Solution Manual For Chemistry, 13th Edition

CHAPTER 2 ATOMS, MOLECULES, AND IONS Problem Categories Biological: 2.79, 2.80. Conceptual: 2.31, 2.32, 2.33, 2.34, 2.61, 2.65, 2.71, 2.72, 2.81, 2.82, 2.93, 2.103, 2.113. Descriptive: 2.24, 2.25, 2.26, 2.51, 2.52, 2.66, 2.70, 2.76, 2.84, 2.85, 2.86, 2.87, 2.88, 2.90, 2.91, 2.92, 2.94, 2.98, 2.101, 2.114. Environmental: 2.122. Organic: 2.47, 2.48, 2.69, 2.105, 2.107, 2.108, 2.115. Difficulty Level Easy: 2.7, 2.8, 2.13, 2.14, 2.15, 2.16, 2.23, 2.31, 2.32, 2.33, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, 2.62, 2.91, 2.92, 2.99, 2.100. Medium: 2.17, 2.18, 2.24. 2.26, 2.34, 2.35, 2.36, 2.49, 2.50, 2.57, 2.58, 2.59, 2.60, 2.61, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, 2.69, 2.70, 2.71, 2.72, 2.73, 2.74, 2.75, 2.76, 2.79, 2.80, 2.81, 2.82, 2.83, 2.84, 2.85, 2.86, 2.88, 2.89, 2.90, 2.93, 2.94, 2.95, 2.96, 2.98, 2.101, 2.102, 2.103, 2.110, 2.112, 2.114, 2.115. Difficult: 2.25, 2.77, 2.78, 2.87, 2.97, 2.104, 2.105, 2.106, 2.107, 2.108, 2.109, 2.111, 2.113. 2.7 First, convert 1 cm to picometers. 1 cm ´ 0.01 m 1 cm ´ 1 pm -12 1 ´ 10 = 1 ´ 1010 pm m ? He atoms = (1 ´ 1010 pm) ´ 2.8 1 He atom 2 1 ´ 10 pm Note that you are given information to set up the unit factor relating meters and miles. ratom = 104 rnucleus = 104 ´ 2.0 cm ´ 2.13 = 1 ´ 10 8 He atoms 1m 100 cm ´ 1 mi 1609 m = 0.12 mi For iron, the atomic number Z is 26. Therefore the mass number A is: A = 26 + 28 = 54 2.14 Strategy: The 239 in Pu-239 is the mass number. The mass number (A) is the total number of neutrons and protons present in the nucleus of an atom of an element. You can look up the atomic number (number of protons) on the periodic table. CHAPTER 2: ATOMS, MOLECULES, AND IONS 35 Solution: mass number = number of protons + number of neutrons number of neutrons = mass number – number of protons = 239 – 94 = 145 2.15 2.16 3 2 He 4 2 He 24 12 Mg 25 12 Mg 48 22Ti 79 35 Br 195 78 Pt No. Protons 2 2 12 12 22 35 78 No. Neutrons 1 2 12 13 26 44 117 15 7N 33 16 S 63 29 Cu 84 38 Sr 130 56 Ba 186 74 W 202 80 Hg No. Protons 7 16 29 38 56 74 80 No. Neutrons 8 17 34 46 74 112 122 No. Electrons 7 16 29 38 56 74 80 Isotope Isotope 23 11 Na (b) 64 28 Ni 2.17 (a) 2.18 The accepted way to denote the atomic number and mass number of an element X is as follows: AX Z where, A = mass number Z = atomic number (a) 2.23 186 74 W (b) 201 80 Hg Helium and selenium are nonmetals whose name ends with ium. (Tellerium is a metalloid whose name ends in ium.) 2.24 2.25 (a) Metallic character increases as you progress down a group of the periodic table. For example, moving down Group 4A, the nonmetal carbon is at the top and the metal lead is at the bottom of the group. (b) Metallic character decreases from the left side of the table (where the metals are located) to the right side of the table (where the nonmetals are located). The following data were measured at 20C. 3 (a) Li (0.53 g/cm ) (b) Au (19.3 g/cm ) (c) Os (22.6 g/cm ) (d) Te (6.24 g/cm ) 3 3 K (0.86 g/cm ) 3 Pt (21.4 g/cm ) 3 H2O (0.98 g/cm ) 3 Hg (13.6 g/cm ) 3 3 Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 36 CHAPTER 2: ATOMS, MOLECULES, AND IONS 2.26 F and Cl are Group 7A elements; they should have similar chemical properties. Na and K are both Group 1A elements; they should have similar chemical properties. P and N are both Group 5A elements; they should have similar chemical properties. 2.31 (a) This is a polyatomic molecule that is an elemental form of the substance. It is not a compound. (b) This is a polyatomic molecule that is a compound. (c) This is a diatomic molecule that is a compound. (a) This is a diatomic molecule that is a compound. (b) This is a polyatomic molecule that is a compound. (c) This is a polyatomic molecule that is the elemental form of the substance. It is not a compound. 2.32 2.33 2.34 2.35 2.36 Elements: N2, S8, H2 Compounds: NH3, NO, CO, CO2, SO2 There are more than two correct answers for each part of the problem. (a) H2 and F2 (d) H2O and C12H22O11 (sucrose) HCl and CO (b) 2+ 3+ (c) 2+ S8 and P4 2- 2- 3- Ion Na+ Ca Al Fe I- F- S No. protons 11 20 13 26 53 9 16 8 7 No. electrons 10 18 10 24 54 10 18 10 10 O N The atomic number (Z) is the number of protons in the nucleus of each atom of an element. You can find this on a periodic table. The number of electrons in an ion is equal to the number of protons minus the charge on the ion. number of electrons (ion) = number of protons – charge on the ion Ion K+ Mg No. protons 19 No. electrons 18 2+ 3+ Fe Br- Mn 12 26 35 10 23 36 3− 2+ 4- C Cu 25 6 29 23 10 27 2.37 − 3− F and N (10 electrons), Ar and P (18 electrons), Fe and V (23 electrons), Sn 2.38 (a) 52 25 Mn 2.45 (a) Sodium ion has a +1 charge and oxide has a -2 charge. The correct formula is Na2O. (b) The iron ion has a +2 charge and sulfide has a -2 charge. The correct formula is FeS. (b) 22 10 Ne (c) 3+ 2+ 107 47 Ag (d) 4+ 127 53 I (e) + and Ag (46 electrons). 239 94 Pu Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. CHAPTER 2: ATOMS, MOLECULES, AND IONS 37 (c) The correct formula is Co2(SO4)3 (d) Barium ion has a +2 charge and fluoride has a -1 charge. The correct formula is BaF2. (a) The copper ion has a +1 charge and bromide has a -1 charge. The correct formula is CuBr. (b) The manganese ion has a +3 charge and oxide has a -2 charge. The correct formula is Mn2O3. (c) We have the Hg2 (d) Magnesium ion has a +2 charge and phosphate has a -3 charge. The correct formula is Mg3(PO4)2. 2.47 (a) CN 2.48 Strategy: An empirical formula tells us which elements are present and the simplest whole-number ratio of 2.46 2+ (b) ion and iodide (I-). The correct formula is Hg2I2. CH (c) C9H20 (d) P2O5 (e) BH3 their atoms. Can you divide the subscripts in the formula by some factor to end up with smaller wholenumber subscripts? Solution: (a) Dividing both subscripts by 2, the simplest whole number ratio of the atoms in Al2Br6 is AlBr3. (b) Dividing all subscripts by 2, the simplest whole number ratio of the atoms in Na2S2O4 is NaSO2. (c) The molecular formula as written, N2O5, contains the simplest whole number ratio of the atoms present. In this case, the molecular formula and the empirical formula are the same. (d) The molecular formula as written, K2Cr2O7, contains the simplest whole number ratio of the atoms present. In this case, the molecular formula and the empirical formula are the same. 2.49 The molecular formula of glycine is C2H5NO2. 2.50 The molecular formula of ethanol is C2H6O. 2.51 Compounds of metals with nonmetals are usually ionic. Nonmetal-nonmetal compounds are usually molecular. 2.52 Ionic: LiF, BaCl2, KCl Molecular: SiCl4, B2H6, C2H4 Compounds of metals with nonmetals are usually ionic. Nonmetal-nonmetal compounds are usually molecular. Ionic: NaBr, BaF2, CsCl. Molecular: CH4, CCl4, ICl, NF3 Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 38 CHAPTER 2: ATOMS, MOLECULES, AND IONS 2.59 (a) sodium chromate (h) phosphorus trifluoride (b) potassium hydrogen phosphate (i) phosphorus pentafluoride (c) hydrogen bromide (molecular compound) (j) tetraphosphorus hexoxide (d) hydrobromic acid (k) cadmium iodide (e) lithium carbonate (l) strontium sulfate (f) potassium dichromate (m) aluminum hydroxide (g) ammonium nitrite (n) 2.60 sodium carbonate decahydrate Strategy: When naming ionic compounds, our reference for the names of cations and anions is Table 2.3 of the text. Keep in mind that if a metal can form cations of different charges, we need to use the Stock system. In the Stock system, Roman numerals are used to specify the charge of the cation. The metals that have only 2+ 2+ one charge in ionic compounds are the alkali metals (+1), the alkaline earth metals (+2), Ag+, Zn , Cd , 3+ and Al . When naming acids, binary acids are named differently than oxoacids. For binary acids, the name is based on the nonmetal. For oxoacids, the name is based on the polyatomic anion. For more detail, see Section 2.7 of the text. Solution: (a) This is an ionic compound in which the metal cation (K+) has only one charge. The correct name is potassium hypochlorite. Hypochlorite is a polyatomic ion with one less O atom than the chlorite ion, ClO2-. (b) silver carbonate (c) This is an ionic compound in which the metal can form more than one cation. Use a Roman numeral to specify the charge of the Fe ion. Since the chloride ion has a -1 charge, the Fe ion has a +2 charge. The correct name is iron(II) chloride. (d) potassium permanganate (e) (g) This is an ionic compound in which the metal can form more than one cation. Use a Roman numeral to specify the charge of the Fe ion. Since the oxide ion has a -2 charge, the Fe ion has a +2 charge. The correct name is iron(II) oxide. (h) iron(III) oxide (i) This is an ionic compound in which the metal can form more than one cation. Use a Roman numeral to specify the charge of the Ti ion. Since each of the four chloride ions has a -1 charge (total of -4), the Ti ion has a +4 charge. The correct name is titanium(IV) chloride. (j) sodium hydride (k) cesium chlorate lithium nitride (f) (l) hypoiodous acid sodium oxide 2- (m) This is an ionic compound in which the metal cation (Na+) has only one charge. The O2 ion is called the peroxide ion. Each oxygen has a -1 charge. You can determine that each oxygen only has a -1 Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. CHAPTER 2: ATOMS, MOLECULES, AND IONS 39 charge, because each of the two Na ions has a +1 charge. Compare this to sodium oxide in part (l). The correct name is sodium peroxide. 2.61 2.62 (n) iron(III) chloride hexahydrate (a) RbNO2 (b) K2S (c) NaHS (d) Mg3(PO4)2 (e) CaHPO4 (f) KH2PO4 (g) IF7 (h) (NH4)2SO4 (i) AgClO4 (j) BCl3 Strategy: When writing formulas of molecular compounds, the prefixes specify the number of each type of atom in the compound. When writing formulas of ionic compounds, the subscript of the cation is numerically equal to the charge of the anion, and the subscript of the anion is numerically equal to the charge on the cation. If the charges of the cation and anion are numerically equal, then no subscripts are necessary. Charges of common cations and anions are listed in Table 2.3 of the text. Keep in mind that Roman numerals specify the charge of the cation, not the number of metal atoms. Remember that a Roman numeral is not needed for some metal cations, because the charge is known. These metals are the alkali metals (+1), the alkaline earth metals (+2), Ag+, 2+ 2+ 3+ Zn , Cd , and Al . When writing formulas of oxoacids, you must know the names and formulas of polyatomic anions (see Table 2.3 of the text). Solution: (a) The Roman numeral I tells you that the Cu cation has a +1 charge. Cyanide has a -1 charge. Since the charges are numerically equal, no subscripts are necessary in the formula. The correct formula is CuCN. (b) Strontium is an alkaline earth metal. It only forms a +2 cation. The polyatomic ion chlorite, ClO2-, has a -1 charge. Since the charges on the cation and anion are numerically different, the subscript of the cation is numerically equal to the charge on the anion, and the subscript of the anion is numerically equal to the charge on the cation. The correct formula is Sr(ClO2)2. (c) Perbromic tells you that the anion of this oxoacid is perbromate, BrO4-. The correct formula is HBrO4(aq). Remember that (aq) means that the substance is dissolved in water. (d) Hydroiodic tells you that the anion of this binary acid is iodide, I-. The correct formula is HI(aq). (e) Na is an alkali metal. It only forms a +1 cation. The polyatomic ion ammonium, NH4+, has a +1 3- charge and the polyatomic ion phosphate, PO4 , has a -3 charge. To balance the charge, you need 2 Na+ cations. The correct formula is Na2(NH4)PO4. (f) The Roman numeral II tells you that the Pb cation has a +2 charge. The polyatomic ion carbonate, 2- CO3 , has a -2 charge. Since, the charges are numerically equal, no subscripts are necessary in the formula. The correct formula is PbCO3. Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 40 CHAPTER 2: ATOMS, MOLECULES, AND IONS (g) The Roman numeral II tells you that the Sn cation has a +2 charge. Fluoride has a -1 charge. Since the charges on the cation and anion are numerically different, the subscript of the cation is numerically equal to the charge on the anion, and the subscript of the anion is numerically equal to the charge on the cation. The correct formula is SnF2. (h) This is a molecular compound. The Greek prefixes tell you the number of each type of atom in the molecule. The correct formula is P4S10. (i) The Roman numeral II tells you that the Hg cation has a +2 charge. Oxide has a -2 charge. Since, the charges are numerically equal, no subscripts are necessary in the formula. The correct formula is HgO. (j) The Roman numeral I tells you that the Hg cation has a +1 charge. However, this cation exists as 2+ 2+ Hg2 . Iodide has a -1 charge. You need two iodide ions to balance the +2 charge of Hg2 . The correct formula is Hg2I2. (k) This is a molecular compound. The Greek prefixes tell you the number of each type of atom in the molecule. The correct formula is SeF6. 2.63 Let’s compare the ratio of the fluorine masses in the two compounds. 3.55 g F 2.37 g F = 1.50 This calculation indicates that there is 1.5 times more fluorine by mass in SF6 compared to the other compound. The value of n is: n = 6 = 4 1.5 This is consistent with the Law of Multiple Proportions which states that if two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in ratios of small whole numbers. In this case, the ratio of the masses of fluorine in the two compounds is 6:4 or 3:2. 2.64 (a) dinitrogen pentoxide (N2O5) (b) boron trifluoride (BF3) (c) dialuminum hexabromide (Al2Br6) 2.65 Uranium is radioactive. It loses mass because it constantly emits alpha (a) particles. 2.66 Changing the electrical charge of an atom usually has a major effect on its chemical properties. The two electrically neutral carbon isotopes should have nearly identical chemical properties. 2.67 The number of protons = 65 – 35 = 30. The element that contains 30 protons is zinc, Zn. There are two 2+ fewer electrons than protons, so the charge of the cation is +2. The symbol for this cation is Zn . Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. CHAPTER 2: ATOMS, MOLECULES, AND IONS 2.68 41 Atomic number = 127 – 74 = 53. This anion has 53 protons, so it is an iodide ion. Since there is one more electron than protons, the ion has a -1 charge. The correct symbol is I-. 2.69 (a) molecular, C3H8 (b) empirical, C3H8 molecular, C2H2 (c) empirical, CH molecular, C2H6 (d) empirical, CH3 molecular, C6H6 empirical, CH 2.70 NaCl is an ionic compound; it doesn’t form molecules. 2.71 Yes. The law of multiple proportions requires that the masses of sulfur combining with phosphorus must be in the ratios of small whole numbers. For the three compounds shown, four phosphorus atoms combine with three, seven, and ten sulfur atoms, respectively. If the atom ratios are in small whole number ratios, then the mass ratios must also be in small whole number ratios. 2.72 2.73 2.74 2.75 2.76 The species and their identification are as follows: (a) SO2 molecule and compound (g) O3 element and molecule (b) S8 element and molecule (h) CH4 molecule and compound (c) Cs element (i) KBr compound (d) N2O5 molecule and compound (j) S element (e) O element (k) P4 element and molecule (f) O2 element and molecule (l) LiF compound (a) Species with the same number of protons and electrons will be neutral. A, F, G. (b) Species with more electrons than protons will have a negative charge. B, E. (c) Species with more protons than electrons will have a positive charge. C, D. (d) A: 105 B (a) Ne, 10 p, 10 n (b) Cu, 29 p, 34 n (c) Ag, 47 p, 60 n (d) W, 74 p, 108 n (e) Po, 84 p, 119 n (f) Pu, 94 p, 140 n (a) BaO, barium oxide (b) Ca3P2, calcium phosphide (c) Al2S3, aluminum sulfide (d) Li3N, lithium nitride (a) Cu Kr B: 147 N3- (b) P (c) + C: 39 19 K (d) 81 E: 35 Br 2+ D: 66 30 Zn Cs (e) Al (f) F: 115 B Sb (g) Cl G: 199 F (h) Sr Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 42 CHAPTER 2: ATOMS, MOLECULES, AND IONS 2.77 When an anion is formed from an atom, you have the same number of protons attracting more electrons. The electrostatic attraction is weaker, which allows the electrons on average to move farther from the nucleus. An anion is larger than the atom from which it is derived. When a cation is formed from an atom, you have the same number of protons attracting fewer electrons. The electrostatic attraction is stronger, meaning that on average, the electrons are pulled closer to the nucleus. A cation is smaller than the atom from which it is derived. 2.78 (a) Rutherford’s experiment is described in detail in Section 2.2 of the text. From the average magnitude of scattering, Rutherford estimated the number of protons (based on electrostatic interactions) in the nucleus. (b) Assuming that the nucleus is spherical, the volume of the nucleus is: V = 4 3 4 p r = p (3.04 ´ 10 13 cm)3 = 1.177 ´ 10 37 cm3 3 3 The density of the nucleus can now be calculated. – 3.82 ´ 10 23 g m d = = = 3.25 ´ 1014 g / cm 3 V 1.177 ´ 10 37 cm 3 To calculate the density of the space occupied by the electrons, we need both the mass of 11 electrons, and the volume occupied by these electrons. The mass of 11 electrons is: – 11 electrons ´ 9.1095 ´ 10 28 g 1 electron – = 1.00205 ´ 10 26 g The volume occupied by the electrons will be the difference between the volume of the atom and the volume of the nucleus. The volume of the nucleus was calculated above. The volume of the atom is calculated as follows: – 186 pm ´ Vatom = 1 ´ 10 12 m 1 pm ´ 1 cm -2 1 ´ 10 – = 1.86 ´ 10 8 cm m 4 3 4 pr = p (1.86 ´ 10 8 cm)3 = 2.695 ´ 10 23 cm3 3 3 Velectrons = Vatom – Vnucleus = (2.695 ´ 10 -23 3 -37 cm ) – (1.177 ´ 10 3 -23 cm ) = 2.695 ´ 10 3 cm As you can see, the volume occupied by the nucleus is insignificant compared to the space occupied by the electrons. Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. CHAPTER 2: ATOMS, MOLECULES, AND IONS 43 The density of the space occupied by the electrons can now be calculated. – d = 1.00205 ´ 10 26 g m = = 3.72 ´ 10 4 g/cm 3 -23 3 V 2.695 ´ 10 cm The above results do support Rutherford’s model. Comparing the space occupied by the electrons to the volume of the nucleus, it is clear that most of the atom is empty space. Rutherford also proposed that the nucleus was a dense central core with most of the mass of the atom concentrated in it. Comparing the density of the nucleus with the density of the space occupied by the electrons also supports Rutherford’s model. 2.79 The molecular formula of caffeine is C8H10N4O2. The empirical formula is C4H5N2O. 2.80 The empirical and molecular formulas of acetaminophen are C8H9NO2. 2.81 (a) Iodate ion is IO32- . The correct formula is Mg(IO3)2. (b) The formula shown is phosphorous acid. The correct formula for phosphoric acid is H3PO4. (c) Sulfite ion is SO32- . The correct formula is BaSO3. (d) NH + 4 is the ammonium ion. The correct formula is NH4HCO3. (a) The charge on the tin cation needs to be specified. The correct name is tin(IV) chloride. (b) The charge on the copper ion is +1. The correct name is copper(I) oxide. (c) The charge on the cobalt cation needs to be specified. The correct name is cobalt(II) nitrate. (d) Cr2 O 27- is the dichromate ion. The correct name is sodium dichromate. 2.82 2.83 2.84 2.85 Symbol 11 5B 54 2+ 26 Fe 31 315 P Protons 5 26 15 79 86 Neutrons 6 28 16 117 136 Electrons 5 24 18 79 86 Net Charge 0 +2 -3 0 0 196 79 Au 222 86 Rn (a) Ionic compounds are typically formed between metallic and nonmetallic elements. (b) In general the transition metals, the actinides, and the lanthanides have variable charges. (a) Li+, alkali metals always have a +1 charge in ionic compounds (b) S (c) I-, halogens have a -1 charge in ionic compounds (d) N (e) Al , aluminum always has a +3 charge in ionic compounds 2- 33+ Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 44 2.86 CHAPTER 2: ATOMS, MOLECULES, AND IONS (f) Cs+, alkali metals always have a +1 charge in ionic compounds (g) Mg , alkaline earth metals always have a +2 charge in ionic compounds. 2+ 23 The symbol Na provides more information than 11Na. The mass number plus the chemical symbol identifies a specific isotope of Na (sodium) while combining the atomic number with the chemical symbol tells you nothing new. Can other isotopes of sodium have different atomic numbers? 2.87 The binary Group 7A element acids are: HF, hydrofluoric acid; HCl, hydrochloric acid; HBr, hydrobromic acid; HI, hydroiodic acid. Oxoacids containing Group 7A elements (using the specific examples for chlorine) are: HClO4, perchloric acid; HClO3, chloric acid; HClO2, chlorous acid: HClO, hypochlorous acid. Examples of oxoacids containing other Group A-block elements are: H3BO3, boric acid (Group 3A); H2CO3, carbonic acid (Group 4A); HNO3, nitric acid and H3PO4, phosphoric acid (Group 5A); and H2SO4, sulfuric acid (Group 6A). Hydrosulfuric acid, H2S, is an example of a binary Group 6A acid while HCN, hydrocyanic acid, contains both a Group 4A and 5A element. 2.88 Mercury (Hg) and bromine (Br2) 2.89 (a) (b) 4 2 He 20 10 Ne 40 18 Ar 84 36 Kr 132 54 Xe No. Protons 2 10 18 36 54 No. Neutrons 2 10 22 48 78 neutron/proton ratio 1.00 1.00 1.22 1.33 1.44 Isotope The neutron/proton ratio increases with increasing atomic number. 2.90 H2, N2, O2, F2, Cl2, He, Ne, Ar, Kr, Xe, Rn 2.91 Cu, Ag, and Au are fairly chemically unreactive. This makes them specially suitable for making coins and jewelry, that you want to last a very long time. 2.92 They do not have a strong tendency to form compounds. Helium, neon, and argon are chemically inert. 2.93 Magnesium and strontium are also alkaline earth metals. You should expect the charge of the metal to be the same (+2). MgO and SrO. 2.94 All isotopes of radium are radioactive. It is a radioactive decay product of uranium-238. Radium itself does not occur naturally on Earth. Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. CHAPTER 2: ATOMS, MOLECULES, AND IONS 2.95 45 Berkelium (Berkeley, CA); Europium (Europe); Francium (France); Scandium (Scandinavia); (a) Ytterbium (Ytterby, Sweden); Yttrium (Ytterby, Sweden). Einsteinium (Albert Einstein); Fermium (Enrico Fermi); Curium (Marie and Pierre Curie); (b) Mendelevium (Dmitri Mendeleev); Lawrencium (Ernest Lawrence). Arsenic, Cesium, Chlorine, Chromium, Iodine. (c) 77 2− 2.96 The atomic number is 77 – 43 = 34. The symbol for the anion is Se . 2.97 The mass of fluorine reacting with hydrogen and deuterium would be the same. The ratio of F atom to hydrogen (or deuterium) is 1:1 in both compounds. This does not violate the law of definite proportions. When the law of definite proportions was formulated, scientists did not know of the existence of isotopes. (a) NaH, sodium hydride (b) B2O3, diboron trioxide (c) Na2S, sodium sulfide (d) AlF3, aluminum fluoride (e) OF2, oxygen difluoride (f) SrCl2, strontium chloride 2.99 (a) Br 2.100 All of these are molecular compounds. We use prefixes to express the number of each atom in the molecule. 2.98 (b) Rn (c) Se (d) Rb (e) Pb The names are nitrogen trifluoride (NF3), phosphorus pentabromide (PBr5), and sulfur dichloride (SCl2). 2.101 alkali metals alkaline earth metals noble gases halogens 8A 1A 2A 3A 4A 5A 6A 7A The metalloids are shown in gray. 2.102 Cation Anion Formula Name HCO3- Mg(HCO3)2 Magnesium bicarbonate 2+ Cl- SrCl2 Strontium chloride 3+ NO2- Fe(NO2)3 Iron(III) nitrite Mg 2+ Sr Fe Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 46 CHAPTER 2: ATOMS, MOLECULES, AND IONS 2+ ClO3- Mn(ClO3)2 Manganese(II) chlorate 4+ Br- SnBr4 Tin(IV) bromide PO4 Co3(PO4)2 Cobalt(II) phosphate Hg2 I- Hg2I2 Mercury(I) iodide Cu+ CO3 Cu2CO3 Copper(I) carbonate Li+ N Li3N Lithium nitride Al2S3 Aluminum sulfide Mn Sn Co 2+ 2+ 3+ Al 2.103 2.104 3- 2 S 3- 2- (a) CO2(s), solid carbon dioxide (f) Ca(OH)2, calcium hydroxide (b) NaCl, sodium chloride (g) NaHCO3, sodium bicarbonate (c) N2O, nitrous oxide (h) Na2CO3⋅10H2O, sodium carbonate decahydrate (d) CaCO3, calcium carbonate (i) CaSO4⋅2H2O, calcium sulfate dihydrate (e) CaO, calcium oxide (j) Mg(OH)2, magnesium hydroxide The change in energy is equal to the energy released. We call this DE. Similarly, Dm is the change in mass. Because m = E c2 , we have Dm = DE c 2 (1.715 ´ 103 kJ) ´ = 8 1000 J 1 kJ 2 (3.00 ´ 10 m/s) – – = 1.91 ´ 10 11 kg = 1.91 ´ 10 8 g æ 1 kg ⋅ m 2 ÷÷ö ç ÷÷ Note that we need to convert kJ to J so that we end up with units of kg for the mass. ççç1 J = ÷÷ 2 çç s ÷ø è We can add together the masses of hydrogen and oxygen to calculate the mass of water that should be formed. 12.096 g + 96.000 = 108.096 g The predicted change (loss) in mass is only 1.91 × 10 -8 g which is too small a quantity to measure. Therefore, for all practical purposes, the law of conservation of mass is assumed to hold for ordinary chemical processes. Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. CHAPTER 2: ATOMS, MOLECULES, AND IONS 2.105 47 CH4, C2H6, and C3H8 each only have one structural formula. H H C H H H H H C C H H H H H H H C C C H H H H C4H10 has two structural formulas. H H H H H H C C C C H H H H HH H C H H C HH C C H H H C5H12 has three structural formulas. H H H 2.106 (a) H H H H H C C C C C H H H H H H HH H C C HH H C C C H H H H H HH H C H H C HH C C C H H H H The volume of a sphere is V = 4 3 pr 3 Volume is proportional to the number of nucleons. Therefore, V µ A (mass number) 3 r µ A 1/3 r µ A (b) Using the equation given in the problem, we can first solve for the radius of the lithium nucleus and then solve for its volume. 1/3 r = r0A -15 r = (1.2 × 10 -15 r = 2.3 × 10 V = 1/3 m)(7) m 4 3 pr 3 Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 48 CHAPTER 2: ATOMS, MOLECULES, AND IONS Vnucleus = (c) 4 p (2.3 ´ 10 15 m)3 = 5.1 ´ 10 44 m 3 3 In part (b), the volume of the nucleus was calculated. Using the radius of a Li atom, the volume of a Li atom can be calculated. Vatom = 4 3 4 pr = p(152 ´ 10 12 m)3 = 1.47 ´ 10 29 m3 3 3 The fraction of the atom’s volume occupied by the nucleus is: Vnucleus Vatom – = 5.1 ´ 10 44 m 3 -29 1.47 ´ 10 m 3 – = 3.5 ´ 10 15 Yes, this calculation shows that the volume of the nucleus is much, much smaller than the volume of the atom, which supports Rutherford’s model of an atom. 2.107 Two different structural formulas for the molecular formula C2H6O are: H H H C C H H H O H H C H O H C H H In the second hypothesis of Dalton’s Atomic Theory, he states that in any compound, the ratio of the number of atoms of any two of the elements present is either an integer or simple fraction. In the above two compounds, the ratio of atoms is the same. This does not necessarily contradict Dalton’s hypothesis, but Dalton was not aware of chemical bond formation and structural formulas. 2.108 (a) Ethane Acetylene 2.65 g C 4.56 g C 0.665 g H 0.383 g H Let’s compare the ratio of the hydrogen masses in the two compounds. To do this, we need to start with the same mass of carbon. If we were to start with 4.56 g of C in ethane, how much hydrogen would combine with 4.56 g of carbon? 0.665 g H ´ 4.56 g C 2.65 g C = 1.14 g H We can calculate the ratio of H in the two compounds. 1.14 g 0.383 g » 3 Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. CHAPTER 2: ATOMS, MOLECULES, AND IONS 49 This is consistent with the Law of Multiple Proportions which states that if two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in ratios of small whole numbers. In this case, the ratio of the masses of hydrogen in the two compounds is 3:1. (b) For a given amount of carbon, there is 3 times the amount of hydrogen in ethane compared to acetylene. Reasonable formulas would be: 2.109 (a) Ethane Acetylene CH3 CH C2H6 C2H2 The following strategy can be used to convert from the volume of the Pt cube to the number of Pt atoms. 3 cm  grams  atoms 1.0 cm 3 ´ 21.45 g Pt 1 cm (b) 3 ´ 1 atom Pt -22 3.240 ´ 10 = 6.6 ´ 10 22 Pt atoms g Pt 22 Since 74 percent of the available space is taken up by Pt atoms, 6.6 ´ 10 atoms occupy the following volume: 3 3 0.74 ´ 1.0 cm = 0.74 cm We are trying to calculate the radius of a single Pt atom, so we need the volume occupied by a single Pt atom. 0.74 cm 3 volume Pt atom = – 6.6 ´ 10 22 Pt atoms = 1.12 ´ 10 23 cm 3 /Pt atom 4 3 pr . Solving for the radius: 3 4 V = 1.12 ´ 10-23 cm3 = pr 3 3 The volume of a sphere is 3 r = 2.67 ´ 10 -24 -8 r = 1.4 ´ 10 cm 3 cm Converting to picometers: – radius Pt atom = (1.4 ´ 10 8 cm) ´ 0.01 m 1 cm ´ 1 pm -12 1 ´ 10 = 1.4 ´ 10 2 pm m Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 50 CHAPTER 2: ATOMS, MOLECULES, AND IONS 2.110 The mass number is the sum of the number of protons and neutrons in the nucleus. Mass number = number of protons + number of neutrons Let the atomic number (number of protons) equal A. The number of neutrons will be 1.2A. Plug into the above equation and solve for A. 55 = A + 1.2A A = 25 The element with atomic number 25 is manganese, Mn. 2.111 S N B I 2.112 The acids, from left to right, are chloric acid, nitrous acid, hydrocyanic acid, and sulfuric acid. 2.113 From the equation derived in Problem 2.106, we can first solve for the radius of the iron nucleus and then solve for its volume. 1/3 r = r0A -15 r = (1.2 × 10 -15 r = 4.6 × 10 V = 1/3 m)(56) m 4 3 pr 3 Vnucleus = 4 p (4.6 ´ 10 15 m)3 = 4.1 ´ 10 43 m3 = 4.1 ´ 10 37 cm3 3 The density of an iron-56 nucleus is: – 9.229 ´ 10 23 g mass 3 density = = = 2.3 ´ 1014 g/cm 37 3 volume 4.1 ´ 10 cm 3 The density of an iron nucleus is 230 trillion grams per 1 cm . Because of this very high density, neutrons are needed to stabilize the nucleus, keeping the protons from repelling each other. It has been postulated that the Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. CHAPTER 2: ATOMS, MOLECULES, AND IONS 51 exterior of the neutron is negatively charged and the interior is positively charged. The negative exteriors of the neutrons attract the protons holding the particles together in this extremely dense arrangement. 2.114 The formula of the ionic compound is XY2. Element X is most likely in Group 4B and element Y is most likely in Group 6A. A possible compound is TiO2, titanium(IV) oxide. Other choices are elements in Group 4A: SnO2 [tin(IV) oxide] and PbO2 [lead(IV) oxide]. 2.115 Let’s compare the ratio of the hydrogen masses in the three compounds. To do this, we need to start with the same mass of carbon. If we were to start with 0.749 g of C in ethane, how much hydrogen would combine with 0.749 g of carbon? If we were to start with 0.749 g of C in propane, how much hydrogen would combine with 0.749 g of carbon? ethane : 0.201 g H ´ propane : 0.183 g H ´ 0.749 g C 0.799 g C = 0.188 g H 0.749 g C 0.817 g C = 0.168 g H We can calculate the ratio of H between methane and propane, and ethane and propane. methane : propane : ethane : propane : 0.251 g 0.168 g 0.188 g 0.168 g = 1.49 = 1.12 This is consistent with the Law of Multiple Proportions which states that if two elements combine to form more than one compound, the masses of one element (in this case hydrogen) that combine with a fixed mass of the other element (in this case carbon) are in ratios of small whole numbers. The ratio of the masses of hydrogen in the three compounds, propane, ethane, and methane is 1:1.12:1.49 or 8:9:12. 2.116 Basic approach: · Determine the charge of an alpha particle (helium nucleus) and gold nucleus in coulombs. · Use Coulomb’s law to solve for the distance at which the electrical potential energy is equal to the initial kinetic energy. When the α particle comes to a stop, its kinetic energy is converted to potential energy. The charge of a proton is −19 +1.6022 × 10 −19 C. An α particle which contains 2 protons and 2 neutrons has a charge, Q1, of 3.2044 × 10 −17 A gold nucleus which contains 79 protons has a charge, Q2, of 1.2657 × 10 C. C. We solve for r, the distance of separation in meters between the alpha particle and the gold nucleus. Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 52 CHAPTER 2: ATOMS, MOLECULES, AND IONS r = 2.117 kQ1Q2 E = æ 3ö çç -19 9 kg ⋅ m ÷÷ C)(1.2657 ´ 10-17 C) çç9.0 ´ 10 2 2 ÷÷ (3.2044 ´ 10 ÷ s ⋅C ø èç æ 2ö çç -14 kg ⋅ m ÷÷ 6.0 10 ´ ÷÷ çç çè s2 ø÷ = 6.1 ´ 10-13 m Basic approach: · Consider that almost all of the volume in an atom or monatomic ion is occupied by the electrons. · Determine the number of electrons in each species, and rank their size according the number of electrons. The volume of each species depends on the outer boundary of the electrons. The number of protons remains the same in all three cases. Li– has the most electrons and therefore the greatest repulsion among them, leading to a larger outer boundary compared to the Li atom, which has one fewer electron. Li+ has the fewest number of electrons and the smallest outer boundary. Thus, the size decreases as follows: Li– > Li > Li+ In general for a given element, the anion is the largest, the atom is second, and the cation is the smallest. In Chapter 8 we will consider a more sophisticated way of predicting the relative sizes of atoms and monatomic ions based on electron configurations and nuclear charge. 2.118 Isotopes of the same element have the same number of electrons, hence following the reasoning in Problem 2.117, they would have the same size. The number of neutrons affects the size of the nucleus, but not the size of the atom. 2.119 Basic approach: · Look up the size of a silver atom. · Calculate the number of silver atoms required to reach the minimum length visible to the human eye, and then calculate the number of silver atoms required to give a surface area that would be visible. –8 A Web search shows that the atomic radius of an Ag atom is 144 pm or 1.44 ´ 10 cm. The number of Ag atoms that must be lined up along one dimension is given by the minimum length humans can see divided by the diameter of a silver atom – 2 ´ 10 5 cm – 2 ´ 1.44 ´ 10 8 cm /Ag atom » 700 Ag atoms But to actually be seen by the human eye, a grouping of silver atoms would need to have both length and width. Assuming a square array of 700 Ag atoms by 700 Ag atoms the number of silver atoms required to be visible would be 700 ´ 700 ≈ 500,000 Ag atoms. Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. CHAPTER 2: ATOMS, MOLECULES, AND IONS 53 700 Ag atoms 700 Ag atoms 2.120 Basic approach: · Estimate the radius of a pea. · Look up the radius of a typical atom and its nucleus. The radius of the atom provides a range of possible distances of the electron from the nucleus. · Use the ratio of the radii for the pea and the atom to calculate the distance of the electron from the nucleus if the nucleus were the size of a pea. The diameter of a pea is about 0.5 cm. Radius of nucleus is about 5 ´ 10 –13 cm. Therefore, the expansion factor for the radius of the nucleus is 0.5 cm /2 – 5 ´ 10 13 cm = 5 ´ 1011 times –8 A typical atom has a radius of about 100 pm (10 cm). Using that value as the distance of the electron from –8 the nucleus in an atom, then if the atom was scaled to the size of a pea, the electron would be (1 ´ 10 cm) ´ 11 3 (5 ´ 10 ) = 5 ´ 10 cm or 50 m (roughly half a football field) from the nucleus! 2.121 Basic approach: · Consider the relative composition of sodium and potassium ions in biological systems (for starters see the Chemistry in Action on p. 49, and then look up the relative compositions in other biological systems). Over long periods of time (on a geological scale), minerals containing potassium and sodium are slowly + + decomposed by wind and rain, and their K and Na ions are converted to more soluble compounds. Eventually, rain leaches these compounds out of the soil and carries them to the sea. Plants take up many of + + the K ions along the way, while the Na ions are free to move on to the sea because they are not needed for biological functions by the plants. Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 54 CHAPTER 2: ATOMS, MOLECULES, AND IONS 2.122 Basic approach: · Estimate the diameter of a typical carbon microsphere and calculate the volume. · Estimate for the density of carbon in the microsphere. · Look up the most common isotope of carbon and calculate the mass of that isotope. · Calculate the number of atoms in the microsphere. A typical microsphere appears to be about 3 mm in diameter, giving a volume of 3 3 æ 2 ö3 4 çæ d ÷ö 4 çæ 3 mm ÷ö ç 10 cm ÷÷ -11 ÷÷ ´ çç pç cm 3 p ç ÷÷ = ÷ » 1´10 ççè106 mm ÷÷ø 3 çè 2 ÷ø 3 çè 2 ÷ø It is reasonable to expect that the density of carbon in the microspheres would be somewhere between that of graphite (2.2 g/cm3) and diamond (3.5 g/cm3), so we assume a density of 3 g/cm3 for the carbon in the microsphere. The mass of a typical carbon microsphere would be – 1 ´ 10 11 cm3 ´ 3 gC cm 3 – = 3 ´ 10 11 g C While this may seem like an exceedingly small mass, it still represents a very large number of carbon atoms which are much smaller and far less massive than the microspheres. In order to determine the number of atoms in a typical microsphere, we need to approximate the mass of an individual carbon atom. An online search tells us that the most common isotope of carbon is 126 C . Taking this isotope as a typical carbon atom and using the data in Table 2.1, we can calculate the mass of one atom by summing the masses of six electrons, six protons, and six neutrons. – – 6 electron (9.10938 ´ 10 28 g/electron) + 6 proton (1.67262 ´ 10 24 g/proton) – – + 6 neutron (1.67493 ´ 10 24 g/neutron) » 2 ´ 10 23 g Therefore, the number of carbon atoms in a typical microsphere would be – 3 ´ 10 11 g C ´ 1 C atom – 2 ´ 10 23 g C = 2 ´ 1012 C atoms This calculation gives us a feel for the incredibly small size of an atom. It should be noted that the mass of the carbon atom used in the calculation is only an approximation. Besides the assumption that all carbon atoms are carbon-12 (only about 99% of carbon atoms are carbon-12), we will see in Chapter 19 that the mass of an atom is actually somewhat less than the sum of the masses of the individual particles. In Chapter 3 we will introduce “atomic mass” which is the average mass of the naturally occurring isotopes of a particular element. Copyright © McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.