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All Textbook Solutions for Principles of Modern Chemistry

Classify the following materials as substances or mixtures: table salt, wood, mercury, air, water, sea water, sodium chloride, and mayonnaise. If they are mixtures, subclassify them as homogeneous or heterogeneous; if they are substances, subclassify them as compounds or elements.Classify the following materials as substances or mixtures: absolute (pure) alcohol, milk (as purchased in a store), copper wire, rust, barium bromide, concrete, baking soda, and baking powder. If they are mixtures, subclassify them as homogeneous or heterogeneous; if they are substances, subclassify them as compounds or elements.A 17th-century chemist wrote of the “simple bodies which enter originally into the composition of mixtures and into which these mixtures resolve themselves or may be finally resolved.” What is being discussed?Since 1800, almost 200 sincere but erroneous reports of the discovery of new chemical elements have been made. Why have mistaken reports of new elements been so numerous? Why is it relatively easy to prove that a material is not a chemical element, but difficult to prove absolutely that a material is an element?A sample of ascorbic acid (vitamin C) is synthesized in the laboratory. It contains 30.0 g carbon and 40.0 g oxygen. Another sample of ascorbic acid, isolated from lemons (an excellent source of the vitamin), contains 12.7 g carbon. Compute the mass of oxygen (in grams) in the second sample.A sample of a compound synthesized and purified in the laboratory contains 25.0 g hafnium and 31.5 g tellurium. The identical compound is discovered in a rock formation. A sample from the rock formation contains 0.125 g hafnium. Determine how much tellurium is in the sample from the rock formation.Nitrogen (N) and silicon (Si) form two binary compounds with the following compositions: a) Compute the mass of silicon that combines with 1.0000 g of nitrogen in each case. (b) Show that these compounds satisfy the law of multiple proportions. If the second compound has the formula Si3N4 , what is the formula of the first compound?Iodine (I) and fluorine (F) form a series of binary compounds with the following compositions: (a) Compute in each case the mass of fluorine that combines with 1.0000 g iodine. (b) By figuring out small whole-number ratios among the four answers in part (a), show that these compounds satisfy the law of multiple proportions.Vanadium (V) and oxygen (O) form a series of compounds with the following compositions: What are the relative numbers of atoms of oxygen in the compounds for a given mass of vanadium?10P 11P 12P Pure nitrogen dioxide (NO2) forms when dinitrogen oxide (N2O) and oxygen (O2) are mixed in the presence of aCertaincatalyst. What volumes of N2O and oxygen are needed to produce 4.0 L NO2 if all gases are held at the same conditions of temperature and pressure?Gaseous methanol (CH3OH) reacts with oxygen (O2) to produce water vapor and carbon dioxide. What volumes of water vapor and carbon dioxide will be produced from 2.0 L methanol if all gases are held at the same temperature and pressure conditions?In J. J. Thompson’s experiment depicted in Figures 1.10 and 1.11, assume that the electrons are initially traveling at a speed of 8.00106ms1 in the +x direction and the electrostatic plates have a length of l=0.10m , between which the electrons are deflected toward the -y direction (downward) by an electric field of magnitude 200Vm1 . (Note that 1volt=1V=1JC1 .) Calculate S, the magnitude of the downward displacement, if the fluorescent screen is located 0.90 m beyond the exit of the region between the two electrostatic plates. No magnetic field is applied to counteract the electrostatic force. (Caution: L is not 1.0 m nor 0.9 m; see Figure 1.11.)In the problem 15 above, what is vy , the y-component of the electron’s velocity, when it has reached the right edge of the plates? Note that ay=vyt (be careful with the sign). How is the ratio S/L related to vx and vy , if vy is calculated at the right edge of the plates? The distances S and L are shown in Figure 1.11.The natural abundances and isotopic masses of the element silicon (Si) relative to 12C=512.00000 are Calculate the atomic mass of naturally occurring silicon.The natural abundances and isotopic masses of the element neon (Ne) are Calculate the atomic mass of naturally occurring neon.19P More than half of all the atoms in naturally occurring zirconium are 90Zr . The other four stable isotopes of zirconium have the following relative atomic masses and abundances: Compute the relative atomic mass of 90Zr to four significant digits, using the tabulated relative atomic mass 91.224 for natural zirconium.The isotope of plutonium used for nuclear fission is 239Pu . Determine (a) the ratio of the number of neutrons in a 239Pu nucleus to the number of protons, and (b) the number of electrons in a single plutonium atom.The last “missing” element from the first six periods was promethium, which was finally discovered in 1947 among the fission products of uranium. Determine (a) the ratio of the number of neutrons in a 145Pm nucleus to the number of protons, and (b) the number of electrons in a single promethium atom.23P In 1982, the production of a single atom of 109266Mt (meitnerium-266) was reported. Describe the composition of a neutral atom of this isotope for protons, neutrons, and electrons.25P 26P Compute the relative molecular masses of the following compounds on the 12C scale: (a) P4O10 (b) BrCl (c) Ca( NO3)2(d) KMnO4 (e) ( NH4)2SO4 28P Suppose that a person counts out gold atoms at the rate of one each second for the entire span of an 80-year life. Has the person counted enough atoms to be detected with an ordinary balance? Explain.A gold atom has a diameter of 2.881010m . Suppose the atoms in 1.00 mol of gold atoms are arranged just touching their neighbors in a single straight line. Determine the length of the line.The vitamin A molecule has the formula C20H30O , and a molecule of vitamin A2 has the formula C20H28O . Determine how many moles of vitamin A2 contain the same number of atoms as 1.000 mol vitamin A.Arrange the following in order of increasing mass: 1.06molSF4;117gCH4;8.71023 molecules of Cl2O7 ; and 4171023 atoms of argon (Ar).Mercury is traded by the “flask,” a unit that has a mass of 34.5 kg. Determine the volume of a flask of mercury if the density of mercury is 13.6gcm3 .Gold costs $400 per troy ounce, and 1troyounce5=31.1035g . Determine the cost of 10.0cm3 gold if the density of gold is 19.32gcm3 at room conditions.Aluminum oxide (Al2O3) occurs in nature as a mineral called corundum, which is noted for its hardness and resistance to attack by acids. Its density is 3.97gcm3 . Calculate the number of atoms of aluminum in 15.0cm3 corundum.36P Soft wood chips weighing 17.2 kg are placed in an iron vessel and mixed with 150.1 kg water and 22.43 kg sodium hydroxide. A steel lid seals the vessel, which is then placed in an oven at 250°C for 6 hours. Much of the wood fiber decomposes under these conditions; the vessel and lid do not react. (a) Classify each of the materials mentioned as a substance or mixture. Subclassify the substances as elements or compounds. (b) Determine the mass of the contents of the iron vessel after the reaction.In a reproduction of the Millikan oil-drop experiment, a student obtains the following values for the charges on nine different oil droplets. (a) Based on these data alone, what is your best estimate of the number of electrons on each of the above droplets? (Hint: Begin by considering differences in charges between adjacent data points, and see into what groups these are categorized.) (b) Based on these data alone, what is your best estimate of the charge on the electron? (c) Is it conceivable that the actual charge is half the charge you calculated in (b)? What evidence would help you decide one way or the other?A rough estimate of the radius of a nucleus is provided by the formula r=kA1/3 , where k is approximately 1.31013cm and A is the mass number of the nucleus. Estimate the density of the nucleus of 127I (which has a nuclear mass of 2.11022g ) in grams per cubic centimeter. Compare with the density of solid iodine, 4.93gcm3 .In a neutron star, gravity causes the electrons to combine with protons to form neutrons. A typical neutron star has a mass half that of the sun, compressed into a sphere of radius 20 km. If such a neutron star contains 6.01056 neutrons, calculate its density in grams per cubic centimeter. Compare this with the density inside a 232Th nucleus, in which 142 neutrons and 90 protons occupy a sphere of radius 9.11013cm . Take the mass of a neutron to be 1.6751024g and that of a proton to be 1.6731024g .41AP Naturally occurring rubidium (Rb) consists of two isotopes: 85Rb (atomic mass 84.9117) and 87Rb (atomic mass 86.9092). The atomic mass of the isotope mixture found in nature is 85.4678. Calculate the percentage abundances of the two isotopes in rubidium.A sample of a gaseous binary compound of boron and chlorine weighing 2.842 g occupies 0.153 L. This sample is decomposed to give 0.664 g solid boron and enough gaseous chlorine (Cl2) to occupy 0.688 L at the same temperature and pressure. Determine the number of atoms of boron and the number of atoms of chlorine in a molecule of this compound.A newly synthesized compound has the molecular Formula ClF2O2PtF6. Compute, to four significant figures, the mass percentage of each of the four elements in this compound.Acetaminophen is the generic name of the pain reliever in Tylenol and some other headache remedies. The compound has the molecular formula C8H9NO2 . Compute, to four significant figures, the mass percentage of each of the four elements in acetaminophen.Arrange the following compounds from left to right in order of increasing percentage by mass of hydrogen: H2O,C12H26,N4H6,LiH .Arrange the following compounds from left to right in order of increasing percentage by mass of fluorine: HF,C6HF5,BrF,UF6 .“Q-gas” is a mixture of 98.70% helium and 1.30% butane (C4H10) by mass. It is used as a filling for gas-flow Geiger counters. Compute the mass percentage of hydrogen in Q-gas.A pharmacist prepares an antiulcer medicine by mixing 286gNa2CO3 with water, adding 150 g glycine (C2H5NO2) , and stirring continuously at 40°C until a firm mass results. The pharmacist heats the mass gently until all the water has been driven away. No other chemical changes occur in this step. Compute the mass percentage of carbon in the resulting white crystalline medicine.Zinc phosphate is used as a dental cement. A 50.00-mg sample is broken down into its constituent elements and gives 16.58 mg oxygen, 8.02 mg phosphorus, and 25.40 mg zinc. Determine the empirical formula of zinc phosphate.Bromoform is 94.85% bromine, 0.40% hydrogen, and 4.75% carbon by mass. Determine its empirical formula.Fulgurites are the products of the melting that occurs when lightning strikes the earth. Microscopic examination of a sand fulgurite shows that it is a globule with variable composition that contains some grains of the definite chemical composition Fe 46.01%, Si 53.99%. Determine the empirical formula of these grains.A sample of a “suboxide” of cesium gives up 1.6907% of its mass as gaseous oxygen when gently heated, leaving pure cesium behind. Determine the empirical formula of this binary compound.Barium and nitrogen form two binary compounds containing 90.745% and 93.634% barium, respectively. Determine the empirical formulas of these two compounds.12P 13P 14P The empirical formula of a gaseous fluorocarbon is CF2 . At a certain temperature and pressure, a 1-L volume holds 8.93 g of this fluorocarbon, whereas under the same conditions, the 1-L volume holds only 1.70 g gaseous fluorine (F2) . Determine the molecular formula of this compound.At its boiling point (280°C) and at atmospheric pressure, phosphorus has a gas density of 2.7gL1 . Under the same conditions, nitrogen has a gas density of 0.62gL1 . How many atoms of phosphorus are there in one phosphorus molecule under these conditions?A gaseous binary compound has a vapor density that is 1.94 times that of oxygen at the same temperature and pressure. When 1.39 g of the gas is burned in an excess of oxygen, 1.21 g water is formed, removing all the hydrogen originally present. (a) Estimate the molecular mass of the gaseous compound. (b) How many hydrogen atoms are there in a molecule of the compound? (c) What is the maximum possible value of the atomic mass of the second element in the compound? (d) Are other values possible for the atomic mass of the second element? Use a table of atomic masses to identify the element that best fits the data. (e) What is the molecular formula of the compound?A gaseous binary compound has a vapor density that is 2.53 times that of nitrogen at 100°C and atmospheric pressure. When 8.21 g of the gas reacts with AlCl3 at 100°C, 1.62 g gaseous nitrogen is produced, removing all of the nitrogen originally present. (a) Estimate the molecular mass of the gaseous compound. (b) How many nitrogen atoms are there in a molecule of the compound? (c) What is the maximum possible value of the atomic mass of the second element? (d) Are other values possible for the atomic mass of the second element? Use a table of atomic masses to identify the element that best fits the data. (e) What is the molecular formula of the compound?19P 20P For each of the following chemical reactions, calculate the mass of the underlined reactant that is required to produce 1.000 g of the underlined product. (a) Mg_+2HClH2_+MgCl2 (b) 2CuSO4_+4KI2CuI+I2_+2K2SO4 (c) NaBH4_+2H2ONaBO2+4H2_22P An 18.6-g sample of K2CO3 was treated in such a way thatall of its carbon was captured in the compound K2Zn3[Fe( CN)6]2 . Compute the mass (in grams) of thisproduct.24P Disilane (Si2H6) is a gas that reacts with oxygen to givesilica (SiO2) and water. Calculate the mass of silica thatwould form if 25.0cm3 disilane (with a density of 2.78103gcm3 ) reacted with excess oxygen.Tetrasilane (Si4H10) is a liquid with a density of 0.825 gcm23. It reacts with oxygen to give silica (SiO2) and water.Calculate the mass of silica that would form if 25.0cm3 tetrasilane reacted completely with excess oxygen.Cryolite (Na3AlF6) is used in the production of aluminumfrom its ores. It is made by the reaction 6NaOH+Al2O3+12HF2Na3AlF6+9H2O Calculate the mass of cryolite that can be prepared by thecomplete reaction of 287gAl2O3 .Carbon disulfide (CS2) is a liquid that is used in the productionof rayon and cellophane. It is manufactured frommethane and elemental sulfur via the reaction CH4+4SCS2+2H2S Calculate the mass of CS2 that can be prepared by thecomplete reaction of 67.2 g sulfur.Potassium nitrate (KNO3) is used as a fertilizer for certaincrops. It is produced through the reaction 4KCl+4HNO3+O24KNO3+2Cl2+2H2O Calculate the minimum mass of KCl required to produce 567gKNO3 . What mass of Cl2 will be generated as well?Elemental phosphorus can be prepared from calciumphosphate via the overall reaction 2Ca3( PO4)2+6SiO2+10C6CaSiO3+P4+10CO Calculate the minimum mass of Ca3( PO4)2 required toproduce 69.8gP4 . What mass of CaSiO3 is generated as aby-product?An element X has a dibromide with the empirical formula XBr2 and a dichloride with the empirical formula XCl2 .The dibromide is completely converted to the dichloridewhen it is heated in a stream of chlorine according to thereaction XBr2+Cl2XCl21Br2 When 1.500 g XBr2 is treated, 0.890 g XCl2 results. (a) Calculate the atomic mass of the element X. (b) By reference to a list of the atomic masses of the elements,identify the element X.An element A has a triiodide with the formula AI3 and atrichloride with the formula ACl3 . The triiodide is quantitativelyconverted to the trichloride when it is heated in astream of chlorine, according to the reaction AI3+32Cl2ACl3+32I2 If 0.8000gAI3 is treated, 0.3776gACl3 is obtained. (a) Calculate the atomic mass of the element A. (b) Identify the element A.A mixture consisting of only sodium chloride (NaCl) andpotassium chloride (KCl) weighs 1.0000 g. When the mixtureis dissolved in water and an excess of silver nitrate isadded, all the chloride ions associated with the originalmixture are precipitated as insoluble silver chloride (AgCl).The mass of the silver chloride is found to be 2.1476 g.Calculate the mass percentages of sodium chloride andpotassium chloride in the original mixture.A mixture of aluminum and iron weighing 9.62 g reactswith hydrogen chloride in aqueous solution according tothe parallel reactions 2Al+6HCl2AlCl3+3H2Fe+2HClFeCl2+H2 A 0.738-g quantity of hydrogen is evolved when the metalsreact completely. Calculate the mass of iron in theoriginal mixture.When ammonia is mixed with hydrogen chloride (HCl),the white solid ammonium chloride (NH4Cl) is produced.Suppose 10.0 g ammonia is mixed with the same mass ofhydrogen chloride. What substances will be presentafterthe reaction has gone to completion, and what will theirmasses be?The poisonous gas hydrogen cyanide (HCN) is producedby the high-temperature reaction of ammonia with methane (CH4) . Hydrogen is also produced in this reaction. (a) Write a balanced chemical equation for the reactionthat occurs. (b) Suppose 500.0 g methane is mixed with 200.0 g ammonia.Calculate the masses of the substances presentafterthe reaction is allowed to proceed to completion.The iron oxide Fe2O3 reacts with carbon monoxide (CO)to give iron and carbon dioxide: Fe2O3+3CO2Fe+3CO2 The reaction of 433.2 g Fe2O3 with excess CO yields254.3 g iron. Calculate the theoretical yield of iron(assuming complete reaction) and its percentage yield.Titanium dioxide, TiO2 , reacts with carbon and chlorineto give gaseous TiCl4 : TiO2+2C+2Cl2TiCl4+2CO The reaction of 7.39 kg titanium dioxide with excess Cand Cl2 gives 14.24 kg titanium tetrachloride. Calculatethe theoretical yield of TiCl4 (assuming complete reaction)and its percentage yield.Human parathormone has the impressive molecularFormula C691H898N125O164S11 . Compute the mass percentagesof all the elements in this compound.A white oxide of tungsten is 79.2976% tungsten by mass.A blue tungsten oxide also contains exclusively tungstenand oxygen, but it is 80.8473% tungsten by mass. Determinethe empirical formulas of white tungsten oxide andblue tungsten oxide.A dark brown binary compound contains oxygen and ametal. It is 13.38% oxygen by mass. Heating it moderatelydrives off some of the oxygen and gives a red binary compoundthat is 9.334% oxygen by mass. Strong heatingdrives off more oxygen and gives still another binary compound,which is only 7.168% oxygen by mass. (a) Compute the mass of oxygen that is combined with1.000 g of the metal in each of these three oxides. (b) Assume that the empirical formula of the first compoundis MO2 (where M representsthe metal). Givethe empirical formulas of the second and thirdcompounds. (c) Name the metal.A binary compound of nickel and oxygen contains78.06% nickel by mass. Is this a stoichiometric or a nonstoichiometriccompound? Explain.Two binary oxides of the element manganese contain,respectively, 30.40% and 36.81% oxygen by mass. Calculatethe empirical formulas of the two oxides.A possible practical way to eliminate oxides of nitrogen(such as NO2 ) from automobile exhaust gases uses cyanuricacid, C3N3(OH)3 . When heated to the relatively lowtemperature of 625°F, cyanuric acid converts to gaseousisocyanic acid (HNCO). Isocyanic acid reacts with NO2 inthe exhaust to form nitrogen, carbon dioxide, and water,all of which are normal constituents of the air. (a) Write balanced equations for these two reactions. (b) If the process described earlier became practical, howmuch cyanuric acid (in kilograms) would be requiredto absorb the 1.71010kgNO2 generated annuallyin auto exhaust in the United States?Aspartame (molecularformula C14H18N2O5 ) is a sugar substitutein soft drinks. Under certain conditions, 1 mol ofaspartame reacts with 2 mol of water to give 1 mol of asparticacid (molecularformula C4H7NO4 ), 1 mol of methanol(molecularformula CH3OH ), and 1 mol of phenylalanine.Determine the molecularformula of phenylalanine.46AP 47AP Citric acid (C6H8O7) is made by fermentation of sugarssuch as sucrose (C12H22O11) in air. Oxygen is consumedand water generated as a by-product. (a) Write a balanced equation for the overall reaction thatoccurs in the manufacture of citric acid from sucrose. (b) What mass of citric acid is made from 15.0 kg sucrose?49AP A sample of a substance with the empirical formula XBr2 weighs 0.5000 g. When it is dissolved in water and all itsbromine is converted to insoluble AgBr by addition of anexcess of silver nitrate, the mass of the resulting AgBr isfound to be 1.0198 g. The chemical reaction is XBr2+2AgNO32AgBr+X( NO3)2 (a) Calculate the molecularmass (that is, formula mass)of XBr2 . (b) Calculate the atomic mass of X and give its name andsymbol.A newspaper article about the danger of global warmingfrom the accumulation of greenhouse gases such as carbondioxide states that “reducing driving your car by 20 milesa week would prevent release of over 1000 pounds of CO2 per year into the atmosphere.” Is this a reasonable statement?Assume that gasoline is octane (molecularFormula C8H18 ) and that it is burned completely to CO2 and H2O in the engine of your car. Facts (or reasonable guesses)about your car’s gas mileage, the density of octane, andother factors will also be needed.In the Solvay process for producing sodium carbonate (Na2CO3) , the following reactions occur in sequence: NH3+CO2+H2ONH4HCO3NH4HCO3+NaClNaHCO3+NH4Cl2NaHCO3heatNa2CO3+H2O+CO2 How many metric tons of sodium carbonate would beproduced per metric ton of NH3 if the process were 100%efficient (1metricton=1000kg) ?A yield of 3.00gKClO4 is obtained from the (unbalanced)reaction KClO3KClO4+KCl when 4.00 g of the reactant is used. What is the percentageyield of the reaction?54AP Silicon nitride (Si3N4) , a valuable ceramic, is made by thedirect combination of silicon and nitrogen at high temperature.How much silicon must react with excess nitrogento prepare 125 g silicon nitride if the yield of thereaction is 95.0%?Before the element scandium was discovered in 1879, it was known as “eka-boron.” Predict the properties of scandium from averages of the corresponding properties of its neighboring elements in the periodic table. Compare your predictions with the observed values in Appendix F.2P 3P 4P 5P A gold nucleus is located at the origin of coordinates, and an electron is brought to a position 3 2 A from the origin in the +y direction. (a) Calculate the force on the gold nucleus exerted by the electron giving its components Fx and Fy . (b) Calculate the potential energy of the gold nucleus and the electron.7P A gold nucleus is located at the origin of coordinates, and a helium nucleus initially at the coordinates (0,2 A) moves to the position (0,1 A) . (a) Calculate the magnitude of the force on the electron at each separation. (b) Calculate the change in the potential energy of the two nuclei. (c) Calculate the change in the kinetic energy of the helium nucleus assuming its value at 2 A is 2.0 MeVif you assume the gold nucleus is so massive that it stays at the origin.9P 10P Use the data in Table 3.1 to plot the logarithm of ionization energy versus the number of electrons removed for Be. Describe the electronic structure of the Be atom.Use the data in Table 3.1 to plot the logarithm of ionization energy versus the number of electrons removed for Ne. Describe the electronic structure of the Ne atom.13P 14P 15P 16P 17P 18P HF has equilibrium bond length of 0.926 A and bond dissociation energy of 565kJmol1 . Compare the effective potential curve for HF with those for H2 and F2 in Problem 20P For each of the following atoms or ions, state the total number of electrons, the number of valence electrons, and the number of core electrons. (a) Rn (b) Sr+ (c) Se2 (d) Sb2 22P Use the data in Figure 3.11 and Table 3.2 to calculate the energy changes (E) for the following pairs of reactions: (a) K(g)+Cl(g)K+(g)+Cl(g) K(g)+Cl(g)K(g)+Cl+(g) (b) Na(g)+Cl(g)Na+(g)+Cl(g) Na(g)+Cl(g)Na(g)+Cl+(g) Explain why K+Cl and Na+Cl form in preference to KCl+ and NaCl+ .Use the data in Figure 3.11 and Table 3.2 to calculate the energy changes (E) for the following pairs of reactions: (a) Na(g)+I(g)Na+(g)+I(g) Na(g)+I(g)Na(g)+I+(g) (b) Rb(g)+Br(g)Rb+(g)+Br(g) Rb(g)+Br(g)Rb(g)+Br+(g) Explain why Na+I and Rb+Br form in preference to NaI+ and RbBr+ .25P In a gaseous RbF molecule, the bond length is 2.2741010m . Using data from Appendix F and making the same oversimplified assumption as in the prior problem on the shape of the potential curve from Rb++F to an internuclear separation of 2.2741010m , calculate the energy in kJmol1 required to dissociate RbF to neutral atoms.The bond lengths of the XH bonds in NH3,PH3 , and SbH3 are 1.02, 1.42, and 1.71 Å, respectively. Estimate the length of the AsH bond in AsH3 , the gaseous compound that decomposes on a heated glass surface in Marsh’s test for arsenic. Which of these four hydrides has the weakest XH bond?Arrange the following covalent diatomic molecules in order of the lengths of the bonds: BrCl, ClF, IBr. Which of the three has the weakest bond (the smallest bond energy)?The bond length in HI(1.62) is close to the sum of the atomic radii of H (0.37 Å) and I (1.33 Å). What does this fact indicate about the polarity of the bond?30P Use electronegativity values to arrange the following bonds in order of decreasing polarity: NO,NN,NP, and CN .Use electronegativity values to rank the bonds in the following compounds from least ionic to most ionic in character: IF, ICl, ClF, BrCl, and Cl2 .33P 34P 35P Estimate the percent ionic character of the bond in each of the following species. All the species are unstable or reactive under ordinary laboratory conditions, but they can be observed in interstellar space.The percent ionic character of a bond can be approximated by the formula 16+3.52 , where is the magnitude of the difference in the electronegativities of the atoms (see Fig. 3.18). Calculate the percent ionic character of HF, HCl, HBr, HI, and CsF, and compare the results with those in Table 3.7.The percent ionic character of the bonds in several interhalogen Molecules (as estimated from their measured dipole moments and bond lengths) are ClF (11%), BrF(15%), BrCl (5.6%), ICl(5.8%), and IBr (10%). Estimate the percent ionic characters for each of these molecules, using the equation in Problem 37, and compare them with the given values.Assign formal charges to all atoms in the following Lewis diagrams. (a) SO42 (b) S2O32 (c) SbF3 (d) SCN Assign formal charges to all atoms in the following Lewis diagrams. (a) ClO4 (b) yu SO2 (c) y BrO2 (d) 1 NO3 Determine the formal charges on all the atoms in the following Lewis diagrams. Which one would best represent bonding in the molecule HNO?the formal charges on all the atoms in the following Lewis diagrams. Which one would best represent bonding in the molecule Cl2O ?43P In each of the following Lewis diagrams, Z represents a main-group element. Name the group to which Z belongs in each case and give an example of such a compound or ion that actually exists.Draw Lewis electron dot diagrams for the following species: (a) AsH3 ; (b) HOCl; (c) KrF+ ; (d) PO2Cl2 (central P atom).46P 47P Acetic acid is the active ingredient of vinegar. Its chemical formula is CH3COOH , and the second carbon atom is bonded to the first carbon atom and to both oxygen atoms. Draw a Lewis diagram for acetic acid and use Table 3.6 to estimate its bond lengths.Under certain conditions, the stable form of sulfur consists of rings of eight sulfur atoms. Draw the Lewis diagram for such a ring.White phosphorus (P4) consists of four phosphorus atoms arranged at the corners of a tetrahedron. Draw the valence electrons on this structure to give a Lewis diagram that satisfies the octet rule.Draw Lewis electron dot diagrams for the following species, indicating formal charges and resonance diagrams where applicable. (a) H3NBF3 (b) CH3COO2 (acetate ion) (c) HCO3 (hydrogen carbonate ion)Draw Lewis electron dot diagrams for the following species, indicating formal charges and resonance diagrams where applicable. (a) HNC (central N atom) (b) SCN (thiocyanate ion) (c) H2CNN (the first N atom is bonded to the carbon and the second N)Draw Lewis diagrams for the two resonance forms of the nitrite ion, NO2 . In what range do you expect the nitrogenoxygen bond length to fall? (Hint: Use Table 3.6.)Draw Lewis diagrams for the three resonance forms of the carbonate ion, CO32- . In what range do you expect the carbonoxygen bond length to fall? (Hint: Use Table 3.6.)Methyl isocyanate, which was involved in the disaster in Bhopal, India, in 1984, has the chemical formula CH3NCO . Draw its Lewis diagram, including resonance forms. (Note: The N atom is bonded to the two C atoms.)56P Draw Lewis diagrams for the following compounds. In the formula the symbol of the central atom is given first. (Hint: The valence octet may be expanded for the central atom.) (a) PF5 (b) SF4 (c) XeO2F2 Draw Lewis diagrams for the following ions. In the formula the symbol of the central atom is given first. (Hint:The valence octet may be expanded for the central atom.) (a) BrO4 (b) PCl6 (c) XeF6+59P 60P For each of the following molecules or molecular ions, give the steric number, sketch and name the approximate molecular geometry, and describe the directions of any distortions from the approximate geometry due to lone pairs. In each case, the central atom is listed first and the other atoms are all bonded directly to it. (a) ICl4 (b) OF2 (c) BrO3 (d) CS2 For each of the following molecules or molecular ions, give the steric number, sketch and name the approximate molecular geometry, and describe the direction of any distortions from the approximate geometry due to lone pairs. In each case, the central atom is listed first and the other atoms are all bonded directly to it. (a) TeH2 (b) AsF3 (c) PCl4+ (d) XeF5+Give an example of a molecule or ion having a formula of each of the following types and structures. (a) AB3 (planar) (b) AB3 (pyramidal) (c) AB2 (bent) (d) AB32 (planar)Give an example of a molecule or ion having a formula of each of the following types and structures. (a) AB4 (tetrahedral) (b) AB2 (linear) (c) AB6 (octahedral) (d) AB3 (pyramidal)For each of the answers in Problem 59, state whether the species is polar or nonpolar.For each of the answers in Problem 60, state whether the species is polar or nonpolar.67P Mixing SbCl3 and GaCl3 in a 1:1 molar ratio (using liquid sulfur dioxide as a solvent) gives a solid ionic compound of empirical formula GaSbCl6 . A controversy arises over whether this compound is (SbCl2+)(GaCl4) or (GaCl2+)(SbCl4) . (a) Predict the molecular structures of the two anions. (b) It is learned that the cation in the compound has a bent structure. Based on this fact, which formulation is more likely to be correct?(a) Use the VSEPR theory to predict the structure of the NNO molecule. (b) The substance NNO has a small dipole moment. Which end of the molecule is more likely to be the positive end, based only on electronegativity?Ozone (O3) has a nonzero dipole moment. In the molecule of O3 , one of the oxygen atoms is directly bonded to the other two, which are not bonded to each other. (a) Based on this information, state which of the following structures are possible for the ozone molecule: symmetric linear, nonsymmetric linear (for example, different OO bond lengths), and bent. (Note: Even an OO bond can have a bond dipole if the two oxygen atoms are bonded to different atoms or if only one of the oxygen atoms is bonded to a third atom.) (b) Use the VSEPR theory to predict which of the structures of part (a) is observed.Assign oxidation numbers to the atoms in each of the following species: SrBr2,Zn(OH)42,SiH4,CaSiO3,Cr2O72,Ca5( PO4)3F,KO2,CsH .72P 73P 74P 75P 76P 77P 78P 79P 80P 81P 82P 83P 84P 85AP 86AP At large interatomic separations, an alkali halide molecule MX has a lower energy as two neutral atoms, M+X ; at short separations, the ionic form (M+)(X) has a lower energy. At a certain distance, Rc , the energies of the two forms become equal, and it is near this distance that the electron will jump from the metal to the halogen atom during a collision. Because the forces between neutral atoms are weak at large distances, a reasonably good approximation can be made by ignoring any variation in potential V(R) for the neutral atoms between Rc and R= . For the ions in this distance range, Rc is dominated by their Coulomb attraction. (a) Express Rc for the first ionization energy of the metal M and the electron affinity of the halogen X. (b) Calculate Rc for LiF, KBr, and NaCl using data fromAppendix F.88AP 89AP Two possible Lewis diagrams for sulfine (H2CSO) are (a) Compute the formal charges on all atoms. (b) Draw a Lewis diagram for which all the atoms in sulfine have formal charges of zero.There is persuasive evidence for the brief existence of the unstable molecule OPCl. (a) Draw a Lewis diagram for this molecule in which the octet rule is satisfied on all atoms and the formal charges on all atoms are zero. (b) The compound OPCl reacts with oxygen to give O2PCl . Draw a Lewis diagram of O2PCl for which all formal charges are equal to zero. Draw a Lewis diagram in which the octet rule is satisfied on all atoms.The compound SF3N has been synthesized. (a) Draw the Lewis diagram of this molecule, supposing that the three fluoride atoms and the nitrogen atom surround the sulfur atom. Indicate the formal charges. Repeat, but assume that the three fluorine atoms and the sulfur atom surround the nitrogen atom. (b) From the results in part (a), speculate about which arrangement is more likely to correspond to the actual molecular structure.93AP The molecular ion S3N3 has the cyclic structure All SN bonds are equivalent. (a) Give six equivalent resonance hybrid Lewis diagrams for this molecular ion. (b) Compute the formal charges on all atoms in the molecular ion in each of the six Lewis diagrams. (c) Determine the charge on each atom in the polyatomic ion, assuming that the true distribution of electrons is the average of the six Lewis diagrams arrived at in parts (a) and (b). (d) An advanced calculation suggests that the actual charge resident on each N atom is 0.375 and on each S atom is +0.041 . Show that this result is consistent with the overall +1 charge on the molecular ion.95AP 96AP 97AP 98AP A stable triatomic molecule can be formed that contains one atom each of nitrogen, sulfur, and fluorine. Three bonding structures are possible, depending on which is the central atom: NSF, SNF, and SFN. (a) Write a Lewis diagram for each of these molecules, indicating the formal charge on each atom. (b) Often, the structure with the least separation of formal charge is the most stable. Is this statement consistent with the observed structure for this molecule—namely, NSF, which has a central sulfur atom? (c) Does consideration of the electronegativities of N, S, and F from Figure 3.18 help rationalize this observed structure? Explain.The gaseous potassium chloride molecule has a measured dipole moment of 10.3 D, which indicates that it is a very polar molecule. The separation between the nuclei in this molecule is 2.67 Å. What would the dipole moment of a KCl molecule be if there were opposite charges of one fundamental unit (1.601019C) at the nuclei?(a) Predict the geometry of the SbCl52 ion, using the VSEPR method. (b) The ion SbCl63 is prepared from SbCl52 by treatment with Cl . Determine the steric number of the central antimony atom in this ion, and discuss the extension of the VSEPR theory that would be needed for the prediction of its molecular geometry.102AP Predict the arrangement of the atoms about the sulfur atom in F4SPO , assuming that double-bonded atoms require more space than single-bonded atoms.104AP 105AP 106AP 107AP 108AP (a) Determine the oxidation number of lead in each of the following oxides: PbO,PbO2,Pb2O3,Pb3O4 . (b) The only known lead ions are Pb2+ and Pb4+ . How can you reconcile this statement with your answer to part (A)?110AP 111CP 112CP A compound is being tested for use as a rocket propellant. Analysis shows that it contains 18.54% F, 34.61% Cl, and 46.85% O. (a) Determine the empirical formula for this compound. (b) Assuming that the molecular formula is the same as the empirical formula, draw a Lewis diagram for this molecule. Review examples elsewhere in this chapter to decide which atom is most likely to lie at the center. (c) Use the VSEPR theory to predict the structure of the molecule from part (b).114CP Some water waves reach the beach at a rate of one every 3.2 s, and the distance between their crests is 2.1 m. Calculate the speed of these waves.The spacing between bands of color in a chemical wave from an oscillating reaction is measured to be 1.2 cm, and a new wave appears every 42 s. Calculate the speed of propagation of the chemical waves.An FM radio station broadcasts at a frequency of 9.86107s1(98.6MHz) . Calculate the wavelength of the radio waves.The gamma rays emitted by 60Co are used in radiation treatment of cancer. They have a frequency of 2.831020s1 . Calculate their wavelength, expressing your answer in meters and in angstroms.Radio waves of wavelength 6.00102m can be used to communicate with spacecraft over large distances. (a) Calculate the frequency of these radio waves. (b) Suppose a radio message is sent home by astronauts in a spaceship approaching Mars at a distance of 8.01010m from Earth. How long (in minutes) will it take for the message to travel from the spaceship to Earth?An argon ion laser emits light of wavelength of 488 nm. (a) Calculate the frequency of the light. (b) Suppose a pulse of light from this laser is sent from Earth, is reflected from a mirror on the moon, and returns to its starting point. Calculate the time elapsed for the round trip, taking the distance from Earth to the moon to be 3.8105km .The speed of sound in dry air at 20°C is 343.5ms1 , and the frequency of the sound from the middle C note on a piano is 261.6s1 (according to the American standard pitch scale). Calculate the wavelength of this sound and the time it will take to travel 30.0 m across a concert hall.Ultrasonic waves have frequencies too high to be detected by the human ear, but they can be produced and detected by vibrating crystals. Calculate the wavelength of an ultrasonic wave of frequency 5.0104s1 that is propagating through a sample of water at a speed of 1.5103ms1 . Explain why ultrasound can be used to probe the size and position of the fetus inside the mother’s abdomen. Could audible sound with a frequency of 8000s1 be used for this purpose?The maximum in the blackbody radiation intensity curve moves to shorter wavelength as temperature increases. The German physicist Wilhelm Wien demonstrated the relation to be max1/T . Later, Planck’s equation showed the maximum to be max=0.20hc/kt . In 1965, scientists researching problems in telecommunication discovered “background radiation” with maximum wavelength 1.05 mm (microwave region of the EM spectrum) throughout space. Estimate the temperature of space.Use the data in Figure 4.8 to estimate the ratio of radiation intensity at 10,000 Å (infrared) to that at 5000 Å (visible) from a blackbody at 5000 K. How will this ratio change with increasing temperature? Explain how this change occurs.Excited lithium atoms emit light strongly at a wavelength of 671 nm. This emission predominates when lithium atoms are excited in a flame. Predict the color of the flame.Excited mercury atoms emit light strongly at a wavelength of 454 nm. This emission predominates when mercury atoms are excited in a flame. Predict the color of the flame.Barium atoms in a flame emit light as they undergo transitions from one energy level to another that is 3.61019J lower in energy. Calculate the wavelength of light emitted and, by referring to Figure 4.3, predict the color visible in the flame.Potassium atoms in a flame emit light as they undergo transitions from one energy level to another that is 4.91019J lower in energy. Calculate the wavelength of light emitted and, by referring to Figure 4.3, predict the color visible in the flame.The sodium D-line is actually a pair of closely spaced spectroscopic lines seen in the emission spectrum of sodium atoms. The wavelengths are centered at 589.3 nm. The intensity of this emission makes it the major source of light (and causes the yellow color) in the sodium arc light. (a) Calculate the energy change per sodium atom emitting a photon at the d-line wavelength. (b) Calculate the energy change per mole of sodium atoms emitting photons at the d-line wavelength. (c) If a sodium arc light is to produce 1.000 kilowatt (1000Js1) of radiant energy at this wavelength, howmany moles of sodium atoms must emit photons per second?The power output of a laser is measured by its wattage, that is, the number of joules of energy it radiates per second (1W=1Js1) . A 10-W laser produces a beam of green light with a wavelength of 520 nm (5.2107m) . (a) Calculate the energy carried by each photon. (b) Calculate the number of photons emitted by the laser per second.In a FranckHertz experiment on sodium atoms, the first excitation threshold occurs at 2.103 eV. Calculate the wavelength of emitted light expected just above this threshold. (Note: Sodium vapor lamps used in street lighting emit spectral lines with wavelengths 5891.8 and 5889.9 Å.)In a FranckHertz experiment on hydrogen atoms, the first two excitation thresholds occur at 10.1 and 11.9 eV. Three optical emission lines are associated with these levels. Sketch an energy-level diagram for hydrogen atoms based on this information. Identify the three transitions associated with these emission lines. Calculate the wavelength of each emitted line.Use the Bohr model to calculate the radius and the energy of the B4+ ion in the n=3 state. How much energy would be required to remove the electrons from 1 mol of B4+ in this state? What frequency and wavelength of light would be emitted in a transition from the n=3 to the n=2 state of this ion? Express all results in SI units.He+ ions are observed in stellar atmospheres. Use the Bohr model to calculate the radius and the energy of He+ in the n=5 state. How much energy would be required to remove the electrons from 1 mol of He+ in this state? What frequency and wavelength of light would be emitted in a transition from the n=5 to the n=3 state of this ion? Express all results in SI units.The radiation emitted in the transition from n=3 to n=2 in a neutral hydrogen atom has a wavelength of 656.1 nm. What would be the wavelength of radiation emitted from a doubly ionized lithium atom (Li2+) if a transition occurred from n=3 to n=2 ? In what region of the spectrum does this radiation lie?22P 23P When an intense beam of green light is directed onto a copper surface, no electrons are ejected. What will happen if the green light is replaced with red light?Cesium frequently is used in photocells because its work function (3.431019J) is the lowest of all the elements. Such photocells are efficient because the broadest range of wavelengths of light can eject electrons. What colors of light will eject electrons from cesium? What colors of light will eject electrons from selenium, which has a work function of 9.51019J ?Alarm systems use the photoelectric effect. A beam of light strikes a piece of metal in the photocell, ejecting electrons continuously and causing a small electric current to flow. When someone steps into the light beam, the current is interrupted and the alarm is triggered. What is the maximum wavelength of light that can be used in such an alarm system if the photocell metal is sodium, with a work function of 4.411019J ?Light with a wavelength of 2.50107m falls on the surface of a piece of chromium in an evacuated glass tube. If the work function of chromium is 7.211019J , determine (a) the maximum kinetic energy of the emitted photoelectrons and (b) the speed of photoelectrons that have this maximum kinetic energy.Calculate the maximum wavelength of electromagnetic radiation if it is to cause detachment of electrons from the surface of metallic tungsten, which has a work function of 7.291019J . If the maximum speed of the emitted photoelectrons is to be 2.00106ms1 , what should the wavelength of the radiation be?29P 30P Calculate the de Broglie wavelength of the following: (a) an electron moving at a speed of 1.00103ms1 (b) a proton moving at a speed of 1.00103ms1 (c) a baseball with a mass of 145 g, moving at a speed of 75kmhr1 Calculate the de Broglie wavelength of the following: (a) electrons that have been accelerated to a kinetic energy of 1.20107Jmol1 (b) a helium atom moving at a speed of 353ms1 (the root-mean-square speed of helium atoms at 20 K) (c) a krypton atom moving at a speed of 299ms1 (the root-mean-square speed of krypton atoms at 300 K)33P 34P (a) The position of an electron is known to be within 10(1.0109m) . What is the minimum uncertainty in its velocity component in this direction? (b) Repeat the calculation of part (a) for a helium atom.No object can travel faster than the speed of light, so it would appear evident that the uncertainty in the speed of any object is at most 3108ms1 . (a) What is the minimum uncertainty in the position of an electron, given that we know nothing about its speed except that it is slower than the speed of light? (b) Repeat the calculation of part (a) for the position of a helium atom.(a) Using Equation 4.36, make a graph of the n=3 wave function and the square of this wave function for a particle in a box with the edges at x=0 and x=7 . Estimate the probability of finding the particle between x1=3 and x2=4 . You may either do an integral or find the area under the curve by counting the number of rectangular boxes (roughly estimating the fractional boxes), and then multiply by the area of each box, watching your units. Show your calculation with units for credit. (b) Verify that the n=3 wave function in (a) is an allowed quantum state (sometimes called an eigenfunction) of by substituting it for in the left side of the equation =E immediately following Eq. 4.32. Calculate the derivatives to see if your result E is a constant multiplied by the original n=3 wavefunction. What does the constant you get tell you about the energy of thiseigenstate? Is it in agreement with the energy for the n=3 level you would calculate from Equation 4.37?Using a simple particle-in-a-box model for the multiple bonding in 1,2-butadiene (see Example 4.7) and the n=2 wave function for the weakest bound electron, calculate the probability of finding the electron in an 0.1 interval centered midway between the two inner carbon atoms (that is, the center is at x=2.11 , so this interval is from x1=2.06 to x2=2.16 ). Then calculate the probability of finding the electron in an 0.1 interval centered midway between an end carbon atom and the carbon atom that is double-bonded to it in the Lewis dot structure. (You may calculate the appropriate integrals or estimate the relevant areas under the curve graphically.) Then recalculate the probabilities by approximating the integral as |( x 0)|2x , where x0 is evaluated in the middle of the range from x1 to x2 . Finally, explain why you can’t approximate the integral needed for Problem 37(a) in this way.Chapter 3 introduced the concept of a double bond between carbon atoms, represented by C=C , with a length near 1.34 Å. The motion of an electron in such a bond can be treated crudely as motion in a one-dimensional box. Calculate the energy of an electron in each of its three lowest allowed states if it is confined to move in a one-dimensional box of length 1.34 Å. Calculate the wavelength of light necessary to excite the electron from its ground state to the first excited state.When metallic sodium is dissolved in liquid sodium chloride, electrons are released into the liquid. These dissolved electrons absorb light with a wavelength near 800 nm. Suppose we treat the positive ions surrounding an electron crudely as defining a three-dimensional cubic box of edge L, and we assume that the absorbed light excites the electron from its ground state to the first excited state. Calculate the edge length L in this simple model.41P 42P 43P 44P A piano tuner uses a tuning fork that emits sound with a frequency of 440s1 . Calculate the wavelength of the sound from this tuning fork and the time the sound takes to travel 10.0 m across a large room. Take the speed of sound in air to be 343ms1 .The distant galaxy called Cygnus A is one of the strongest sources of radio waves reaching Earth. The distance of this galaxy from Earth is 31024m . How long (in years) does it take a radio wave of wavelength 10 m to reach Earth? What is the frequency of this radio wave?Hot objects can emit blackbody radiation that appears red, orange, white, or bluish white, but never green. Explain.Compare the energy (in joules) carried by an X-ray photon (wavelength=0.20nm) with that carried by an AM radio wave photon (=0.20m) . Calculate the energy of 1.00 mol of each type of photon. What effect do you expect each type of radiation to have for inducing chemical reactions in the substances through which it passes?The maximum in Planck’s formula for the emission of blackbody radiation can be shown to occur at a wavelength max=0.20hc/kT . The radiation from the surface of the sun approximates that of a blackbody with max=465nm . What is the approximate surface temperature ofthe sun?50AP When ultraviolet light of wavelength 131 nm strikes a polished nickel surface, the maximum kinetic energy of ejected electrons is measured to be 7.041019J . Calculate the work function of nickel.Express the speed of the electron in the Bohr model in terms of the fundamental constants (me,e,h,0) , the nuclear charge Z, and the quantum number n. Evaluate the speed of an electron in the ground states of He+ ion and U91+ . Compare these speeds with the speed of light c. As the speed of an object approaches the speed of light, relativistic effects become important. In which kinds of atoms do you expect relativistic effects to be greatest?Photons are emitted in the Lyman series as hydrogen atoms undergo transitions from various excited states to the ground state. If ground-state He+ are present in the same gas (near stars, for example), can they absorb these photons? Explain.54AP The energies of macroscopic objects, as well as those of microscopic objects, are quantized, but the effects of the quantization are not seen because the difference in energy between adjacent states is so small. Apply Bohr’s quantization of angular momentum to the revolution of Earth (mass6.01024kg) , which moves with a speed of 3.0104ms1 in a circular orbit (radius1.51011m) about the sun. The sun can be treated as fixed. Calculate the value of the quantum number n for the present state of the Earthsun system. What would be the effect of an increase in n by 1?56AP 57AP It has been suggested that spacecraft could be powered by the pressure exerted by sunlight striking a sail. The force exerted on a surface is the momentum p transferred to the surface per second. Assume that photons of 6000 Å light strike the sail perpendicularly. How many must be reflected per second by 1cm2 of surface to produce a pressure of 106 atm?59AP The normalized wave function for a particle in a one-dimensional box in which the potential energy is zero is (x)=2/Lsin(nx/L) , where L is the length of the box (with the left wall at x=0 ). What is the probability that the particle will lie between x=0 and x=L/4 if the particle is in its n=2 state?A particle of mass m is placed in a three-dimensional rectangular box with edge lengths 2L, L, and L. Inside the box the potential energy is zero, and outside it is infinite; therefore, the wave function goes smoothly to zero at the sides of the box. Calculate the energies and give the quantum numbers of the ground state and the first five excited states (or sets of states of equal energy) for the particle in the box.Which of the following combinations of quantum numbers are allowed for an electron in a one-electron atom? Which are not? (a) n=2,l=2,m=1,ms=12 (b) n=3,l=1,m=0,ms=12 (c) n=5,l=1,m=2,ms=12 (d) n=4,l=1,m=0,ms=12 Which of the following combinations of quantum numbers are allowed for an electron in a one-electron atom? Which are not? (a) n=2,l=2,m=1,ms=0 (b) n=2,l=0,m=0,ms=12 (c) n=7,l=2,m=2,ms=12 (d) n=3,l=3,ms=12 Label the orbitals described by each of the following sets of quantum numbers: (a) n=4,l=1 (b) n=2,l=0 (c) n=6,l=3 Label the orbitals described by each of the following sets of quantum numbers: (a) n=3,l=2 (b) n=7,l=4 (c) n=5,l=1 Estimate the probability of finding an electron which is excited into the 2s orbital of the H atom, looking in a cubical box of volume 0.751036m3 centered at the nucleus. Then estimate the probability of finding the electron if you move the volume searched to a distance of 105.8 pm from the nucleus in the positive z direction. (Note that since these volumes are small, it does not matter whether the volume searched is cubical or spherical.)Using Table 5.2, write down the mathematical expression for the 2px wave function for an electronically excited H atom. Estimate the probability of finding the 2px electron if you look in a cubical box of volume of 0.8(pm)3 centered at a distance of 0.5001010m in the =/2 , =0 direction. Does this probability change as you change ? At what angles is the probability of finding the electron smallest and at what angles is the probability the largest? (Note that =2 is the same location as =0 , so don’t double count.)How many radial nodes and how many angular nodes does each of the orbitals in Problem 3 have?How many radial nodes and how many angular nodes does each of the orbitals in Problem 4 have?Use the mathematical expression for the 2pz wave function of a one-electron atom (see Table 5.2) to show that the probability of finding an electron in that orbital anywhere in the x-y plane is 0. What are the nodal planes for a dxz orbital and for a dx2y2 orbital?(a) Use the radial wave function for the 3p orbital of a hydrogen atom (see Table 5.2) to calculate the value of r for which a node exists. (b) Find the values of r for which nodes exist for the 3s wave function of the hydrogen atom.Calculate the average distance of the electron from the nucleus in a hydrogen atom when the electron is in the 2s orbital. Repeat the calculation for an electron in the 2p orbital.The helium ion He+ is a one-electron system whose wave functions and energy levels are obtained from those for H by changing the atomic number to Z=2 . Calculate the average distance of the electron from the nucleus in the 2s orbital and in the 2p orbital. Compare your results with those in Problem 11 and explain the difference.Spectroscopic studies show that Li can have electrons in its 1s, 2s, and 2p Hartree orbitals, and that Zeff(2s)=1.28 for the 1s22s1 configuration. Estimate the energy of the 2s orbital of Li. Calculate the average distance of the electron from the nucleus in the 2s orbital of Li.Spectroscopic studies of Li also show that Zeff(2p)=1.02 . Estimate the energy of the 2p orbital of Li. Calculate the average distance of the electron from the nucleus in the 2p orbital of Li. Comparing your results with those in Problem 13 shows that the energy values differ by about 50%, whereas the average distances are nearly equal. Explain this observation.Spectroscopic studies show that Na can have electrons in its 1s, 2s, 2p, and 3s Hartree orbitals, and that Zeff(3s)=1.84 . Using data from Problem 13, compare the energies of the Na 3s orbital, the Li 2s orbital, and the H 1s orbital.Using data from Problems 13 and 15, calculate the average distance of the electron from the nucleus in the Na 3s orbital, the Li 2s orbital, and the H 1s orbital. Explain the trend in your results.Give the ground-state electron configurations of the following elements: (a) C (b) Se (c) Fe Give the ground-state electron configurations of the following elements: (a) P (b) Tc (c) Ho 19P Write ground-state electron configurations for the ions Li,B+,F,Al3+,S,Ar+,Br+, and Te . Which do you expect to be paramagnetic due to the presence of unpaired electrons?Identify the atom or ion corresponding to each of the following descriptions: (a) an atom with ground-state electron configuration [Kr]4d105s25p1 (b) an ion with charge 22 and ground-state electron configuration [Ne]3s23p6 (c) an ion with charge +4 and ground-state electron configuration [Ar]3d3 Identify the atom or ion corresponding to each of the following descriptions: (a) an atom with ground-state electron configuration [Xe]4f145d66s2 (b) an ion with charge 1 and ground-state electron configuration [He]2s22p6 (c) an ion with charge +5 and ground-state electron configuration [Kr]4d6 Predict the atomic number of the (as yet undiscovered) element in the seventh period that is a halogen.(a) Predict the atomic number of the (as yet undiscovered) alkali-metal element in the eighth period. (b) Suppose the eighth-period alkali-metal atom turned out to have atomic number 137. What explanation would you give for such a high atomic number (recall that the atomic number of francium is only 87)?Suppose that the spin quantum number did not exist, and therefore only one electron could occupy each orbital of a many-electron atom. Give the atomic numbers of the first three noble-gas atoms in this case.Suppose that the spin quantum number had three allowed values (ms=0,+12,12) . Give the atomic numbers of the first three noble-gas atoms in this case.Photoelectron spectra of mercury (Hg) atoms acquired with radiation from a helium lamp at 584.4 Å show a peak in which the photoelectrons have kinetic energy of 11.7 eV. Calculate the ionization energy of electrons in that level.

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