CHAPTER 2 ATOMS AND THE ATOMIC THEORY

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1 1A 1B 2A 2B A CHAPTER 2 ATOMS AND THE ATOMIC THEORY PRACTICE EXAMPLES The total mass must be the same before and after reaction. mass before reaction = 0.82 g magnesium g nitrogen =.04 g mass after reaction = magnesium nitride mass g nitrogen =.04 g magnesium nitride mass =.04 g g = g magnesium nitride Again, the total mass is the same before and after the reaction. mass before reaction = 7.12 g magnesium g bromine = 8.92 g mass after reaction = 2.07 g magnesium bromide + magnesium mass = 8.92 g magnesium mass = 8.92 g 2.07 g = 6.85 g magnesium In Example 2-2 we are told that g MgO contains 0.01 g of Mg. With this information, we can determine the mass of magnesium needed to form g magnesium oxide g Mg mass of Mg = g MgO = 1.20 g Mg g MgO The remainder of the 2.00 g of magnesium oxide is the mass of oxygen mass of oxygen = 2.00 g magnesium oxide 1.20 g magnesium = 0.80 g oxygen In Example 2-2, we see that a g sample of MgO has 0.01 g Mg, hence, it must have g O 2. From this we see that if we have equal masses of Mg and O 2, the oxygen is in excess. First we find out how many grams of oxygen reacts with g of Mg g O2 mass oxygen =10.00 g Mg 6.61 g O 2 (used up) 0.01 g Mg Hence, g g =.9 g O 2 unreacted. Mg is the limiting reactant. MgO(s) mass = mass Mg + Mass O 2 = g g = g MgO. There are only two substances present, g of MgO (product) and.9 g of unreacted O Silver has 47 protons. If the isotope in question has 62 neutrons, then it has a mass number of 109. This can be represented as Ag. 2 B Tin has 50 electrons and 50 protons when neutral, while a neutral cadmium atom has 48 electrons. This means that we are dealing with Sn 2+. We do not know how many neutrons tin has. so there can be more than one answer. For instance, Sn, Sn, Sn, Sn, and Sn are all possible answers A The ratio of the masses of 202 Hg and 12 C is: 202 Hg u = = C 12u 17

2 4B Atomic mass is 12 u = u. The isotope is Gd. Using an atomic mass of u for 16 O, the mass of 158 Gd relative to O is u relative mass to oxygen-16 = u 5A The average atomic mass of boron is , which is closer to than to Thus, boron-11 is the isotope that is present in greater abundance. 5B The average atomic mass of indium is , and one isotope is known to be 11 In. Since the weighted- average atomic mass is almost 115, the second isotope must be larger than both In-11 and In-114. Clearly, then, the second isotope must be In-115 ( 115 In). Since the average atomic mass of indium is closest to the mass of the second isotope, In- 115, then 115 In is the more abundant isotope. 6A Weighted-average atomic mass of Si = ( u 0.92) u ( u ) 1.58 u ( u ) u u We should report the weighted-average atomic mass of Si as u. 6B We let x be the fractional abundance of lithium u = x u + 1x u = x u u x u u u = x u x u = x u u u x = = Percent abundances : 7.5% lithium - 6, 92.5% lithium u 7A We assume that atoms lose or gain relatively few electrons to become ions. Thus, elements that will form cations will be on the left-hand side of the periodic table, while elements that will form anions will be on the right-hand side. The number of electrons lost when a cation forms is usually equal to the last digit of the periodic group number; the number of electrons added when an anion forms is typically eight minus the last digit of the group number. Li is in group 1(1A); it should form a cation by losing one electron: Li +. S is in group 6(6A); it should form an anion by adding two electrons: S 2. Ra is in group 2(2A); it should form a cation by losing two electrons: Ra 2+. F and I are both group 17(7A); they should form anions by gaining an electron: F and I. A1 is in group 1(A); it should form a cation by losing three electrons: Al +. 18

3 7B Main-group elements are in the A families, while transition elements are in the B families. Metals, nonmetals, metalloids, and noble gases are color coded in the periodic table inside the front cover of the textbook. Na is a main-group metal in group 1(1A). Re is a transition metal in group 7(7B). S is a main-group nonmetal in group 16(6A). I is a main-group nonmetal in group 17(7A). Kr is a nonmetal in group 18(8A). Mg is a main-group metal in group 2(2A). U is an inner transition metal, an actinide. Si is a main-group metalloid in group 14(4A). B is a metalloid in group 1(A). A1 is a main-group metal in group 1(A). As is a main-group metalloid in group 15(5A). H is a main-group nonmetal in group 1(1A). (H is believed to be a metal at extremely high pressures.) 8A This is similar to Practice Examples 2-8A and 2-8B. 1 mol Cu g Cu 24 Cu mass = Cu atoms atoms 1 mol Cu = 248 g Cu 8B Of all lead atoms, 24.1% are lead-206, or Pb atoms in every 1000 lead atoms. First we need to convert a 22.6 gram sample of lead into moles of lead (below) and then, by using Avogadro s constant, and the percent natural abundance, we can determine the number of 206 Pb atoms. 1 mole Pb n = 22.6 g Pb mol Pb Pb Pb atoms 241 Pb atoms Pb atoms = mol Pb 1mol Pb 1000 Pb atoms = Pb atoms g Pb A Both the density and the molar mass of Pb serve as conversion factors g 1 mol Pb Pb atoms atoms of Pb = 0.105cm Pb = Pb atoms 21 1 cm g 1mol Pb 9B First we find the number of rhenium atoms in mg of the element. 1 g 1 mol Re Reatoms mg. 10 Reatoms 1000 mg g Re 1 mol Re atoms Re % abundance Re= 100% = 62.5% Re atoms 19

4 INTEGRATIVE EXAMPLE A. Stepwise approach: First, determine the total number of Cu atoms in the crystal, by determining the volume of the crystal and calculating the mass of Cu from density. Then we can determine the amount of 6 Cu by noting its relative abundance 1 cm nm = cm 7 Volume of crystal = (1 10 nm) Mass of Cu in crystal = D V = 8.92 g/cm = g # of Cu atoms = 16 1 mol Cu Cu atoms g Cu = Cu atoms g Cu 1 mol Cu Therefore, the number of 6 Cu atoms, assuming 69.17% abundance, is atoms. Conversion pathway approach: 8.92 g Cu 1 cm (25 nm) 1 mol Cu Cu atoms 7 1 cm (1 10 nm) crystal g Cu 1 mol Cu atoms of Cu 100 Cu atoms atoms of Cu B. Stepwise approach: Calculate the mass of Fe in a serving of cereal, determine mass of 58 Fe in that amount of cereal, and determine how many servings of cereal are needed to reach 58 g of 58 Fe. Amount of Fe in a serving of cereal = 18 mg 0.45 = 8.1 mg Fe per serving First calculate the amount of Fe 1 mol Fe g Fe mol Fe g Fe Then calculate 58 Fe amount: mol Fe mol Fe = mol 58 Fe 100 mol Fe Converting mol of 58 F to # of servings: mol Fe 57.9 g Fe g Fe per serving 58 1serving 1 mol Fe Total # of servings = 58 g total / per serving = serving 20

5 Conversion Pathway Approach: The number of servings of dry cereal to ingest 58 g of 58 Fe = mol Fe 100 mol Fe g Fe 1 cereal serving 58.0 g Fe g Fe mol Fe 1 mol Fe g Fe servings 1year 65 serving servings 6706 years EXERCISES Law of Conservation of Mass 1. The observations cited do not necessarily violate the law of conservation of mass. The oxide formed when iron rusts is a solid and remains with the solid iron, increasing the mass of the solid by an amount equal to the mass of the oxygen that has combined. The oxide formed when a match burns is a gas and will not remain with the solid product (the ash); the mass of the ash thus is less than that of the match. We would have to collect all reactants and all products and weigh them to determine if the law of conservation of mass is obeyed or violated.. By the law of conservation of mass, all of the magnesium initially present and all of the oxygen that reacted are present in the product. Thus, the mass of oxygen that has reacted is obtained by difference. mass of oxygen = g MgO g Mg = g oxygen 5. We need to compare the mass before reaction (initial) with that after reaction (final) to answer this question. initial mass = g calcium hydroxide g ammonium chloride = g final mass = 14.6 g solid residue + ( ) g of gases = g These data support the law of conservation of mass. Note that the gain in the mass of water is equal to the mass of gas absorbed by the water. Law of Constant Composition 7. (a) (b) (c) ( ) g Ratio of O:MgO by mass = g 0.00 g Ratio of O:Mg in MgO by mass = = g g Mg Percent magnesium by mass= 100% = 60.% g MgO 21

6 9. In the first experiment, 2.18 g of sodium produces 5.54 g of sodium chloride. In the second experiment, 2.10 g of chlorine produces.46 g of sodium chloride. The amount of sodium contained in this second sample of sodium chloride is given by mass of sodium =.46 g sodium chloride 2.10 g chlorine = 1.6 g sodium. We now have sufficient information to determine the % Na in each of the samples of sodium chloride. 2.18g Na 1.6g Na %Na = 100% = 9.4% Na %Na = 100% = 9.% Na 5.54g cmpd.46g cmpd Thus, the two samples of sodium chloride have the same composition. Recognize that, based on significant figures, each percent has an uncertainty of 0.1%. 11. The mass of sulfur (0.12 g) needed to produce 0.6 g sulfur dioxide provides the information required for the conversion factor. 0.12g sulfur sulfur mass = g sulfur dioxide = g sulfur 0.6g sulfur dioxide Law of Multiple Proportions 1. By dividing the mass of the oxygen per gram of sulfur in the second sulfur-oxygen compound (compound 2) by the mass of oxygen per gram of sulfur in the first sulfur-oxygen compound (compound 1), we obtain the ratio (shown to the right): g of O (cpd 2) g of S g of O (cpd 1) g of S = To get the simplest whole number ratio we need to multiply both the numerator and the denominator by 2. This gives the simple whole number ratio /2. In other words, for a given mass of sulfur, the mass of oxygen in the second compound (SO ) relative to the mass of oxygen in the first compound (SO 2 ) is in a ratio of :2. These results are entirely consistent with the Law of Multiple Proportions because the same two elements, sulfur and oxygen in this case, have reacted together to give two different compounds that have masses of oxygen that are in the ratio of small positive integers for a fixed amount of sulfur. 15. (a) First of all we need to fix the mass of nitrogen in all three compounds to some common value, for example, g. This can be accomplished by multiplying the masses of hydrogen and nitrogen in compound A by 2 and the amount of hydrogen and nitrogen in compound C by 4/ (1.): Cmpd. A: normalized mass of nitrogen normalized mass of hydrogen = g N 2 = g N = g H 2 = g H Cmpd. C: normalized mass of nitrogen normalized mass of hydrogen = g N 1. = g N = g H 1. = g H Next, we divide the mass of hydrogen in each compound by the smallest mass of hydrogen, namely, g. This gives.000 for compound A, for 22

7 (b) compound B, and for compound C. The ratio of the amounts of hydrogen in the three compounds is (cmpd A) : 1 (cmpd B) : 2 (cmpd C) These results are consistent with the Law of Multiple Proportions because the masses of hydrogen in the three compounds end up in a ratio of small whole numbers when the mass of nitrogen in all three compounds is normalized to a simple value (1.000 g here). The text states that compound B is N 2 H 2. This means that, based on the relative amounts of hydrogen calculated in part (a), compound A might be N 2 H 6 and compound C, N 2 H 4. Actually, compound A is NH, but we have no way of knowing this from the data. Note that the H:N ratios in NH and N 2 H 6 are the same, H:1N. 17. One oxide of copper has about 20% oxygen by mass. If we assume a 100 gram sample, then ~ 20 grams of the sample is oxygen (~1.25 moles) and 80 grams is copper (~1.26 moles). This would give an empirical formula of CuO (copper(ii) oxide). The second oxide has less oxygen by mass, hence the empirical formula must have less oxygen or more copper (Cu:O ratio greater than 1). If we keep whole number ratios of atoms, a plausible formula would be Cu 2 O (copper(i) oxide), where the mass percent oxygen is 11%. Fundamental Charges and Mass-to-Charge Ratios 19. We can calculate the charge on each drop, express each in terms of express each in terms of e = C. drop 1: C = 8e drops 2&: C C = 4e drop 4 : C C = 1e drop 5: C C = 2e C, and finally We see that these values are consistent with the charge that Millikan found for that of the electron, and he could have inferred the correct charge from these data, since they are all multiples of e. 21. (a) (b) Determine the ratio of the mass of a hydrogen atom to that of an electron. We use the mass of a proton plus that of an electron for the mass of a hydrogen atom. mass of proton mass of electron 1.007u u mass of electron u mass of electron 1 4 or mass of proton mass of electron The only two mass-to-charge ratios that we can determine from the data in Table 2-1 are those for the proton (a hydrogen ion, H + ) and the electron.

8 24 mass g 5 For the proton : = = g/c 19 charge C 28 mass g 9 For the electron : = = g/c 19 charge C The hydrogen ion is the lightest positive ion available. We see that the mass-tocharge ratio for a positive particle is considerably larger than that for an electron. Atomic Number, Mass Number, and Isotopes. (a) cobalt Co (b) phosphorus P (c) iron Fe (d) radium-226 Ra a Name Symbol number of protons number of electrons number of neutrons mass number (E) sodium 11Na silicon 28 14Si a rubidium 85 7Rb 7 7 a potassium 40 19K arsenic a 75 As a neon Ne bromine b 80 5Br lead b Pb a This result assumes that a neutral atom is involved. b Insufficient data. Does not characterize a specific nuclide; several possibilities exist. The minimum information needed is the atomic number (or some way to obtain it, such as from the name or the symbol of the element involved), the number of electrons (or some way to obtain it, such as the charge on the species), and the mass number (or the number of neutrons). 27. (a) A 108 Pd atom has 46 protons, and 46 electrons. The atom described is neutral, hence, the number of electrons must equal the number of protons. Since there are 108 nucleons in the nucleus, the number of neutrons is 62 a= 108 nucleons 46 protonsf. (b) The ratio of the two masses is determined as follows: Pd u = = C 12u 29. The mass of 16 O is u. isotopic mass = u = u 24

9 1. Each isotopic mass must be divided by the isotopic mass of 12 C, 12 u, an exact number (a) Cl C = u 12u = (b) (c) Mg C = u 12u = Rn C = u 12u = First, we determine the number of protons, neutrons, and electrons in each species. species: Mg 47 24Cr Co 5 17Cl Th 90 8Sr protons neutrons electrons (a) The numbers of neutrons and electrons are equal for 17Cl (b) 27Co has protons (27), neutrons (), and electrons (24) in the ratio 9:11: (c) The species 50Sn has a number of neutrons (74) equal to its number of protons (50) plus one-half its number of electrons 48 2 = If we let n represent the number of neutrons and p represent the number of protons, then p + 4 = n. The mass number is the sum of the number of protons and the number of neutrons: p + n = 44. Substitution of n = p + 4 yields p + p + 4 = 44. From this relation, we see p = 20. Reference to the periodic table indicates that 20 is the atomic number of the element calcium. 7. The number of protons is the same as the atomic number for iodine, which is 5. There is one more electron than the number of protons because there is a negative charge on the ion. Therefore the number of electrons is 54. The number of neutrons is equal to 70, mass number minus atomic number. 9. For americium, Z = 95. There are 95 protons, 95 electrons, and = 146 neutrons in a single atom of americium-241. Atomic Mass Units, Atomic Masses 41. There are no chlorine atoms that have a mass of u. The masses of individual chlorine atoms are close to integers and this mass is about midway between two integers. It is an average atomic mass, the result of averaging two (or more) isotopic masses, each weighted by its natural abundance. 4. To determine the weighted-average atomic mass, we use the following expression: average atomic mass = isotopic mass fractional natural abundance Each of the three percents given is converted to a fractional abundance by dividing it by 100. Mg atomic mass = u u u = 18.95u u u = 24.1 u 25

10 45. We will use the expression to determine the weighted-average atomic mass u = u Ag = u Ag u u u Ag = u Ag u Since the three percent abundances total 100%, the percent abundance of 40 K is found by difference. 40 % K = % % 6.702% = % Then the expression for the weighted-average atomic mass is used, with the percent abundances converted to fractional abundances by dividing by 100. Note that the average atomic mass of potassium is u u = u u K = 6.68u u K u 6.68 u u mass of K = Mass Spectrometry = u 49. (a) Mass Number Relative Number of atoms (b) As before, we multiply each isotopic mass by its fractional abundance, after which, we sum these products to obtain the (average) atomic mass for the element = = 72.6 = average atomic mass of germanium The result is only approximately correct because the isotopic masses are given to only two significant figures. Thus, only a two-significant-figure result can be quoted. The Periodic Table 51. (a) Ge is in group 14 and in the fourth period. 26

11 (b) (c) (d) Other elements in group 16(6A) are similar to S: O, Se, and Te. Most of the elements in the periodic table are unlike S, but particularly metals such as Na, K, and Rb. The alkali metal (group 1), in the fifth period is Rb. The halogen (group 17) in the sixth period is At. 5. If the seventh period of the periodic table is 2 members long, it will be the same length as the sixth period. Elements in the same family (vertical group), will have atomic numbers 2 units higher. The noble gas following radon will have atomic number = = 118. The alkali metal following francium will have atomic number = = 119. The Avogadro Constant and the Mole 55. (a) (b) (c) atoms Fe 24 atoms of Fe = 15.8 mol Fe = atoms Fe 1 mol Fe atoms Ag 20 atoms of Ag = mol Ag = atoms Ag 1 mol Ag atoms Na 1 atoms of Na = mol Na = atoms Na 1 mol Na 57. (a) (b) (c) (d) 1 mol Zn moles of Zn = g Zn = 6.47 mol Zn 65.9 g Zn 1 mol Cr atoms Cr 27 # of Cr atoms = 147,400 g Cr = atoms Cr g Cr 1 mol Cr 12 1 mol Au g Au 10 mass Au = atoms Au.10 g Au atoms Au 1 mol Au g F 1 mol F g F mass of F atom = 1 mol F atoms F 1 atom F For exactly 1 F atom, the number of sig figs in the answer is determined by the least precise number in the calculation, namely the mass of fluorine. 59. Determine the mass of Cu in the jewelry, then convert to moles and finally to the number of atoms. If sterling silver is 92.5% by mass Ag, it is = 7.5% by mass Cu. Conversion pathway approach: 7.5 g Cu number of Cu atoms =.24 g sterling g sterling g Cu 1 mol Cu 22 number of Cu atoms = Cu atoms 1 mol u atoms Cu 27

12 Stepwise approach: 7.5 g Cu.24 g sterling 2.49 g Cu g sterling 1mol Cu 2.49 g Cu 0.09 mol Cu g Cu atoms Cu mol Cu = Cu atoms 1mol Cu 61. We first need to determine the number of Pb atoms of all types in 215 mg of Pb, and then use the percent abundance to determine the number of 204 Pb atoms present g 1 mol Pb atoms 14 Pb atoms Pb atoms = 215 mg Pb 1000 mg 207.2g Pb 1mol Pb 1000Pb atoms = atoms Pb 6. We will use the average atomic mass of lead, g/mol, to answer this question. 0 μgpb 1dL 1gPb 1molPb 6 (a) mol Pb / L 1dL 0.1L 10 μg Pb g (b) mol Pb 1 L atoms L 1000mL 1mol Pb atoms / ml 65. To answer this question, we simply need to calculate the ratio of the mass (in grams) of each sample to its molar mass. Whichever elemental sample gives the largest ratio will be the one that has the greatest number of atoms. (a) Iron sample: 10 cm 10 cm 10 cm 7.86 g cm - = 7860 g Fe 1 mol Fe 7860 g Fe = 141 moles of Fe atoms g Fe g H (b) Hydrogen sample: 2 1 mol H = 496 mol of H 2 molecules = 2 ( g H) 992 mol of H atoms g S (c) Sulfur sample: 1 mol S = 624 moles of S atoms g S 454 g Hg (d) Mercury sample: 76 lb Hg 1 lb Hg 1 mol Hg = 172 mol of Hg atoms g Hg Clearly, then, it is the 1.00 kg sample of hydrogen that contains the greatest number of atoms. 28

13 INTEGRATIVE AND ADVANCED EXERCISES volume of nucleus(single proton) π r (0.510 cm ) 5 10 cm g 15 density 10 g/cm cm Let Z = # of protons, N = # of neutrons, E = # of electrons, and A = # of nucleons = Z + N. (a) Z + N = 4 The mass number is 4 and the species is an atom. N = Z The atom has 60.0% more neutrons than protons. Next we will substitute the second expression into the first and solve for Z. Z N 4 Z Z Z 4 Z 90 protons Thus this is an atom of the isotope Th. (b) Z = E + 2 The ion has a charge of +2. Z = E There are 10.0% more protons than electrons. By equating these two expressions and solving for E, we can find the number of electrons. E E EE E E 20 electrons Z , (titanium) The ion is Ti. There is not enough information to determine the mass number. (c) Z + N = 110 The mass number is 110. Z = E + 2 The species is a cation with a charge of +2. N = 1.25 E Thus, there are 25.0% more neutrons than electrons. By substituting the second and third expressions into the first, we can solve for E, the number of electrons. 108 (E 2 ) E E E E Then Z , (the element is Sn) N Thus, it is Sn. 74. A = Z + N = 2.50 Z The mass number is 2.50 times the atomic number The neutron number of selenium-82 equals 82 4 = 48, since Z = 4 for Se. The neutron number of isotope Y also equals 48, which equals 1. times the atomic number of isotope Y. 48 Thus Z Y ZY 6 1. The mass number of isotope Y = = 84 = the atomic number of E, and thus, the element is Po. Thus, from the relationship in the first line, the mass number of 210 E 2.50 Z The isotope E is Po. 29

14 by x and that of To solve this question, represent the fractional abundance of N (1 x). Then use the expression for determining average atomic mass x (1 x) x x OR x 14 N by % 99.64% percent abundanceof 14 N. Thus,0.6% percent abundance of 15 N. x In this case, we will use the expression for determining average atomic mass- the sum of products of nuclidic mass times fractional abundances (from Figure 2-14)- to answer the question. 196 Hg: u u Hg : u u 199 Hg : u u 200 Hg : u u 201 Hg : u u 202 Hg : u u 204 Hg : u u Atomic weight = u u +.51 u u u u u = u 2.50 cm volume = (15.0 cm12.5 cm0.00 cm) (.1416) (0.00 cm) 2 volume = (56.25 cm 1.47 cm) = 54.8 cm 8.80 g mass of object 54.8 cm 482 g Monel metal 1 cm Then determine the number of silicon atoms in this quantity of alloy g Si 1 mol Si Si atoms g Monel metal 2.10 Si atoms g metal g Si 1 mol Si 2 Finally, determine the number of 0 Si atoms in this quantity of silicon Si atoms 19 0 number of Si atoms = (2. 10 Si atoms) = Si 100 Si atoms 86. The relative masses of Sn and Pb are g Pb (assume one mole of Pb) to ( g/mol Sn =) 24 g Sn. Then the mass of cadmium, on the same scale, is 207.2/1.78 = 116 g Cd. 24gSn 24gSn %Sn 100% 100% 50.1%Sn g alloy 647g alloy %Pb 207.2g Pb 100% 2.0% Pb 647g alloy %Cd 116g Cd 647g alloy 100% 17.9% Cd 0

15 87. We need to apply the law of conservation of mass and convert volumes to masses: Calculate the mass of zinc: 125 cm 7.1 g/cm = 891 g Calculate the mass of iodine: 125 cm 4.9 g/cm = 616 g Calculate the mass of zinc iodide: 164 cm 4.74 g/cm = 777 g Calculate the mass of zinc unreacted: ( ) g = 70 g Calculate the volume of zinc unreacted: 70 g 1cm / 7.1 g = 102 cm FEATURE PROBLEMS 89. The product mass differs from that of the reactants by =.12 grains. In order to determine the percent gain in mass, we need to convert the reactant mass to grains. 8gros 72grains 1 onces = 104 gros gros = 762 grains 1 once 1 gros % mass increase =.12 grains increase grains original 100% = % mass increase The sensitivity of Lavoisier s balance can be as little as 0.01 grain, which seems to be the limit of the readability of the balance; alternatively, it can be as large as.12 grains, which assumes that all of the error in the experiment is due to the (in)sensitivity of the balance. Let us convert 0.01 grains to a mass in grams. 1 gros 1 once 1 livre 0.59 g 5 minimum error = 0.01 gr = 10 g = 0.0 mg 72 gr 8 gros 16 once 1 livre 5 10 g maximum error =.12 gr = 9 10 g = 9 mg 0.01 gr The maximum error is close to that of a common modern laboratory balance, which has a sensitivity of 1 mg. The minimum error is approximated by a good quality analytical balance. Thus we conclude that Lavoisier s results conform closely to the law of conservation of mass. 92. We begin with the amount of reparations and obtain the volume in cubic kilometers with a series of conversion factors. Conversion pathway approach: 9 1troy oz Au 1.10g Au 1mol Au atoms Au V = \$ \$ troy oz Au g Au 1mol Au 1ton seawater 2000lb seawater 45.6 g sea water 1cm seawater Au atoms 1ton seawater 1 lb sea water 1.0g seawater 1m 1km = km 100cm 1000 m 5 1

16 Stepwise approach: \$ troy oz Au = g Au atoms Au 1troy oz Au 1.10g Au \$ troyoz Au 10 1mol Au atoms Au g Au mol Au atoms Au g Au 1mol Au 1ton seawater 2000 lb seawater tons seawater lbs seawater Au atoms 1ton seawater g seawater 20 1cm seawater lbs seawater g seawater 1 lb seawater 1.0g seawater 1m 1km cm seawater = km 100cm 1000 m cm seawater 9. We start by using the percent natural abundances for 87 Rb and 85 Rb along with the data in the spiked mass spectrum to find the total mass of Rb in the sample. Then, we calculate the Rb content in the rock sample in ppm by mass by dividing the mass of Rb by the total mass of the rock sample, and then multiplying the result by 10 6 to convert to ppm. 87 Rb = 27.8% natural abundance 85 Rb = 72.17% natural abundance 87 Rb(natural) Therefore, = 27.8% 85 Rb(natural) 72.17% = For the 87 Rb(spiked) sample, the 87 Rb peak in the mass spectrum is 1.12 times as tall as the Rb(natural)+ Rb(spiked) Rb peak. Thus, for this sample = Rb(natural) Using this relationship, we can now find the masses of both 85 Rb and 87 Rb in the sample. 87 Rb(natural) So, = 0.856; Rb(natural) Rb(natural) = 85 Rb(natural) Rb(natural) Rb (natural) Rb(spiked) = = Rb(natural) Rb(spiked) = Rb(natural) Rb(natural)+ Rb(spiked) Rb(natural)+ Rb(spiked) and = = Rb(natural) Rb(natural) Since the mass of 87 Rb(spiked) is equal to g, the mass of 87 Rb(natural) must be μg = g of 87 Rb(natural) So, the mass of μg of Rb(natural) Rb(natural) = = g of 85 Rb(natural)

17 Therefore, the total mass of Rb in the sample = g of 87 Rb(natural) g of 85 Rb(natural) = g of Rb. Convert to grams: 1 g Rb = g of Rb = g Rb μg Rb g Rb Rb content (ppm) = 10 6 = 159 ppm Rb 0.50 g of rock SELF-ASSESSMENT EXERCISES 97. The answer is (b). If all of the zinc reacts and the total amount of the product (zinc sulfide) is 14.9 g, then 4.9 g of S must have reacted with zinc. Therefore,.1 g of S remain. 98. The answer is (d). It should be remembered that atoms combine in ratios of whole numbers. Therefore: (a) 16 g O (1 mol O/16 g O) = 1 mol O, and 85.5 g Rb (1 mol Rb/85.5 g Rb) = 1 mol Rb Therefore, the O:Rb ratio is 1:1. (b) Same calculations as above give an O:Rb ratio of 0.5:0.5, or 1:1. (c) Same type calculation gives an O:Rb ratio of 2:1. Because all of the above combine in O and Rb in whole number ratios, they are all at least theoretically possible. 99. The answer is (c). Cathode rays are beams of electrons, and as such have identical properties to β particles, although they may not have the same energy The answer is (a), that the greatest portion of the mass of an atom is concentrated in a small but positively charged nucleus The answer is (d). A hydrogen atom has one proton and one electron, so its charge is zero. A neutron has the same charge as a proton, but is neutral. Since most of the mass of the atom is at the nucleus, a neutron has nearly the same mass as a hydrogen atom Cl 10. The answer is (d), calcium, because they are in the same group (a) Group 18, (b) Group 17, (c) Group 1 and Group 1 (d) Group (d) and (f)

18 106. (c), because it is not close to being a whole number 107. The answer is (d). Even with the mass scale being redefined based on 84 Xe, the mass ratio between 12 C and 84 Xe will remain the same. Using 12 C as the original mass scale, the mass ratio of 12 C : 84 Xe is 12 u/ u = Therefore, redefining the mass scale by assigning the exact mass of 84 u to 84 Xe, the relative mass of 12 C becomes = u The answer is (b) 1000 g 1 mol Fe kg Fe = 100 mol. Fe 1 kg g Fe 1 mol C g C = 50.0 mol C 12 g C Therefore, 100 moles of Fe has twice as many atoms as 50.0 moles of C mol Fe 2.27 g Fe = mol Fe g Fe 1 mol O g C = mol O g O Dividing the two mole values to obtain the mole ratio, we get: / = That is, 1.50 moles (or atoms) of O per 1 mole of Fe, or moles of O per 2 moles of Fe (Fe 2 O ). Performing the above calculations for a compound with g of Fe to g of O yields mol of Fe and mol of O, or a mole ratio of 1., or a 4: ratio (Fe O 4 ) The weighted-average atomic mass of Sr is expressed as follows: atomic mass of Sr = amu = 8.914(0.0056) x [1-( x)] (0.8258) Rearrange the above equation and solve for x, which is or 9.5%, which is the relative abundance of 86 Sr. Therefore, the relative abundance of 87 Sr is or 7.%. The reason for the imprecision is the low number of significant figures for 84 Sr This problem lends itself well to the conversion pathway: 0.15 mg Au 1 ton seawater 1 kg 1.0 g seawater 250 ml 1 ton seawater 1000 kg 1000 mg 1 ml seawater sample 1 g Au 1 mol Au atoms 1000 mg Au g Au 1 mol Au atoms of Au 4

Chapter 2 Atoms, Ions, and the Periodic Table

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