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Chapter 3 Assignment: Periodic Trends in Atomic Properties Why? Many properties of atoms have a repeating pattern when plotted with respect to atomic number. The similarities are due to the repeating pattern of electron configurations involving S, p, d, and f orbitals. These experimentally observed periodic trends in fact provide evidence for the orbital and shell structure of atoms and the meaningful arrangement of elements in the periodic table. Your ability to recognize the properties of the elements from their positions in the periodic table will prove useful in handling chemical compounds safely, developing new materials, finding applications of known materials, or using chemistry in medical applications. Learning Objectives Use electron configurations and position in the Periodic Table to account for the relative sizes, ionization energies, and electron affinities of different atoms. Order elements by atomic radius, ionization energy, and electron affinity Information Properties such as the size of an atom (atomic radius), the energy required to remove an electron from an atom (ionization energy), and the energy change that occurs when an electron is added to an atom (electron affinity) can be understood in terms of the electron configuration of the atom and the balance between electron - nucleus attraction and electron-electron repulsion. An electron in an atom is attracted by the positively charged nucleus and repelled by the other electrons. How this attraction and repulsion is balanced depends on how effective the electrons are in getting close to each other or close to the nucleus. If the electron-nucleus attraction (e-n) has a large effect, then the atom is small, has a high ionization energy, and highly negative electron affinity. If the electron-electron repulsion (e-e) has a large effect, then the atom is large, the ionization energy is small, and the electron affinity is less negative or zero. Model 1: Electron Configurations of Atoms The electron configuration of an atom specifies the number of electrons in each atomic orbital. For example, the electron configuration for an atom of carbon is: Is22s22p2. This notation for the electron configuration means that 2 electrons are in the 1s orbital, 2 are in the 2s orbital, and 2 are in 2p orbitals. Electron configurations can also be represented by orbital box diagrams as shown on the following page. In these diagrams an electron is represented by an upward or a downward pointing arrow. An upward pointing arrow indicates that the electron has positive spin angular momentum in one direction and a downward pointing arrow indicates that it has negative spin angular momentum in that direction. The following questions will help you Adapted from Foundations of Chemistry by David M. Hanson - Activity 20 identify the principles or rules that account for the electron configurations by helping you examine the orbital box diagrams below. Orbital Diagrams 1s 2s 2px 2py 2p2 1s 2s 2px 2py 2p2 H C He N Li O Be 1 F B It Ne Questions 1. According to the orbital box diagrams in Model 1, do electrons fill the lower or higher energy orbitals first? 2. What is the maximum number of electrons that can go in each orbital? 3. If multiple orbitals with the same energy are available, e.g. in the case of 2p orbitals, do the electrons all go in one orbital or do they go in different orbitals? 4. Fill in the orbital box diagrams for N, O, F, and Ne. Adapted from Foundations of Chemistry by David M. Hanson - Activity 20 Information The electron configurations of atoms are understood in terms of quantum mechanics and Schrödinger's equation which have produced the following three principles. The Aufbau Principle says that, electrons are added first to the lowest energy atomic orbitals available before they fill higher energy orbitals. The name derives from aufbau in German, which means building up. The Aufbau Principle makes sense because it produces the lowest energy or most stable arrangement of the electrons in the atom. The Pauli Exclusion Principle says that two electrons in an atom cannot have the same set of quantum numbers simultaneously. This principle determines the number of electrons that can occupy each orbital. In addition to the quantum numbers, n, l, and mi, there is a fourth quantum number, ms, or the spin angular momentum. There are two possible values for ms: +1/2 and - -1/2. So, two electrons can be in each orbital and have the same values for n, l, and mi, as long as they have different values for ms (one as +1/2 and the other as -1/2). The two different spin angular momentum states for electrons (+1/2 and -1/2) are represented in orbital diagrams by up and down arrows. Hund's Rule says that if multiple orbitals with the same energy are available, then the unoccupied orbitals will be filled by electrons with the same spin before electrons with different spins pair up in occupied orbitals. Hund's Rule makes sense because electrons repel each other. If they are in the same orbital, they will be close together and their energy will by higher than it would be if they are separated in different orbitals. Questions 5. In the orbital box diagram for carbon (shown in model 1), why aren't both 2p electrons in the 2px orbital? 6. Why isn't the electron configuration for carbon 1s²2s³? Adapted from Foundations of Chemistry by David M. Hanson - Activity 20 Model 2: Electron - Electron and Electron - Nucleus Interactions in Atoms Dominant Interparticle Forces in Helium e electron - nucleus attraction electron - electron repulsion 2+ electron - nucleus attraction e- Dominant Interparticle Forces in Lithium e e- 3+ e- Information The diagrams in Model 2 illustrate how electron-electron repulsions can effectively reduce the attraction of an electron to the nucleus, and how this shielding effect depends on the electron configuration. In helium, both of the electrons are in the same atomic orbital (1s) and consequently do not shield each other very well from the +2 charge of the nucleus; so the two electrons are strongly attracted to the nucleus. In lithium, the outer electron is in a 2s orbital and is shielded very effectively from the +3 charge of the nucleus by the two electrons in the inner 1s orbital. As a result of this shielding and because it is farther from the nucleus, the outer electron experiences a smaller nuclear charge. Consequently, in lithium, the outer electron is not strongly attracted to the nucleus. Adapted from Foundations of Chemistry by David M. Hanson - Activity 20 Questions 7. Is the electron - nucleus interaction attractive or repulsive? Explain. 8. Is the electron - electron interaction attractive or repulsive? Explain. 9. Based on your interpretation of the figures for Model 2, do you agree or disagree with the following statements? Explain your reasons. a. Electrons in the same shell do not shield each other from the nuclear charge very effectively, so for the case of helium their attraction to the nucleus is characteristic of a nuclear charge less than but close to +2. b. Electrons in inner shells are very good at shielding outer electrons from the nuclear charge, so for the case of lithium, the electron - electron repulsion reduces the effective nuclear charge to a value much less than +3. Information The ionization energy is defined as the energy required to remove the highest energy electron from an atom, corresponding to the following reaction equation. The ionization energy is a positive quantity. X X+ + e The electron affinity is defined as the energy change that occurs when an electron is added to an atom, corresponding to the following reaction equation. The electron affinity is a negative value (or zero). Y + e Y- Adapted from Foundations of Chemistry by David M. Hanson - Activity 20 Questions 10. Will attraction of electrons to the nucleus tend to increase or decrease each of the following? Explain. a. the size of an atom b. the ionization energy c. the electron affinity 11. Will an electron being repelled by other electrons tend to increase or decrease each of the following? Explain. a. the size of the atom b. the ionization energy c. the electron affinity 12. In going from hydrogen to helium, there is a change in the atomic radius (from 37pm to 32pm) and a change in ionization energy (from 1311kJ/mole to 2377 kJ/mole). Identify what these changes suggest about the relative magnitudes of the changes in the electron- nucleus attractions and the electron-electron repulsions. Adapted from Foundations of Chemistry by David M. Hanson - Activity 20 13. Using what you've learned in Model 2, explain why you would expect lithium to be larger and have a smaller ionization energy than helium. Model 3: Variation of Atomic Properties with Atomic Number The unit for atomic radii is pm; the unit for ionization energies and electron affinities is kJ/mole. 250 200 150 100 50 2500 2000 1500 1000 500 - -350 300 -250 -200 150 100 50 5 10 15 20 25 30 35 40 45 50 55 Atomic Number Adapted from Foundations of Chemistry by David M. Hanson - Activity 20 Questions 14. In the same way that the Periodic Table is organized with the atomic number of the elements increasing from the beginning to the end, the X-axis for all graphs in Model 3 is the atomic number of the element. In going from one element to the next across the x-axis, what happens to the number of protons and the number of electrons? 15. Do additional protons tend to increase or decrease the electron-nucleus attraction? Explain. 16. Do additional electrons tend to increase or decrease the electron-electron repulsions? Explain. 17. Using the information from the graphs in Model 3, describe what happens to the atomic radii and ionization energy as you go across a row in the Periodic Table, e.g. from Li to Ne and Na to Ar. 18. Why do the trends that you identified in Question 17 occur? In your explanation use the increase in nuclear charge and the effectiveness of electron shielding of the nuclear charge by electrons in the same orbital as illustrated in Model 2. Adapted from Foundations of Chemistry by David M. Hanson - Activity 20 19. Using the information from the graphs in Model 3, describe what happens to the atomic radii and ionization energies in going down a group in the Periodic Table, e.g., from Ne to Xe or Li to Rb. 20. Why do the trends that you identified in Question 19 occur? In your explanation, use the increase in nuclear charge, the effect of electron shielding of the nuclear charge by electrons in inner shells, and the size of the outer shell. 21. How can you use the Periodic Table and electron configurations to predict relative atomic radii and ionization energies for two atoms? 22. Identify the larger atom of each pair and explain why that one is larger. a. calcium (Ca) or potassium (K) b. nitrogen (N) or oxygen (O) c. copper (Cu) or gold (Au) Adapted from Foundations of Chemistry by David M. Hanson - Activity 20 23. Identify which of the elements in each pair has the higher ionization energy and explain why for each. a. barium (Ba) or cesium (Cs) b. bromine (Br) or krypton (Kr) c. silicon (Si) or carbon (C) 24. In the periodic table, ionization energies tend to increase across a period from left to right. For the ionization energies in the second period (Li to Ne), identify where the exceptions to this general trend occur (see the graph in Model 3). Explain the following exceptions using your knowledge of the differences in electron configurations between neighboring atoms. a. Why is the first ionization energy of beryllium (Be) more than the first ionization energy of boron (B)? b. Why is the first ionization energy of nitrogen (N) more than the first ionization energy of oxygen (O)? 25. Variations in electron affinities can also be explained by analyzing the effects of electron shielding and nuclear charge, and comparing electron configurations. For the following pairs of atoms, identify the atom that has the more negative electron affinity and explain why. a. He or Li b. Cl or S Adapted from Foundations of Chemistry by David M. Hanson - Activity 20

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