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General Chemistry--Unit 1

04/25/09

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Quantum Mechanics and Periodic Law


�Before You Begin:

To master this material, you should have an understanding of the fundamentals of quantum mechanics from the previous section. In particular, you will need to remember the concept of shells, subshells, and orbitals and the reasons for the Pauli Aufbau filling order. This material also presumes that you are familiar with the periodic table and periodic properties of the elements. Before you begin, you should look over the ĎPrep Chemí section that reviews periodic law


Periodic Law

Periodic Table and Quantum Mechanics

The periodic table is arranged by atomic number, so it is arranged by increasing electron count. The ground state electron configuration follows the Pauli Aufbau filling order, so the periodic table is arranged according to quantum mechanics. Periods correspond roughly to n values. Block regions on the table correspond to subshells.

 

Electron Configuration from the Periodic Table

The Aufbau filling order is 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p7s 5f 6d 7p.

Note that the first shell to have a p is subshell is shell number 2; the first to have a d is subshell is shell number 3; and the first to have an f subshell is shell number 4.

Groups 1 and 2 of the periodic table are referred to as the s block because these elements have outer electrons in an s orbital. Groups 13 through 18 are referred to as the p block because these elements have outer electrons in a p subshell. Groups 3 through 12 are referred to as the d block and the inner transition elements are f block. To use a periodic table to remember the Aufbau filling order, draw a new place holder for helium next to hydrogen. Next, fill in the regions of the periodic table with these four letters and four numbers:

 

periodic table with the location of the s, p, d, and f blocks

 

Start at the upper left with the space for hydrogen and the 1s orbital. Read left to right until you reach the end of the period assigning electrons by counting the boxes in each block. Continue until you reach the element you are working on. As an example, we will show the process for Te, marked with a star on the table above.

  1. Start with the upper left, 1s, and count boxes in that period: 1s2.
  2. Drop to the next period, the next two boxes are 2s2. Note that these elements have to represent 2s electrons because the 1s electrons have already been counted.
  3. Skip across to the p block in the same period. This is 2p and there are 6 electrons (count the boxes) or 2p6. Note that it canít be 1p, because the first shell doesnít have p orbitalsóthat is why we wrote the number two as a reminder.
  4. Drop to the next period and count: 3s2.
  5. Skip to the p block and count: 3p6.
  6. Drop to the next period and count: 4s2.
  7. Skip to the d block. These are 3d electrons (NOT 4d!). The first shell with d orbitals is shell number 3 and these lie between the 4s and 4p in energy. Count the boxes to remind yourself that there are 10 d electrons to get 3d10.
  8. Skip to the p block and count: 4p6. Note that this is 4p since we already did the 3p. If you lose track, count down from your reminder Ď2í at the corner of the p block.
  9. Drop to the next period and count: 5s2.
  10. Skip to the d block and count: 4d10.
  11. Skip to the p block and count: 5p4. We stop at four because Te is in the fourth box.

Write the totals to get Te: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p4.

 


4Concept Check: What is the electron configuration of Barium?

Answer: Ba: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p4 6s2


 

 

Periodic Trends

The historical periodic table was an arrangement of the known elements ranked by either increasing mass or atomic number such that chemically similar elements were grouped together. As experimental techniques improved and the arrangement was refined, a host of physical and chemical properties were found to fall in cyclic patterns when the elements were arranged by atomic number. The name Ďperiodicí comes from the mathematical term for a repeating function.

 

Valence

The valence is the number of outer shell electrons. These are the electrons available to take part in chemical reactions, so it is important for us to know their number and how tightly they are attracted to the nucleus. The periodic trend for valence works well for the representative elements, which are in groups 1, 2, 13, 14, 15, 16, 17, and 18 (the Ďtallí parts of the table). Reading left to right, the valence for each of the main groups increases from one to 8. The noble gas elements, with 8 valence electrons, are especially stable. From this information we can deduce the octet rule and the common monatomic ion charges.

 

periodic table with the number of valence electrons for the representative elements

 

 

When counting the valence electrons, we generally count only the s and p block outer electrons because any d block electrons are technically in a lower numbered shell. A periodic table follows the Aufbau filling order, so, reading left to right across a period and counting the s and p electron totals give the valence. Elements that fall in the transition metal area of the periodic table have less easily predictable valence because they can promote s orbital electrons into their partially filled d orbitals.

 

Common Charge

The most common oxidation state of the monatomic ion of an element is also a periodic trend.

For the s block electrons, the atom can gain stability by emptying its outer shell, so group 1 and group 2 form +1and +2 charged ions, respectively.

For the p block elements, there are too many valence electrons to lose them all. An atom can gain stability by filling its outer shell. The elements in group 18 donít form ions readily because they already have a filled outer shell. The elements in group 17 form -1 charged ions because they are one electron shy of having a full outer shell. The elements in group 16 form -2 ions.

 

periodic table with the common charges of the monatomic ions of the representative elements

Elements in the transition region have variable charges if they can lose either or both s electrons and/or promote them to the d orbitals. For example, iron has a +3 charge ion because it can lose both s electrons (its valence) and lose one of the paired d electrons so that it obeys Hundís Rule.

 


4Concept Check: Tin can form two ions, +2 and +4. Which electrons does tin tend to lose?

Answer: Tin will lose two of the 5p electrons to empty that subshell. It can also lose the 5s electrons to empty that subshell. The 4d electrons remain intact.


 

 

Atomic Radius

There are different ways of describing the size of an atom. The bonding radius is defined as one half the distance between two atoms that are bonded together. We define the radius this way because, because an atomís orbitals are based on probabilities. In a free atom, the probability of finding an electron at the farthest possible point is very low. Atoms that are bonded together find a natural distance between nuclei that minimizes the energy of the electrons shared. The atomic bonding radius indicates the smallest effective size of an atom.

The periodic trend for atomic radius is that the atoms increase in size at the bottom of a family or group and decrease in size at the right of a period. The element helium is the smallest and francium is the largest.

periodic table with the periodic trend for increasing atomic radius (increases down and to the left)

 

One factor that influences the atomic radius is the number of shells that are occupied in an atomís ground state. The greater the value of the principle quantum number is, the farther the electrons are from the nucleus. As you move down a row on the periodic table, the elements have higher numbered shells occupied by electrons. Higher numbered shells have electrons farther from the nucleus, so atoms are bigger as you go down a period.

Another factor that influences an atomís size is the effective nuclear charge. Electrons are negative and the nucleus is positive, so they attract one another. Inner core electrons screen some of the positive charge from the outer electrons. As electron count increases, so does proton count. The nucleus gets progressively more positive as you go across a period. As you move across a period, each successive electron enters the same shell. Electrons in the same shell donít screen one another from the nucleus very well, yet the nucleus gets more positive. Therefore, the shells contract, and the radius drops across a period.

 


4Concept Check: This is a list of atomic radii (in Angstrom) for the first four elements in period 4: K is 1.96 , Ca is1.74, Sc is 1.44 , and Ti is 1.36. Why is there a relatively big decrease from Ca to Sc?

Answer: Each atom in the succession has one extra proton making the nucleus more positive. the extra electron in Sc enters the 3d orbital set, which is in a lower numbered shell. It is closer to the nucleus than the 4s orbital. 


 

 

Ionization Energy

The ionization energy is the amount of energy needed to remove an outer electron. This is harder to do if the electrons are closer to the nucleus, so the trend is the reverse of the radius trend: the ionization energy increases as you go across a period and increases as you go up a row.

periodic table with the periodic trend of ionization energy (incresing up and to the right)

 

If you compare the ionizations energies of the noble gases, helium is higher than neon, which is higher than argon, and etc. Heliumís outer electron is in shell number one close to the nucleus, so it takes a lot of energy to remove that electron. Neonís outer electron is in shell number two. This is farther from the nucleus and not quite as difficult to remove. Argonís outer electron is in shell number three, farther from the nucleus and easier to remove.

 

line graph with atomic number on the x axis and ionization energy on the y axis

Data provided by the National Institute of Standards and Technology, NIST, Elemental Data Index.

 

 

Because like charges repel, two electrons paired in a single orbital have higher energy than one electron in the same orbital. This idea and the fact that higher numbered shells are higher in energy and that inner core electrons shield the outer electrons lead to some general electron energy trends:

  • The energy of an atom is lower if its outer shell is completely full (note that the next shell is completely empty).
  • If an atom has a partially filled shell, it will be lower in energy if lower l value subshells are completely full and higher l value subshells are completely empty (s full and p empty, for example).
  • If a subshell is partially full, it is lower in energy for all of the orbitals to have one electron than for some of the orbitals to be filled while others are empty (Hundís Rule).

The ionization energy increases across a period because extra electrons enter the same shell yet extra protons pull all of the electrons more strongly. If we examine the ionization energies across the second period, we see that lithium has the lowest, and beryllium has higher ionization energy than lithium. However, boron has lower ionization energy than beryllium, even though it has a smaller radius. Its outer electron is in the 2p subshell, nicely shielded from the nucleus by the filled 2s subshell. It is easier for boron to empty its 2p subshell than it is for beryllium to partly empty its 2s subshell. The trend continues to increase nicely until we reach oxygen. The ionization energy of oxygen is lower than that of nitrogen even though oxygen has a smaller radius. Oxygen has four electrons in the 2p subshell. It can obey Hundís rule if it loses one. From here the trend continues nicely until period number three.

The ionization energy trend works well for the s and p block elements, less well for the d and f blocks.

The second ionization energy is the energy needed to remove of an electron from a positive ion. These are always higher than first due to increased attraction of the nucleus. The second ionization energy may be less high than expected, if the element commonly forms a stable 2+ ion. It will be much higher than expected if the second electron is in the inner core.

 


4Concept Check: Which has the higher ionization energy, oxygen or polonium? Why?

Answer: Oxygen has the higher ionization energy. Oxygen has its outermost ground state electrons in shell number 2 while polonium has its outermost ground state electrons in shell number 6. Oxygen's outer electrons are much closer to the nucleus and much harder to remove, so the ionization energy is higher. In fact, polonium is a metal and tends to form a positive ion while oxygen is a non-metal and tends to form a negative ion.


 

 

Electron Affinity

The electron affinity is the energy released when an atom gains an electron to form a negative ion. Conceptually, the electron affinity is a measure of the ease with which an atom becomes a negative ion.

It is easier for an atom to gain an electron if the lowest energy unoccupied orbital is close to the nucleus. In that case, the positively charged nucleus exerts a stronger pull on any available extra electron. The periodic trend for electron affinity is the opposite of that for radius: the atoms to the right and top of the periodic table have the highest electron affinity.

The major exception to this trend is the noble gas group. These atoms have filled shells and resist gaining additional electrons.

Note that the ionization energy and the electron affinity are opposites: the ionization energy relates to removal of an electron and the electron affinity relates to the gain of an extra electron. Even so, the periodic trends are the same: both increase left to right across a period and bottom to top up a group. They are opposites yet have the same trend because, conceptually, ionization energy is the difficulty of removing an electron and electron affinity is the ease of gaining one.

 


4Concept Check: Which has a higher electron affinity, phosphorus or chlorine? Why?

Answer: chlorine has a higher electron affinity than silicon. It is farther to the right on the periodic table. both elements have their outermost ground state electrons in the third shell. But chlorine has three extra protons in its nucleus. The extra positive charge pull more strongly on all of the electrons, so it is easier to gain an extra electron (more energy is released compared to when silicon gains an extra electron.  to make matters worse, when chlorine gains an electron, it will have a full 3p subshell, which is good. When phosphorus gains an electron, it will have four electrons to distribute in the 3p subshell , which is not great.


 

 

Electronegativity

Electronegativity is the strength with which an atom pulls on the electrons it shares in a covalent bond. If the electronegatively values for two bonded atoms are the same, the electrons are shared evenly. A bond of this type is called non-polar. If there is a significant difference in the electronegativity values for two bonded atoms, the electrons are more likely to be found close to one atom than the other. A bond of this type is called polar covalent. Although the atom does not gain an extra electron at another atomís expense, the idea is similar to that of electron affinity.

The periodic trend for electronegativity is the same as for electron affinity: it increases from left to right across a period and increases from bottom to top up a group. The positively charged nucleus pulls on the outer electrons, so the smaller the atom the higher the electronegativity. Also like electron affinity, the noble gas group does not obey the trend due to the stability they gain from having full outer shells.

 

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