SOLUTIONS - CHAPTER 4 Problems 1) Classify each of the following elements as a metal, a nonmetal, or a metalloid. Also identify the element as an alkali metal, alkaline earth metal, halogen, noble gas, or transition metal, as appropriate. a) As metalloid b) Cl nonmetal (halogen) c) Xe nonmetal (noble gas) d) Ba metal (alkaline earth metal) e) Fe metal (transition metal) f) P nonmetal g) Li metal (alkali metal) h) I nonmetal (halogen) i) B metalloid j) Si metalloid 2) What are valence electrons? Valence electrons are the outermost electrons in an atom. For the main group elements the valence electrons are all of the electrons found in orbitals with the highest value for n. For transition metals, lanthanides, and actinides valence electrons can be defined in different ways, but the concept of valence electrons is not important for those elements. 3) For main group elements the number of valence electrons and the approximate value for Zeff (effective charge of the nucleus observed by the valence electrons) are equal to its group number. Show that this is true for the following elements by writing the electron configuration for the element, finding the number of valence electrons, finding the approximate value for Zeff, and comparing the result to the group number for the atom. Recall that the approximate value for Zeff is given by the relationship Zeff # protons - # core electrons = atomic number - number of core electrons a) Al [Ne] 3s 2 3p 1 3 valence electrons Zeff 3 (group 3) b) Sr [Kr] 5s 2 2 valence electrons Z eff 2 (group 2) c) K [Ar] 4s 1 1 valence electron Zeff 1 (group 1) d) Br [Ar] 4s 2 3d 10 4p 5 7 valence electrons Zeff 7 (group7) e) P [Ne] 3s 2 3p 3 5 valence electrons Zeff 5 (group 5) f) S [Ne] 3s 2 3p 4 6 valence electrons Zeff 6 (group 6) g) C 1s 2 2s 2 2p 2 4 valence electrons Zeff 4 (group 4) 4) (Burdge, 4.16) Group the following electron configurations in pairs that would represent elements with similar chemical properties: a) 1s 2 2s 2 2p 6 3s 2 b) 1s 2 2s 2 2p 3 c) 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 d) 1s 2 2s 2 e) 1s 2 2s 2 2p 6 f) 1s 2 2s 2 2p 6 3s 2 3p 3 Elements with the same valence electron configuration are expected to have similar chemical properties, and so a + d, 2 valence electrons b + f, 5 valence electrons c + e, 8 valence electrons 1
5) Identify how the atomic radius changes in going from left to right in the periodic table, and explain why this behavior is seen. Atomic radius decreases in going from left to right in a particular row of the periodic table. This is because Zeff increases, and so electrons are pulled closer to the nucleus. 6) Identify how the atomic radius changes in going from top to bottom in the periodic table, and explain why this behavior is seen. Atomic radius increases in going from top to bottom in a particular group in the periodic table. This is because all atoms have approximately the same value for Zeff, and so the larger the value for n for the valence electrons the larger the atom. 7) a) Define ionization energy. b) Explain why ionization energy measurements are usually made when atoms are in the gas state. c) Why is the second ionization energy always greater than the first ionization energy for any element? a) Ionization energy is the minimum energy required to remove an electron from an atom, molecule, or ion in the gas phase. b) Ionization energy is measured in the gas state so that there are no surrounding atoms or ions that might affect the value for the ionization energy. c) Since the easiest electron to remove will always be removed first (since ionization energy is the minimum energy required to remove an electron) it follows that IE1 < IE2 < IE3 < where IE1 is the first ionization energy, and so forth. 8) (Burdge, 4.34) a) Define electron affinity. b) Explain why electron affinity measurements are made with gaseous atoms. c) Ionization energy is always a positive quantity, whereas electron affinity may be either positive or negative. Explain. a) Electron affinity is the minimum (in magnitude) energy required to add an electron to an atom, molecule, or ion. b) Like ionization energy, electron affinity is measured in the gas phase to make sure that the experimental value for ionization energy is not affected by surrounding atoms or ions. c) For atoms that are more stable adding an electron (like the halogens, which have space in their valence p orbitals for one more electron) electron affinity is negative, meaning the atom wants to add an electron For atoms which do not have a desire to add an electron (like the noble gases, which have a filled valence shell) the electron affinity will be positive. 2
9) On the basis of their position in the periodic table, select the atom with the larger atomic radius in each of the following pairs: a) Na, Si Na > Si (size decreases from left to right) b) Ba, Be Ba > Be (size increases from top to bottom) c) N, F N > F (size decreases from left to right) d) Br, Cl Br > Cl (size increases from top to bottom) e) Ne, Kr Kr > Ne (size increases from top to bottom) 10) (Burdge, 4.50) Arrange the following in order of increasing first ionization energy: Na, Cl, Al, S, Cs. First ionization energy increases from left to right, and decreases from top to bottom. Therefore Na < Al < S < Cl Cs < Na elements in same row elements in same group We can combine these to get Cs < Na < Al < S < Cl 11) Which element in each of the following sets is expected to have the largest value for first ionization energy? Why? a) Mg, Na, Sr Mg Mg > Na because first ionization energy increases from left to right in a particular row of the periodic table, and Mg > Sr because first ionization energy increases as you go from bottom to top in a particular group of the periodic table. b) As, Cl, P Cl Cl > P because first ionization energy increases from left to right in a particular row of the periodic table, and P > As because first ionization energy increases as you go from bottom to top in a particular group of the periodic table. 12) (Burdge, 4.54) The first and second ionization energies for K are 419. kj/mol and 3052. kj/mol, and for Ca are 590. kj/mol and 1145. kj/mol. Compare their values and comment on the differences. There is a much larger jump in second ionization energy for K than for Ca. We can use the electron configurations involved to see why this occurs K 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 Ca 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 K + 1s 2 2s 2 2p 6 3s 2 3p 6 Ca + 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 For Ca and Ca + the electron being removed sees an effective nuclear charge of approximately +2, and so there is not a large change in ionization energy. For K, the electron is being removed from the 4s orbital (Zeff = +1) while for K + the electron is being removed from a 3p orbital (Zeff = +9). Because Zeff is so much larger for removal of the second electron from potassium, there is a big jump in the second ionization energy relative to the first ionization energy. 3
13) The following ionization energies are observed for an atom of a particular main group element: IE1 = 787. kj/mol IE2 = 1577. kj/mol IE3 = 3231. kj/mol IE4 = 4356. kj/mol IE5 = 16091. kj/mol IE6 = 19784. kj/mol IE7 = 23783. kj/mol Which group is the element most likely a member of? Why? The largest percentage increase in ionization energy is between IE4 and IE5, where the ionization energy increases by almost a factor of 4. That suggests that there are four valence electrons for the atom, and that after they have been removed, core electrons begin to be removed, requiring a large jump in the energy required. The element is therefore most likely a member of group 4A. 14) (Burdge, 4.61) Explain why alkali metals have a greater affinity for electrons than alkaline earth metals. For the alkali metals there is space in the valence s orbital to hold one more electron. For the alkaline earth metals the valence s orbital is filled, and so an additional electron would have to go into a p or d orbital, which are higher in energy. So the electron affinity for the alkaline earth metals is expected to be positive. 15) Compare the physical and chemical properties of metals and nonmetals. Metals are good conductors of heat and electricity; nonmetals are poor conductors of heat and electricity Metals have a shiny and metallic appearance; solid nonmetals are usually dull in appearance Metals tend to form cations in ionic compounds; nonmetals tend to form anions in ionic compounds Metals are ductile and malleable; nonmetals are not (in fact, solid nonmetals are often brittle) 16) (Burdge, 4.68) Write the ground state electron configurations of the following ions: a) Li + 1s 2 = [He] b) H - 1s 2 = [He] c) N 3-1s 2 2s 2 2p 6 = [Ne] d) F - 1s 2 2s 2 2p 6 = [Ne] e) S 2-1s 2 2s 2 2p 6 3s 2 3p 6 = [Ar] f) Al 3+ 1s 2 2s 2 2p 6 = [Ne] g) Se 2-1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 = [Kr] h) Br - 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 = [Kr] 4
17) (Burdge, 4.72) Write the ground state electron configurations of the following transition metal ions. Recall that for transition metal cations we start with the configuration for the atom, and then remove electrons from the orbital with the highest n (or highest for orbitals with the same value for n) a) Sc 3+ Sc [Ar] 4s 2 3d 1 so Sc 3+ [Ar] b) Ti 4+ Ti [Ar] 4s 2 3d 2 so Ti 4+ [Ar] c) V 5+ V [Ar] 4s 2 3d 3 so V 5+ [Ar] d) Cr 3+ Cr [Ar] 4s 1 3d 5 so Cr 3+ [Ar] 3d 3 e) Mn 2+ Mn [Ar] 4s 2 3d 5 so Mn 2+ [Ar] 3d 5 18) (Burdge, 4.89) Indicate which one of the two species in each of the following pairs is smaller: a) Cl or Cl - Cl is smaller (same nuclear charge + smaller number of electrons) b) Na or Na + Na + is smaller (same nuclear charge + smaller number of electrons) c) O 2- or S 2- O 2- is smaller (same group, same valence electron configuration, and n is larger for the valence electrons in S 2- ) d) Mg 2+ or Al 3+ Al 3+ is smaller (ions have the same number of electrons, so the larger the charge of the nucleus the smaller the ion) e) Au + or Au 3+ Au 3+ is smaller (same nuclear charge + smaller number of electrons) 19) For each of the following main group elements give the ion most likely to form. a) Mg Mg 2+ b) F F - c) Se Se 2- d) Rb Rb + e) O O 2- f) Ba Ba 2+ 20) As a group the noble gases are very stable chemically. Why? The effective nuclear charge for the valence electrons for a noble gas is Zeff = +8 (except for helium, where it is +2) and so the noble gases do not want to give up electrons. Since adding an electron would place it in a higher energy s orbital (which would have Zeff approximately equal to zero) the noble gases also have no tendency to add electrons. It is therefore difficult to form chemical substances with the noble gases. Or, in short - the noble gases have a stable electron configuration and so do not want to change it. 5
21) State whether each of the properties of the main group elements generally increases or decreases from left to right across the period, and from top to bottom within a group a) metallic character - generally decreases from left to right; generally increases from top to bottom. b) atomic size - generally decreases from left to right; generally increases from top to bottom c) first ionization energy - generally increases from left to right; generally decreases from top to bottom 22) (Burdge, 4.98) Write equations representing the following processes: a) The electron affinity of S - S - (g) + e - S 2- (g) b) The third ionization energy for titanium Ti 2+ (g) Ti 3+ (g) + e - c) The electron affinity of Mg 2+ Mg 2+ (g) + e - Mg + (g) d) The ionization energy for O 2- O 2- (g) O - (g) + e - 6