. - Because the 4s and 3d orbitals are so close in their relative energy, ordering depends on the exact element under consideration; this causes some irregular behavior in the transition metals. - Half filled (d5) and filled (d10) sublevels are more stable. - For the inner transition metals, the principal quantum number of the f orbitals that fill across each row is the row number minus 2, e.g. 7s matches with 5f. The closer energy spacing of the 5d and 4f orbitals sometimes cause an electron to enter a 5d orbital instead of the expected 4f orbital. - Electron filling: ns, (n-2)f, (n-1)d, np

Noble gases (Group 8A)

- Have electron configurations with the full outer principal quantum levels (ns2np6), so they're the most chemically inert family. - Density increases as we move down the column, and the ionization energy decreases. - All are gases at room temperature and must be cooled to extremely low temperatures before they liquify. Thus, some noble gases can be cryogenic liquids, which are liquids used to cool other substances to low temperatures. - Have very high ionization energies as a result of their completely full other quantum levels. Are exceptionally unreactive.

Alkali metals (Group 1A)

- Have ns1 outer electron configurations; the single valence electrons that keeps these metals from having noble gas configurations is easily removed (the metals have low ionization energies), making these elements the most reactive metals. - Density increases as we move down the column (except for K). The increase in mass as we move down the column outpaces the increase in volume. - Have low melting points, which decrease as we move down the column. - Excellent reducing agents because of their low ionization energies; they're readily oxidized, losing electrons to other substances. Often exist in nature as their oxidized states, either in compounds or as dissolved ions. - Reactivities tend to increase as we move down the column (because ionization energy decreases). The lower ionization energy of an alkali metal, the greater tendency it has to lose its electron and the more reactive it is.

Halogens (Group 7A)

- Have ns2np5 outer electron configurations. The one electron needed to obtain a noble gas configuration is easily acquired (the halogens have highly negative electron affinities), making these elements among the most active nonmetals. - Density increases as we move down the column. - Have various states are room temperature: some are gases, some are solids, some are liquids. - All are powerful oxidizing agents: they are readily reduced, gaining electrons from other substances. - React with metals to form metal halides according to the equation: 2 M + nX2 = 2MXn, where M is the metal, X is the halogen, and MXn is the metal halide. - Metal halides form between metals and nonmetals and contain ionic bonds. - Halogens react with hydrogen to form hydrogen halides according to the equation: H2(g) + X2 = 2HX(g). The hydrogen halides form between 2 nonmetals and have covalent bonds. All of the hydrogen halides form acidic solutions when combined with water. - Halogens also react with each other to form interhalogen compounds. Interhalogen compounds contain covalent bonds.

Ionic radii

- In general, cations are smaller than their corresponding atoms, and corresponding atoms are smaller than anions. - Cations < atoms. Anions > atoms. - Isoelectronic series: ions with the same number of electrons, e.g. group 6A ions that have gained 2 electrons. Although ions may have the same number of electrons, their size is also affected by the number of protons they have. A greater number of protons = a smaller atom. Less protons = larger atom.

Ionization energy

- Ionization energy (IE): the energy required to remove an electron form the atom or ion in the gaseous state; always positive because removing an electron always takes energy; the process is similar to an endothermic reaction. - The energy required to remove the first electron is called the first ionization energy. The energy required to remove the second electron is called the second ionization energy. The energy required to remove the third electron is called the third ionization energy, and so on. - Each ionization energy removes only ONE electron.

Development of the periodic table

- Johann Dobermänner first to organize elements according to similarities in their properties; he grouped them in triads. - John Newlands organized elements into octaves, similar to musical notes. - The modern periodic table is credited to Dmitri Mendeleev; his table is based on periodic law, which states that when elements are arranged in order of increasing mass, certain properties recur periodically. In the table, masses increase from left to right, and elements with similar properties fall in the same columns. - Henry Mosely showed that listing elements according to atomic number, rather than atomic mass, resulted in better correlation with elemental properties. - Laws summarize behavior; theories explain behavior. The theory that explains the reasons behind the the periodic law is quantum-mechanical theory, which describes the behavior of electrons in atoms.

Metallic character

- Metallic character: important because of the high proportion of metals in the periodic table. - Metals are good conductors of heat and electricity, are malleable and ductile, are shiny, tend to lose electrons. - Nonmetals have varying properties: some are solids at room temperatures while others are gases, but all tend to gain electrons, and most are poor conductors of heat and electricity. - As we move right across a row in the periodic table, metallic character decreases. As we move down a column, metallic character increases. - Metals are found on the left side and toward the center of the periodic table. Nonmetals are found on the upper right side.

Periodic trend: atomic size

- One way to define atomic radii is to consider the distance between non-bonding atoms that are in direct contact. An atomic radius determined in this way is called the nonbonding atomic radius or the van der Waals radius. The van der Waals radius represents the radius of an atom when it's not bonded to another atom; it's equal to one-half the distance between adjacent nuclei in an atomic nuclei. - Another way to define the size of an atom is the bonding atomic radius or covalent radius, which is defined differently for metals and nonmetals: for nonmetals, it is one-half the distance between 2 of the atoms bonded together; for metals it's one-half the distance between two of the atoms next to each other in a crystal of the metal. - The atomic radius refers to a set of average bonding radii determined from measurements on a large number of elements and compounds. The atomic radius represents the radius of an atom when it's bonded to another atom and is always smaller than the van der Waals radius. The approximate bond length of any 2 covalently bonded atoms is the sum of their atomic radii. - As we move down a column, atomic radius increases. As we move across a row, atomic radius decreases. - Atomic radius is largely determined by valence electrons, and as we move down a column, the highest principal quantum number increases, resulting in larger orbitals and therefore larger atoms. - Exceptions: O > N, F > N, Ne = N. Te > Sb > Sn. The middle transition elements, such as Mn, Cu, Zn, Rh, Pd, Ag, and Cd.

Electron spin and the Pauli exclusion principle

- Orbital diagram: gives information about electron spin but symbolizes the electron as an arrow and the orbital as a box. - In an orbital diagram, the direction of the arrow (up or down) represents the orientation of the electron's spin. +1/2 = up, -1/2 = down. The electrons in about half of the atoms are spin up, and the electrons in the other half are spin down. Spin up is usually filled in the diagram first. - Pauli exclusion principle: no two electrons in an atom can have the same 4 quantum numbers. Since 2 electrons occupying the same orbital have 3 identical quantum numbers (n, l, and ml), they must have different spin numbers. Since there are only two values of ms, the Pauli exclusion principle implies that each orbital can have a maximum of only 2 electrons, with opposing spins.

Explanatory power of the quantum-mechanical model

- The chemical properties of elements are largely determined by the valence electrons they contain. - Since elements within a column have the same number of valence electrons, they also have similar chemical prorates. - Elements with electron figurations close to those of noble gases are the most reactive because they can attain noble gas electron configuration by losing or gaining a small number of electrons. Alkali metals (1A) and halogens (7A) are very reactive.

Orbital blocks in the periodic table

- The first 2 columns of the left side of the periodic table (1A and 2A) comprise the s block. The 6 columns on the right side of the table (3A, 4A, 5A, 6A, 7A, and 8A) comprise the p block. The transition elements comprise the d block, and the lanthanides and actinides (inner transition elements) comprise the f block. - The number of columns in a block corresponds to the maximum number of electrons that can occupy the particular sublevel of that block. - Except for helium, the number of valence electrons for any main-group element is equal to its lettered group number. - Exceptions: Cr (4s1 3d5), Cu (4s1 3d10), Nb (5s1 4d4), Mo (5s1 4d5), Ru (5s1 4d7), Rh (5s1 4d8), Pd (4d10), Ag (5s1 4d10), Pt (6s1 5d9), Au (6s1 5d10). - For main-group elements, the row number in the periodic table is equal to the number (or n value) of the highest principal energy level.

Writing electron configuration

- The inner electron configuration of an element is that of the noble gas that precedes it in the periodic table. - The outer electron configuration is the configuration of the electrons beyond the previous noble gas.

Electron spatial distributions and sublevel splitting

- The radial distribution function for an atomic orbital shows the total probability of finding the electron within a thin spherical shell at a distance r from the nucleus. - In general, an electron in the 2p orbital has a greater probability of being found closer to the nucleus than an electron in a 2s orbital. The 2s orbital is lower in energy, but only when the 1s orbital is occupied (when the 1s orbital is empty, the 2s and 2p orbitals are degenerate). The reason is the bump near the nucleus (r = 0) for the 2s orbital; this bump represents a significant probability of the electron being found very close to the nucleus. More importantly, this area of probability penetrates into the 1s where the shielding by the 1s electrons is less effective. - In contrast, the radial distribution function of the 2p orbital mostly lies outside the distribution of the 1s orbital. Thus, almost all of the 2p orbital is shielded from nuclear charge by the 1s orbital. - Since the 2s orbital experiences more of the nuclear charge due to its greater penetration, it has a lower energy than the 2p orbital. These results are similar for the 3s, 3p, and 3d orbitals: the s orbitals penetrate more fully than the p orbitals, and the p orbitals penetrate more fully than the d orbitals. - Because of penetration, the sublevels of each principal level are not degenerate for multielectron atoms. - In the 4th and 5th principal levels, the effects of penetration become so important that the 4s orbital has a lower energy than the 3d orbitals, and the 5s orbital has lower energy than the 4d orbital. - The energy separations between one set of orbitals and the next become smaller for 4s orbitals and beyond, and the relative energy ordering of these orbitals can actually vary among electrons. These variations result in irregularities in the electron configurations of transition metals and their ions.

Atomic radii and the transition elements

- The transition elements (with a few exceptions) don't follow the same general trend in atomic radii as the main-group elements (the radii stay roughly constant across the row instead of decreasing in size). This is because, the number of electrons in the outermost principal energy level (highest n value) is nearly constant because the 4s orbital fills before the 3d. The number of outermost electrons stays constant and they experience a roughly constant effective nuclear charge, keeping the radius approximately constant.

Trends in second and successive ionization energy

- Valence electrons are held more loosely than core electrons. Elements with a noble gas configuration are more stable. - When an ionization energy requires removing a core electron, it becomes MUCH higher. - Ionization energy increases fairly uniformly with each successive removal of an outermost electron, but then takes a large jump with the removal of the first core electron.

Valence electrons and electron configuration

- With each subsequent row (or period) in the periodic table, the highest principal quantum number increases by one. - As we move down a column, the number of electrons in the outermost principal energy level (highest n value) remains the same. - Valence electrons: important in chemical bonding; electrons in the outermost principal energy level for main-group elements. For transition elements, we count the outermost d electrons among the valence electrons (even though they're not in an outermost principal energy level). The chemical properties of an electron depend on its valence electrons because these electrons are held most loosely and are therefore the easiest to lose or share. - Thus, elements in a column have similar chemical properties because they have the same number of valence electrons. - Core electrons: those in complete principal energy levels and those in complete d and f sub levels.