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All Textbook Solutions for Chemistry & Chemical Reactivity
A 15.5-g piece of chromium, heated to 100.0 C, is dropped into 55.5 g of water at 16.5 C. The final temperature of the metal and the water is 18.9 C. What is the specific heat capacity of chromium? (Assume no energy is lost to the container or to the surrounding air.)Calculate the amount of energy necessary to raise the temperature of 1.00 L of ethanol (d = 0.7849 g/cm3) from 25.0 C to its boiling point (78.3 C) and then to vaporize the liquid. (Cethanol = 244 J/g K; heat of vaporization at 78.3 C = 38.56 kJ/mol.)To make a glass of iced tea, you pour 250 mL of tea, whose temperature is 18.2 C, into a glass containing five ice cubes. Each cube has a mass of 15 g. What quantity of ice will melt, and how much ice will remain floating in the tea? Assume iced tea has a density of 1.0 g/mL and a specific heat capacity of 4.2 J/g K, that energy is transferred only as heat within the system, ice is at 0.0 C, and no energy is transferred between system and surroundings.Nitrogen gas (2.75 L) is confined in a cylinder under constant atmospheric pressure (1.01 105 pascals). The volume of gas decreases to 2.10 L when 485 J of energy is transferred as heat to the surroundings. What is the change in internal energy of the gas?The combustion of ethane, C2H6, has an enthalpy change of 2857.3 kJ for the reaction as written below. Calculate H for the combustion of 15.0 g of C2H6. 2 C2H6(g) + 7 O2(g) 4 CO2(g) + 6 H2O(g) rH=2857.3kJ/mol-rxnAssume 200. mL of 0.400 M HCl is mixed with 200. mL of 0.400 M NaOH in a coffee-cup calorimeter The temperature of the solutions before mixing was 25.10 C; after mixing and allowing the reaction to occur, the temperature is 27.78 C. What is the enthalpy change when one mole of acid is neutralized? (Assume that the densities of all solutions are 1.00 g/mL and their specific heat capacities are 4.20 J/g K.)A 1.00-g sample of ordinary table sugar (sucrose, C12H22O11) is burned in a bomb calorimeter. The temperature of 1.50 103 g of water in the calorimeter rises from 25.00 C to 27.32 C. The heat capacity of the bomb is 837 J/K, and the specific heat capacity of the water is 4.20 J/g K. Calculate (a) the heat evolved per gram of sucrose and (b) the heat evolved per mole of sucrose.Use Hesss law to calculate the enthalpy change for the formation of CS2() from C(s) and S(s) [C(s) + 2 S(s) CS2()] from the following enthalpy values. C(s)+O2(g)CO2(g)rH1=393.5kJ/mol-rxnS(s)+O2(g)SO2(g)rH2=296.8kJ/mol-rxnCS2(l)+3O2(g)CO2(g)+2SO2(g)rH3=1103.9kJ/mol-rxnCalculate the standard enthalpy of combustion for benzene, C6H6. C6H6() + 15/2 O2(g) 6 CO2(g) + 3 H2O() rH = ? The enthalpy of formation of benzene is known [rH[C6H6()] = +49.0 kJ/mol], and other values needed can be found in Appendix L.The standard enthalpies of formation of KNO3(s) and K2S(s) are 494.6 kJ/mol and 376.6 kJ/mol, respectively. a. Determine the standard enthalpy change for the reaction of black powder according to the balanced equation on the previous page. b. Determine the enthalpy change that occurs when 1.00 g of black powder decomposes according to the stoichiometry of the balanced equation above. (Even though black powder is a mixture, assume that we can designate 1 mol of black powder as consisting of exactly 2 mol of KNO3, 3 mol of C, and 1 mol of S.)1.2ACPThe decomposition of nitroglycerin (C3H5N3O9) produces carbon dioxide, nitrogen, water, and oxygen gases. a. Write a balanced chemical equation for the decomposition of nitroglycerin. b. If the decomposition of 1.00 g nitroglycerin releases 6.23 kJ/g of energy in the form of heat, what is the standard molar enthalpy of formation of nitroglycerin?2.1ACP2.2ACP2.3ACP2.4ACP2.5ACPDefine the terms system and surroundings. What does it mean to say that a system and its surroundings are in thermal equilibrium?What determines the directionality of energy transfer as heat?Identify whether the following processes are exothermic or endothermic. Is the sign on qsys positive or negative? (a) combustion of methane (b) melting of ice (c) raising the temperature of water from 25 C to 100 C (d) heating CaCO3(s) to form CaO(s) and CO2(g)Identify whether the following processes are exothermic or endothermic. Is the sign on qsys positive or negative? (a) the reaction of Na(s) and C12(g) (b) cooling and condensing gaseous N2 to form liquid N2 (c) cooling a soft drink from 25 C to 0 C (d) heating HgO(s) to form Hg() and O2(g)The molar heat capacity of mercury is 28.1 J/mol K What is the specific heat capacity of this metal in J/g K?The specific heat capacity of benzene (C6H6) is 1.74 J/g K. What is its molar heat capacity (in J/moI K)?The specific heat capacity of copper metal is 0.385 J/g K. How much energy is required to heat 168 g of copper from 12.2 C to +25.6 C?How much energy as heat is required to raise the temperature of 50.00 mL of water from 25.52 C to 28.75 C? (Density of water at this temperature = 0.997 g/mL.)The initial temperature of a 344-g sample of iron is 18.2 C. If the sample absorbs 2.25 kJ of energy as heat, what is its final temperature?After absorbing 1.850 kJ of energy as heat, the temperature of a 0.500-kg block of copper is 37 C. What was its initial temperature?A 45.5-g sample of copper at 99.8 C is dropped into a beaker containing 152 g of water at 18.5 C. What is the final temperature when thermal equilibrium is reached?One beaker contains 156 g of water at 22 C, and a second beaker contains 85.2 g of water at 95 C. The water in the two beakers is mixed. What is the final water temperature?A 182-g sample of gold at some temperature was added to 22.1 g of water. The initial water temperature was 25.0 C, and the final temperature was 27.5 C. If the specific heat capacity of gold is 0.128 J/g K, what was the initial temperature of the gold sample?When 108 g of water at a temperature of 22.5 C is mixed with 65.1 g of water at an unknown temperature, the final temperature of the resulting mixture is 47.9 C. What was the initial temperature of the second sample of water?A 13.8-g piece of zinc is heated to 98.8 C in boiling water and then dropped into a beaker containing 45.0 g of water at 25.0 C. When the water and metal come to thermal equilibrium, the temperature is 27.1 C. What is the specific heat capacity of zinc?A 237-g piece of molybdenum, initially at 100.0 C, is dropped into 244 g of water at 10.0 C. When the system comes to thermal equilibrium, the temperature is 15.3 C. What is the specific heat capacity of molybdenum?How much energy is evolved as heat when 1.0 L of water at 0 C solidifies to ice? (The heat of fusion of water is 333 J/g.)The energy required to melt 1.00 g of ice at 0 C is 333 J. If one ice cube has a mass of 62.0 g and a tray contains 16 ice cubes, what quantity of energy is required to melt a tray of ice cubes to form liquid water at 0 C?How much energy is required to vaporize 125 g of benzene, C6H6, at its boiling point, 80.1 C? (The heat of vaporization of benzene is 30.8 kJ/mol.)Chloromethane, CH3CI, arises from microbial fermentation and is found throughout the environment. It is also produced industrially, is used in the manufacture of various chemicals, and has been used as a topical anesthetic. How much energy is required to convert 92.5 g of liquid to a vapor at its boiling point, 24.09 C? (The heat of vaporization of CH3Cl is 21.40 kJ/mol.)The freezing point of mercury is 38.8 C. What quantity of energy, in joules, is released to the surroundings if 1.00 mL of mercury is cooled from 23.0 C to 38.8 C and then frozen to a solid? (The density of liquid mercury is 13.6 g/cm3. Its specific heat capacity is 0.140 J/g K and its heat of fusion is 11.4 J/g.)What quantity of energy, in joules, is required to raise the temperature of 454 g of tin from room temperature, 25.0 C, to its melting point, 231.9 C, and then melt the tin at that temperature? (The specific heat capacity of tin is 0.227 J/g K, and the heat of fusion of this metal is 59.2 J/g.)Ethanol, C2HsOH, boils at 78.29 C. How much energy, in joules, is required to raise the temperature of 1.00 kg of ethanol from 20.0 C to the boiling point and then to change the liquid to vapor at that temperature? (The specific heat capacity of liquid ethanol is 2.44 J/g K, and its enthalpy of vaporization is 855 J/g.)A 25.0-mL sample of benzene at 19.9 C was cooled to its melting point, 5.5 C, and then frozen How much energy was given off as heat in this process? (The density of benzene is 0.80 g/mL, its specific heat capacity is 1.74 J/g K, and its heat of fusion is 127 J/g.)As a gas cools, it is compressed from 2.50 L to 1.25 L under a constant pressure of 1.01 105 Pa. Calculate the work (in J) required to compress the gas.A balloon expands from 0.75 L to 1.20 L as it is heated under a constant pressure of 1.01 105 Pa. Calculate the work (in J) done by the balloon on the environment.A balloon does 324 J of work on the surroundings as it expands under a constant pressure of 7.33 104 Pa. What is the change in volume (in L) of the balloon?As the gas trapped in a cylinder with a movable piston cools, 1.34 kJ of work is done on the gas by the surroundings. If the gas is at a constant pressure of 1.33 105 Pa, what is the change of volume (in L) of the gas?When 745 J of energy in the form of heat is transferred from the environment to a gas, the expansion of the gas does 312 J of work on the environment. What is the change in internal energy of the gas?The internal energy of a gas decreases by 1.65 kJ when it transfers 1.87 kJ of energy in the form of heat to the surroundings. (a) Calculate the work done by the gas on the surroundings. (b) Does the volume of gas increase or decrease?A volume of 1.50 L of argon gas is confined in a cylinder with a movable piston under a constant pressure of 1.22 105 Pa. When 1.25 kJ of energy in the form of heat is transferred from the surroundings to the gas, the internal energy of the gas increases by 1.11 kJ. What is the final volume of argon gas in the cylinder?Nitrogen gas is confined in a cylinder with a movable piston under a constant pressure of 9.95 104 Pa. When 695 J of energy in the form of heat is transferred from the gas to the surroundings, its volume decreases by 1.88 L. What is the change in internal energy of the gas?Nitrogen monoxide, a gas recently found to be involved in a wide range of biological processes, reacts with oxygen to give brown NO2 gas. 2 NO(g) + O2(g) NO2(g)rH = 114.1 kJ/mol-rxn Is this reaction endothermic or exothermic? What is the enthalpy change if 1.25 g of NO is converted completely to NO2?Calcium carbide, CaC2, is manufactured by the reaction of CaO with carbon at a high temperature. (Calcium carbide is then used to make acetylene.) CaO(s) + 3 C(s) CaC2(s) + CO(g) rH = +464.8 kJ/mol-rxn Is this reaction endothermic or exothermic? What is the enthalpy change if 10.0 g of CaO is allowed to react with an excess of carbon?Isooctane (2,2,4-trimethylpentane), one of the many hydrocarbons that make up gasoline, burns in air to give water and carbon dioxide. 2 C8H18() + 25 O2(g) 16 CO2(g) + 18 H2O() rH = 10,922 kJ/mol-rxn What is the enthalpy change if you burn 1.00 L of isooctane (d = 0.69 g/mL)?Acetic acid. CH3CO2H, is made industrially by the reaction of methanol and carbon monoxide. CH3OH () + CO(g) CH3CO2H() rH= 134.6 kJ/mol-rxn What is the enthalpy change for producing 1.00 L of acetic acid (d = 1.044 g/mL) by this reaction?You mix 125 mL of 0.250 M CsOH with 50.0 mL of 0.625 M HF in a coffee-cup calorimeter, and the temperature of both solutions rises from 21.50 C before mixing to 24.40 C after the reaction. CsOH(aq) + HF(aq) CsF(aq) + H2O() What is the enthalpy of reaction per mole of CsOH? Assume the densities of the solutions are all 1.00 g/mL, and the specific heat capacities of the solutions are 4.2 J/g K.You mix 125 mL of 0.250 M CsOH with 50.0 mL of 0.625 M HF in a coffee-cup calorimeter, and the temperature of both solutions rises from 21.50 C before mixing to 24.40 C after the reaction. CsOH(aq) + HF(aq) CsF(aq) + H2O() What is the enthalpy of reaction per mole of CsOH? Assume the densities of the solutions are all 1.00 g/mL, and the specific heat capacities of the solutions are 4.2 J|/g K.A piece of titanium metal with a mass of 20.8 g is heated in boiling water to 99.5 C and then dropped into a coffee-cup calorimeter containing 75.0 g of water at 21.7 C. When thermal equilibrium is reached, the final temperature is 24.3 C. Calculate the specific heat capacity of titanium.A piece of chromium metal with a mass of 24.26 g is heated in boiling water to 98.3 C and then dropped into a coffee-cup calorimeter containing 82.3 g of water at 23.3 C. When thermal equilibrium is reached, the final temperature is 25.6 C. Calculate the specific heat capacity of chromium.Adding 5.44 g of NH4NO3(s) to 150.0 g of water in a coffee-cup calorimeter (with stirring to dissolve the salt) resulted in a decrease in temperature from 18.6 C to 16.2 C. Calculate the enthalpy change for dissolving NH4NO3(s) in water, in kJ/mol. Assume the solution (whose mass is 155.4 g) has a specific heat capacity of 4.2 J/g K. (Cold packs take advantage of the fact that dissolving ammonium nitrate in water is an endothermic process.)You should use care when dissolving H2SO4 in water because the process is highly exothermic. To measure the enthalpy change, 5.2 g of concentrated H2SO4() was added (with stirring) to 135 g of water in a coffee-cup calorimeter. This resulted in an increase in temperature from 20.2 C to 28.8 C. Calculate the enthalpy change for the process H2SO4() H2SO4(aq), in kf/mol.Sulfur (2.56 g) was burned in a constant-volume calorimeter with excess O2(g). The temperature increased from 21.25 C to 26.72 C. The bomb has a heat capacity of 923 J/K, and the calorimeter contained 815 g of water. Calculate U per mole of SO2 formed for the reaction S8(s) + 8 O2(g) 8 SO2(g)Suppose you burned 0.300 g of C(s) in an excess of O2(g) in a constant-volume calorimeter to give CO2(g). C(s) + O2(g) CO2(g) The temperature of the calorimeter, which contained 775 g of water, increased from 25.00 C to 27.38 C. The heat capacity of the bomb is 893 J/K. Calculate U per mole of carbon.Suppose you burned 1.500 g of benzoic acid, C6H5CO2H, in a constant-volume calorimeter and found that the temperature increased from 22.50 C to 31.69 C. The calorimeter contained 775 g of water, and the bomb had a heat capacity of 893 J/K. Calculate U per mole of benzoic acid.A 0.692-g sample of glucose, C6H12O6, was burned in a constant-volume calorimeter. The temperature rose from 21.70 C to 25.22 C. The calorimeter contained 575 g of water, and the bomb had a heat capacity of 650 J/K. What is U per mole of glucose?An ice calorimeter can be used to determine the specific heat capacity of a metal. A piece of hot metal is dropped onto a weighed quantity of ice. The energy transferred from the metal to the ice can be determined from the amount of ice melted. Suppose you heated a 50.0-g piece of silver to 99.8 C and then dropped it onto ice. When the metals temperature had dropped to 0.0 C. it is found that 3.54 g of ice had melted. What is the specific heat capacity of silver?A 9.36-g piece of platinum was heated to 98.6 C in a boiling water bath and then dropped onto ice. (See Study Question 47.) When the metals temperature had dropped to 0.0 C, it was found that 0.37 g of ice had melted. What is the specific heat capacity of platinum?The enthalpy changes for the following reactions can be measured: CH4(g) + 2 O2(g) CO2(g) + 2 H2O(g) rH = 802.4 kJ/mol-rxn CH3OH(g) + 32 O2(g) CO2(g) + 2 H2O(g) rH = 676 kJ/mol-rxn (a) Use these values and Hesss law to determine the enthalpy change for the reaction CH4(g) + O2(g) CH3OH(g) (b) Draw an energy level diagram that shows the relationship between the energy quantities involved in this problem.The enthalpy changes of the following reactions can be measured: C2H4(g) + 3 O2(g) 2 CO2(g) + 2 H2O() rH = 1411.1 kJ/mol-rxn Q2H5OH() + 3 O2(g) 2 CO2(g) + 3 H2O() rH = 1367.5 kJ/mol-rxn (a) Use these values and Hesss law to determine the enthalpy change for the reaction C2H4(g) + H2O() C2H5OH() (b) Draw an energy level diagram that shows the relationship between the energy quantities involved in this problem.Enthalpy changes for the following reactions can be determined experimentally: N2(g) + 3 H2(g) 2 NH3(g) rH = 91.8 kJ/mol-rxn 4 NH3(g) + 5 O2(g) 4 NO(g) + 6 H2O(g) rH = 906.2 kJ/mol-rxn H2(g) + O2(g) H2O(g) rH = 241.8 kl/mol-rxn Use these values to determine the enthalpy change for the formation of NO(g) from the elements (an enthalpy change that cannot be measured directly because the reaction is reactant-favored). N2(g) + O2(g) NO(g) rH = ?You wish to know the enthalpy change for the formation of liquid PCl3 from the elements. P4(s) + 6 Cl2(g) 4 PCl3() rH = ? The enthalpy change for the formation of PC15 from the elements can be determined experimentally, as can the enthalpy change for the reaction of PCl3 () with more chlorine to give PCl5(s): P4(s) + 10 Cl2(g) 4 PCl5(s) rH = 1774.0 kJ/mol-rxn PCl3() + Cl2(g) PC15(s) rH = 123.8 kJ/mol-rxn Use these data to calculate the enthalpy change for the formation of 1.00 mol of PCl3() from phosphorus and chlorine.Write a balanced chemical equation for the formation of CH3OH() from the elements in their standard states. Find the value for rH for CH3OH() in Appendix L.Write a balanced chemical equation for the formation of CaCO3(s) from the elements in their standard states. Find the value for rH for CaCO3(s) in Appendix L.(a) Write a balanced chemical equation for the formation of 1 mol of Cr2O3(s) from Cr and O2 in their standard states. (Find the value for fH for Cr2O3(s) in Appendix L.) (b) What is the standard enthalpy change if 2.4 g of chromium is oxidized to Cr2O3(s)?(a) Write a balanced chemical equation for the formation of 1 mol of MgO(s) from the elements in their standard states. (Find the value for fH for MgO(s) in Appendix L.) (b) What is the standard enthalpy change for the reaction of 2.5 mol of Mg with oxygen?Use standard enthalpies of formation in Appendix L to calculate enthalpy changes for the following: (a) 1.0 g of white phosphorus burns, forming P4Ol0(s) (b) 0.20 mol of NO(g) decomposes to N2(g) and O2(g) (c) 2.40 g of NaCl(s) is formed from Na(s) and excess Cl2(g) (d) 250 g of iron is oxidized with oxygen to Fe2O3(s)Use standard enthalpies of formation in Appendix L to calculate enthalpy changes for the following: (a) 0.054 g of sulfur burns, forming SO2(g) (b) 0.20 mol of HgO(s) decomposes to Hg() and O2(g) (c) 2.40 g of NH3(g) is formed from N2(g) and excess H2(g) (d) 1.05 102 mol of carbon is oxidized to CO2(g)The first step in the production of nitric acid from ammonia involves the oxidation of NH3. 4 NH3(g) + 5 O2(g) 4 NO(g) + 6 H2O(g) (a) Use standard enthalpies of formation to calculate the standard enthalpy change for this reaction. (b) How much energy is evolved or absorbed as heat in the oxidation of 10.0 g of NH3?The Romans used calcium oxide, CaO, to produce a strong mortar to build stone structures. Calcium oxide was mixed with water to give Ca(OH)2, which reacted slowly with CO2 in the air to give CaCO3. Ca(OH)2(s) + CO2(g) CaCO3(s) + H2O(g) (a) Calculate the standard enthalpy change for this reaction. (b) How much energy is evolved or absorbed as heat if 1.00 kg of Ca(OH)2 reacts with a stoichiometric amount of CO2?The standard enthalpy of formation of solid barium oxide, BaO, is 553.5 kJ/mol, and the standard enthalpy of formation of barium peroxide, BaO2, is 634.3 kJ/mol. (a) Calculate the standard enthalpy change for the following reaction. Is the reaction exothermic or endothermic? 2 BaO2(s) 2 BaO(s) + O2(g) (b) Draw an energy level diagram that shows the relationship between the enthalpy change of the decomposition of BaO2, to BaO and O2, and the enthalpies of formation of BaO2(s) and BaO2(s).An important step in the production of sulfuric acid is the oxidation of SO2 to SO3. SO2(g) + O2(g) SO3(g) Formation of SO3 from the air pollutant SO2 is also a key step in the formation of acid rain. (a) Use standard enthalpies of formation to calculate the enthalpy change for the reaction. Is the reaction exothermic or endothermic? (b) Draw an energy level diagram that shows the relationship between the enthalpy change for the oxidation of SO2 to SO3 and the enthalpies of formation of SO3(g) and SO3(g).The enthalpy change for the oxidation of naphthalene, C10Hg, is measured by calorimetry. C10H8(s) + 12 O2(g) 10 CO2(g) + 4 H2O() rH = 5156.1 kJ/mol-rxn Use this value, along with the standard enthalpies of formation of CO2(g) and H2O(), to calculate the enthalpy of formation of naphthalene, in kJ/mol.The enthalpy change for the oxidation of styrene. C8H8, is measured by calorimetry. C8H8() + 10 O2(g) 8 CO2(g) + 4 H2O() rH = 4395.0 kJ|/mol-rxn Use this value, along with the standard enthalpies of formation of CO2(g) and H2O(), to calculate the enthalpy of formation of styrene. in kJ/mol.65GQ66GQFor each of the following, define a system and its surroundings, and give the direction of energy transfer between system and surroundings. (a) Methane burns in a gas furnace in your home. (b) Water drops, sitting on your skin after a swim, evaporate. (c) Water, at 25 C, is placed in the freezing compartment of a refrigerator, where it cools and eventually solidifies. (d) Aluminum and Fe2O3(s) are mixed in a flask sitting on a laboratory bench. A reaction occurs, and a large quantity of energy is evolved as heat.68GQUse Appendix L to find the standard enthalpies of formation of oxygen atoms, oxygen molecules (O2), and ozone (O3). What is the standard state of oxygen? Is the formation of oxygen atoms from O2 exothermic? What is the enthalpy change for the formation of 1 mol of O3 from O2?You have a large balloon containing 1.0 mol of gaseous water vapor at 80 C. How will each step affect the internal energy of the system? (a) The temperature of the system is raised to 90 C. (b) The vapor is condensed to a liquid, at 40 C.Determine whether energy as heat is evolved or required, and whether work was done on the system or whether the system does work on the surroundings, in the following processes at constant pressure: (a) Liquid water at 100 C is converted to steam at 100 C. (b) Dry ice, CO2(s), sublimes to give CO2(g).Determine whether energy as heat is evolved or required, and whether work was done on the system or whether the system does work on the surroundings, in the following processes at constant pressure; (a) Ozone, O3, decomposes to form O2. (b) Methane burns: CH4(g) + 2 O2(g) CO2(g) + 2 H2O()Use standard enthalpies of formation to calculate the enthalpy change that occurs when 1.00 g of SnCl4() reacts with excess H2O() to form SnO2(s) and HCl(aq).Which evolves more energy on cooling from 50 C to 10 C: 50.0 g of water or 100. g of ethanol (Cethanol = 2.46 J/g K)?You determine that 187 J of energy as heat is required to raise the temperature of 93.45 g of silver from 18.5 C to 27.0 C. What is the specific heat capacity of silver?Calculate the quantity of energy required to convert 60.1 g of H2O(s) at 0.0 C to H2O(g) at 100.0 C. The enthalpy of fusion of ice at 0 C is 333 J/g; the enthalpy of vaporization of liquid water at 100 C is 2256 J/g.You add 100.0 g of water at 60.0 C to 100.0 g of ice at 0.00 C. Some of the ice melts and cools the water to 0.00 C. When the ice and water mixture reaches thermal equilibrium at 0 C, how much ice has melted?Three 45-g ice cubes at 0 C are dropped into 5.00 102 mL of tea to make iced tea. The tea was initially at 20.0 C; when thermal equilibrium was reached, the final temperature was 0 C. How much of the ice melted, and how much remained floating in the beverage? Assume the specific heat capacity of tea is the same as that of pure water.Suppose that only two 45-g ice cubes had been added to your glass containing 5.00 102 mL of tea (see Study Question 78). When thermal equilibrium is reached, all of the ice will have melted, and the temperature of the mixture will be somewhere between 20.0 C and 0 C. Calculate the final temperature of the beverage. (Note: The 90 g of water formed when the ice melts must be warmed from 0 C to the final temperature.)You take a diet cola from the refrigerator and pour 240 mL of it into a glass. The temperature of the beverage is 10.5 C. You then add one ice cube (45 g) at 0 C. Which of the following describes the system when thermal equilibrium is reached? (a) The temperature is 0 C, and some ice remains. (b) The temperature is 0 C, and no ice remains. (c) The temperature is higher than 0 C, and no ice remains. Determine the final temperature and the amount of ice remaining, if any.The standard molar enthalpy of formation of diborane, B2H6(g), cannot be determined directly because the compound cannot be prepared by the reaction of boron and hydrogen. It can be calculated from other enthalpy changes, however. The following enthalpy changes can be measured. 4 B(s) + 3 O2(g) 2 B2O3(s) rH = 2543.8 kJ/mol-rxn H2(g) + O2(g) H2O(g) rH = 241.8 kl/mol-rxn B2H6(g) + 3 O2(g) B2O3(s) + 3 H2O(g) rH = 2032.9 kJ/mol-rxn (a) Show how these equations can be added together to give the equation for the formation of B2H6(g) from B(s) and H2(g) in their standard states. Assign enthalpy changes to each reaction. (b) Calculate fH for B2H6(g). (c) Draw an energy level diagram that shows how the various enthalpies in this problem are related. (d) Is the formation of B2H6(g) from its elements exo- or endothermic?Chloromethane, CH3Cl, a compound found throughout the environment, is formed in the reaction of chlorine atoms with methane. CH4(g) + 2 Cl(g) CH3Cl(g) + HCl(g) (a) Calculate the enthalpy change for the reaction of CH4(g) and CI atoms to give CH3CI(g) and HCl(g). Is the reaction exo- or endothermic? (b) Draw an energy level diagram that shows how the various enthalpies in this problem are related.83GQCamping stoves are fueled by propane (C3H8), butane [C4H10(g), fH = 127.1 kJ/mol]. gasoline. or ethanol (C2H5OH). Calculate the enthalpy of combustion per gram of each of these fuels. [Assume that gasoline is represented by isooctane, C8H18(), with fH = 259.3 kJ/mol.) Do you notice any great differences among these fuels? How are these differences related to their composition?85GQ86GQ(a) Calculate the enthalpy change, rH, for the formation of 1.00 mol of strontium carbonate (the material that gives the red color in fireworks) from its elements. Sr(s) + C(s) + 32, O2(g) SrCO3(s) The experimental information available is Sr(s) + O2(g) SrO(s) fH = 592 kJ/mol-rxn SrO(s) + CO2(g) SrCO3(s) rH = 234 kJ/mol-rxn C(graphite) + O2(g) CO2(g) fH = 394 kJ/mol-rxn (b) Draw an energy level diagram relating the energy quantities in this problem.You drink 350 mL of diet soda that is at a temperature of 5 C. (a) How much energy will your body expend to raise the temperature of this liquid to body temperature (37 C)? Assume that the density and specific heat capacity of diet soda are the same as for water. (b) Compare the value in part (a) with the caloric content of the beverage. (The label says that it has a caloric content of 1 Calorie.) What is the net energy change in your body resulting from drinking this beverage? (1 Calorie = 1000 kcal = 4184 J.) (c) Carry out a comparison similar to that in part (b) for a nondiet beverage whose label indicates a caloric content of 240 Calories.Chloroform, CHCl3, is formed from methane and chlorine in the following reaction. CH4(g) + 3 Cl2(g) 3 HCl(g) + CHCl3(g) Calculate rH, the enthalpy change for this reaction, using the enthalpies of formation of CO2(g), H2O(), CHCI3(g) (fH = 103.1 kJ/mol), and the enthalpy changes for the following reactions: CH4(g) + 2 O2(g) 2 H2O() + CO2(g) rH = 890.4 kJ/mol-rxn 2 HCl(g) H2(g) + Cl2(g) rH = +184.6 kJ/mol-ransWater gas, a mixture of carbon monoxide and hydrogen, is produced by treating carbon (in the form of coke or coal) with steam at high temperatures. (See Study Question 83.) C(s) + H2O(g) CO(g) + H2(g) Not all of the carbon available is converted to water gas since some is burned to provide the heat for the endothermic reaction of carbon and water. What mass of carbon must be burned (to CO2 gas) to provide the energy to convert 1.00 kg of carbon to water gas?Using standard enthalpies of formation, verify that 2680 kJ of energy is released in combustion of 100.0 g of ethanol. C2H5OH() + 3 O2(g) 2 CO2(g) + 3 H2O(g)A piece of lead with a mass of 27.3 g was heated to 98.90 C and then dropped into 15.0 g of water at 22.50 C. The final temperature was 26.32 C. Calculate the specific heat capacity of lead from these data.A 192-g piece of copper is heated to 100.0 C in a boiling water bath and then dropped into a beaker containing 751 g of water (density = 1.00 g/cm3) at 4.0 C. What was the final temperature of the copper and water after thermal equilibrium was reached? (CCu = 0.385 J/g K.)Insoluble AgCl(s) precipitates when solutions of AgNO3(aq) and NaCl(aq) are mixed. AgNO3(aq) + NaCl(aq) AgCl(s) + NaNO3(aq) rH = ? To measure the energy evolved in this reaction, 250. mL of 0.16 M AgNO3(aq) and 125 mL of 0.32 M NaCl(aq) are mixed in a coffee-cup calorimeter. The temperature of the mixture rises from 21.15 C to 22.90 C. Calculate the enthalpy change for the precipitation of AgCl(s), in kJ/mol. (Assume the density of the solution is 1.0 g/mL and its specific heat capacity is 4.2 J/g K.)Insoluble PbBr2(s) precipitates when solutions of Pb(NO3)2(aq) and NaBr(aq) are mixed. Pb(NO3)2(aq) + 2 NaBr(aq) PbBr2(s) + 2 NaNO3(aq) rH = ? To measure the enthalpy change, 200. mL. of 0.75 M Pb(NO3)2(aq) and 200. mL of 1.5 M NaBr(aq) are mixed in a coffee-cup calorimeter. The temperature of the mixture rises by 2.44 C. Calculate the enthalpy change for the precipitation of PbBr2(s), in kJ/mol. (Assume the density of the solution is 1.0 g/mL., and its specific heat capacity is 4.2 J/g K.)The value of U for the decomposition of 7.647 g of ammonium nitrate can be measured in a bomb calorimeter. The reaction that occurs is NH4NO3(s) N2O(g) + 2 H2O(g) The temperature of the calorimeter, which contains 415 g of water, increases from 18.90 C to 20.72 C. The heat capacity of the bomb is 155 J/K. What is the value of U for this reaction, in kl/mol?A bomb calorimetric experiment was run to determine the enthalpy of combustion of ethanol. The reaction is C2H5OH() + 3 O2(g) 2 CO2(g) + 3 H2O() The bomb had a heat capacity of 550 J/K, and the calorimeter contained 650 g of water. Burning 4.20 g of ethanol, C2HsOH() resulted in a rise in temperature from 18.5 C to 22.3 C. Calculate U for the combustion of ethanol, in kJ/mosl.The meals-ready-to-eat (MREs) in the military can be heated on a flameless heater. You can purchase a similar product called Heater Meals. Just pour water into the heater unit, wait a few minutes, and you have a hot meal. The source of energy in the heater is Mg(s) + 2 H2O() Mg(OH)2(OH)2(s) + H2(g) The heater meal uses the reaction of magnesium with water as a source of energy as heat. Calculate the enthalpy change under standard conditions, in joules, for this reaction. What quantity of magnesium is needed to supply the energy required to warm 25 mL of water (d = 1.00 g/mL) from 25 C to 85 C? (See W. Jensen: Journal of Chemical Education, Vol. 77, pp. 713-717, 2000.)On a cold day, you can warm your hands with a heat pad, a device that uses the oxidation of iron to produce energy as heat. 4 Fe(s) + 3 O2(g) 2 Fe2O3(s) A hand warmer uses the oxidation of iron as a source of thermal energy. What mass of iron is needed to supply the energy required to warm 15 mL of water (d = 1.00 g/mL) from 23 C to 37 C?Without doing calculations, decide whether each of the following is exo- or endothermic. (a) the combustion of natural gas (b) the decomposition of glucose, C6H12O6, to carbon and water102SCQYou want to determine the value for the enthalpy of formation of CaSO4(s), but the reaction cannot be done directly. Ca(s) + S(s) + 2 O2(g) CaSO4(s) You know, however, that (a) both calcium and sulfur react with oxygen to produce oxides in reactions that can be studied calorimetrically, and (b) the basic oxide CaO reacts with the acidic oxide SO3(g) to produce CaSO4(s) with rH = 402.7 kJ. Outline a method for determining fH for CaSO4(s), and identify the information that must be collected by experiment. Using information in Appendix L, confirm that fH for CaSO4(s) = 1433.5 kJ/mol.Prepare a graph of specific heat capacities for metals versus their atomic weights. Combine the data in Figure 5.4 and the values in the following table. What is the relationship between specific heat capacity and atomic weight? Use this relationship to predict the specific heat capacity of platinum. The specific heat capacity for platinum is given in the literature as 0.133 J/g K. How good is the agreement between the predicted and actual values?105SCQYou are attending summer school and living in a very old dormitory. The day is oppressively hot. there is no air conditioner, and you cant open the windows of your room. There is a refrigerator in the room, however. In a stroke of genius, you open the door of the refrigerator, and cool air cascades out. The relief does not last long, though. Soon the refrigerator motor and condenser begin to run, and not long thereafter the room is hotter than it was before. Why did the room warm up?107SCQ108SCQ109SCQPeanuts and peanut oil are organic materials and bum in air. How many burning peanuts does it take to provide the energy to boil a cup of water (250 mL of water)? To solve this problem, we assume each peanut, with an average mass of 0.73 g, is 49% peanut oil and 21% starch; the remainder is noncombustible We further assume peanut oil is palmitic acid, C16H32O2, with an enthalpy of formation of 848.4 kJ/mol. Starch is a long chain of C6H10O5 units, each unit having an enthalpy of formation of 960 kJ.Isomers are molecules with the same elemental composition but a different atomic arrangement. Three isomers with the formula C4H8 are shown in the models below. The enthalpy of combustion (cH) of each isomer, determined using a calorimeter, is as follows: (a) Draw an energy level diagram relating the energy content of the three isomers to the energy content of the combustion products, CO2(g) and H2O(). (b) Use the cH data in part (a), along with the enthalpies of formation of CO2(g) and H2O() from Appendix L, to calculate the enthalpy of formation for each of the isomers. (c) Draw an energy level diagram that relates the enthalpies of formation of the three isomers to the energy of the elements in their standard states. (d) What is the enthalpy change for the conversion of cis-2-butene to trans-2-butene?112SCQ113SCQA piece of gold (10.0 g, CAu = 0.129 J/g K) is heated to 100.0 C. A piece of copper (also 10.0 g, CCu = 0.385 J/g K) is chilled in an ice bath to 0 C. Both pieces of metal are placed in a beaker containing 150. g H2O at 20 C. Will the temperature of the water be greater than or less than 20 C when thermal equilibrium is reached? Calculate the final temperature.Methane, CH4, can be converted to methanol, which, like ethanol, can be used as a fuel. The energy level diagram shown here presents relationships between energies of the fuels and their oxidation products. Use the information in the diagram to answer the following questions. (The energy terms are per mol-rxn.) (a) Which fuel, methanol or methane, yields the most energy per mole when burned? (b) Which fuel yields the most energy per gram when burned? (c) What is the enthalpy change for the conversion of methane to methanol by reaction with O2(g)? (d) Each arrow on the diagram represents a chemical reaction. Write the equation for the reaction that converts methane to methanol.Calculate rH for the reaction 2 C(s) + 3 H2(g) + O2(g) C2H5OH() given the information below. C(s) + O2(g) CO2(g) rH = 393.5 kJ/mol-rxn 2 H2(g) + O2(g) 2 H2O() rH = 571.6 kJ/mol-rxn C2H5OH() + 3 O2(g) 2 CO2(g) + 3 H2O() rH= 1367.5 kJ/mol-rxnYou have the six pieces of metal listed below, plus a beaker of water containing 3.00 102 g of water. The water temperature is 21.00 C. (a) In your first experiment you select one piece of metal and heat it to 100 C, and then select a second piece of metal and cool it to 10 C. Both pieces of metal are then placed in the beaker of water and the temperatures equilibrated. You want to select two pieces of metal to use, such that the final temperature of the water is as high as possible. What piece of metal will you heat? What piece of metal will you cool? What is the final temperature of the water? (b) The second experiment is done in the same way as the first. However, your goal now is to cause the temperature to change the least, that is, the final temperature should be as near to 21.00 C as possible. What piece of metal will you heat? What piece of metal will you cool? What is the final temperature of the water?Sublimation of 1.0 g of dry ice. CO2(s), forms 0.36 L of CO2(g) (at 78 C and 1.01 105 Pa). The expanding gas can do work on the surroundings (Figure 5.8). Calculate the amount of work done on the surroundings.In the reaction of two moles of gaseous hydrogen and one mole of gaseous oxygen to form two moles of gaseous water vapor, two moles of products are formed from three moles of reactants. If this reaction is done at 1.01 104 Pa (and at 0 C), the volume is reduced by 22.4 L. (a) In this reaction, how much work is done on the system (H2, O2, H2O) by the surroundings? (b) The enthalpy change for this reaction is 483.6 kJ. Use this value, along with the answer to (a), to calculate rU, the change in internal energy in the system.(a) Which color in the visible spectrum has the highest frequency? Which has the lowest frequency? (b) Is the wavelength of the radiation used in a microwave oven (2.45 GHz) longer or shorter than that from your favorite FM radio station (for example, 91.7 MHz)? (c) Are the wavelengths of x-rays longer or shorter than those of ultraviolet light? (d) Calculate the frequency of green light with a wavelength of 510. nm.Calculate the energy per mole of photons for the laser used in Blu-ray players ( = 405 nm)6.3CYUThe Lyman series of spectral lines for the H atom, in the ultraviolet region, arises from transitions from higher levels to n = 1. Calculate the frequency and wavelength of the least energetic line in this series.Calculate the wavelength associated with a neutron having a mass of 1.675 x 1024 g and a kinetic energy of 6.21 x 1021 j. (The kinetic energy of a moving particle is E = 1/2mv2.)Which has the longer wavelength, visible light or ultraviolet light? The higher frequency? The higher energy per photon?
Calculate the energy per mole of photons (in kJ/mol) for red light with a wavelength of 700 nm. Calculate the energy per mole of photons (in kJ/mol) for UV-B light with a wavelength of 300 nm. How many times more energetic is this UV-B than this red light?
2.1ACPDoes the main emission line for SrCl2 have a longer or shorter wavelength than that of the yellow line from NaCI?
2.3ACPHelium absorbs light at 587.6 nm. What is the frequency of this light?
3.2ACP3.3ACP3.4ACP3.5ACPAnswer the following questions based on Figure 6.2: (a) Which type of radiation involves less energy, x-rays or microwaves? (b) Which radiation has the higher frequency, radar or red light? (c) Which radiation has the longer wavelength, ultraviolet or infrared light?Consider the colors of the visible spectrum. (a) Which colors of light involve less energy than green light? (b) Which color of light has photons of greater energy, yellow or blue? (c) Which color of light has the higher frequency, blue or green?Traffic signals are often now made of LEDs (light-emitting diodes). Amber and green ones are pictured here. (a) The light from an amber signal has a wave-length of 595 nm, and that from a green signal has a wavelength of 500 nm. Which has the higher frequency? (b) Calculate the frequency of amber light.Suppose you are standing 225 m from a radio transmitter. What is your distance from the transmitter in terms of the number of wavelengths if (a) the station is broadcasting at 1150 kHz (on the AM radio band)? (1kHz = 1 103 Hz) (b) the station is broadcasting at 98.1 MHz (on the FM radio band)? (1 MHz 106 Hz)Green light has a wavelength of 5.0 102 nm. What is the energy, in joules, of one photon of green light? What is the energy, in joules, of 1.0 mol of photons of green light?Violet light has wavelength of about 410 nm. What is its frequency? Calculate the energy of one photon of violet light. What is the energy of 1.0 mol of violet photons? Compare the energy of photons of violet light with those of red light. Which is more energetic?The most prominent line in the emission spectrum of aluminum is at 396.15nm. What is the frequency of this line? What is the energy of one photon with this wavelength? Of 1.00 mol of these photons?The most prominent line in the emission spectrum of magnesium is 285.2 nm. Other lines are found at 383.8 and 518.4 nm. In what region of the electromagnetic spectrum are these lines? What is the energy of 1.00 mol of photons with the wavelength of the most energetic line?Place the following types of radiation in order of increasing energy per photon: (a) yellow light from a sodium lamp (b) X-rays from an instrument in a dentists office (c) microwaves in microwave oven (d) your favorite FM music station at 91.7 MHzPlace the following types of radiation in order of increasing energy per photon: (a) radiation within a microwave oven (b) your favorite radio station (c) gamma rays from a nuclear reaction (d) red light from a neon sing (e) ultraviolet radiation from a sun lampAn energy of 3.3 1019 J/atom is required to cause a cesium atom on a metal surface to lose an electron. Calculate the longest possible wavelength of light that can ionize a cesium atom. In what region of the electromagnetic spectrum is that radiation found?You are an engineer designing a switch that works by the photoelectric effect. The metal you wish to use in your device requires 6.7 1019 J/atom to remove an electron. Will the switch work if the light falling on the metal has a wavelength of 540 nm or greater? Why or why not?The most prominent line in the spectrum of mercury is at 253.652 nm. Other lines are located at 365.015 nm, 404.656 nm, 435.833 nm, and 101.975 nm. (a) which of these lines represents the most energetic light? (b) what is the frequency of the most prominent line? What is the energy of one photon with this wavelength? (c) Are any of these lines found in the spectrum of mercury shown in figure 6.6? What color or colors are these lines?The most prominent line in the spectrum of neon is found at 865.438 nm. Other lines are located at 837.761 nm, 878.062 nm, 878.375 nm, and 885.387 nm. (a) In what region of the electromagnetic spectrum are these lines found? (b) Are any of these lines found in the spectrum nein shown in Figure 6.6? (c) which of these lines represents the most energetic radiation? (d) What is the frequency of the most prominent line? What is the energy of one photon with this wavelength?A line in the Balmer series of emission lines of excited H atoms has a wavelength of 410.2 nm (Figure 6.10). What color is the light emitted in this transition? What quantum levels are involved in this emission line? That is, what are the values of ninitial and nfinal?What are the wavelength and frequency of the radiation involved in the least energetic emission line in the Lyman series? What are the values of ninitial and nfinal?Consider only transitions involving the n = 1 through n = 5 energy levels for the H atom (see Figures 6.7 and 6.10). (a) How many emission lines are possible, considering only the five quantum levels? (b) Photons of the highest frequency are emitted in a transition from the level with n = ______ to a level with n = ______. (c) The emission line having the longest wavelength corresponds to a transition from the level with n = ______ to the level with n = _________.Consider only transitions involving the n = 1 through n = 4 energy levels for the hydrogen atom (see Figures 6.7 and 6.10). (a) How many emission lines are possible, considering only the four quantum levels? (b) Photons of the lowest energy are emitted in a transition from the level with n = ____to a level with n = ____ (c) The emission line having the shortest wavelength corresponds to a transition from the level with n = ____ to the level with n = _____The energy emitted when an electron moves from a higher energy state to a lower energy state in any atom can be observed as electromagnetic radiation. (a) Which involves the emission of less energy in the H atom, an electron moving from n = 4 to n = 2 or an electron moving from n = 3 to n = 2? (b) Which involves the emission of more energy in the H atom, an electron moving from n = 4 to n = 1 or an electron moving from n = 5 to n = 2? Explain fully.If energy is absorbed by a hydrogen atom in its ground state, the atom is excited to a higher energy state. For example, the excitation of an electron from n = 1 to n = 3 requires radiation with a wavelength of 102.6 nm. Which of the following transitions would require radiation of longer wave- length than this? (a) n = 2 to n = 4 (b) n = 1 to n = 4 (c) n = 1 to n = 5 (d) n = 3 to n = 5Calculate the wavelength and frequency of light emitted when an electron changes from n = 3 to n = 1 in the H atom. In what region of the spectrum is this radiation found?Calculate the wavelength and frequency of light emitted when an electron changes from n = 4 to n = 3 in the H atom. In what region of the spectrum is this radiation found?An electron moves with a velocity of 2.5 X 108 cm/s. What is its wavelength?A beam of electrons (m = 9.11 X 1031 kg/electron) has an average speed of 1.3 X 108 m/s. What is the wavelength of electrons having this average speed?Calculate the wavelength, in nanometers, associated with a 46-g golf ball moving at 30. m/s (about 67 mph). At what speed must the ball travel to have a wavelength of 5.6 103 nm?A rifle bullet (mass = 1.50 g) has a velocity of 7.00 x 102 mph (miles per hour). What is the wavelength associated with this bullet?(a) When n = 4, what are the possible values of ? (b) When is 2, what are the possible values of m (c) For a 4s orbital, what are the possible values of n, , and m (d) For a 4f orbital, what are the possible values of n, , and m?ss(a) When n = 4, = 2, and m = 1, to what orbital type does this refer? (Give the orbital label, such as 1s.) (b) How many orbitals occur in the n = 5 electron shell? How many subshells? What are the letter labels of the subshells? (c) How many orbitals occur in an f subshell? What are the values of m?A possible excited state of the H atom has the electron in a 4p orbital. List all possible sets of quantum numbers n, , and m for this electron.A possible excited state for the H atom has an electron in a 5d orbital. List all possible sets of quantum numbers n, , and m for this electron.How many subshells occur in the electron shell with the principal quantum number n = 4?32PSExplain briefly why each of the following is not a possible set of quantum numbers for an electron in an atom. (a) n = 2, = 2, m = 0 (b) n = 3, = 0, m = -2 (c) n = 6, = 0, m = 1Which of the following represent valid sets of quantum numbers? For a set is invalid, explain briefly why it is not correct. (a) n = 3, = 3, m = 0 (b) n = 2, = 1, m = 0 (c) n = 6, = 5, m = 1 (d) n = 4, = 3, m = 4What is the maximum number of orbitals that can be identified by each of the following sets of quantum numbers? When none is the correct answer, explain your reasoning. (a) n = 3, = 0, m = +1 (b) n = 5, = 1, (c) n = 7, = 5, (d) n = 4, = 2, m = 2What is the maximum number of orbitals that can be identified by each of the following sets of quantum numbers? When none is the correct answer, explain your reasoning. (a) n = 4, = 3 (b) n = 5 (c) n = 2, = 2 (d) n = 3, = 1, m = 1Explain briefly why each of the following is not a possible set of quantum numbers for an electron in an atom. In each case, change the incorrect value (or values) to make the set valid. (a) n = 4, = 2, m = 0, ms = 0 (b) n = 3, = 1, m = 3, ms = 1/2 (c) n = 3, = 3, m = 1, ms = +1/2Explain briefly why each of the following is not a possible set of quantum numbers for an electron in an atom. In each case, change the incorrect value (or values) to make the set valid. (a) n = 2, = 2, m = 0, ms = +1/2 (b) n = 2, = 1, m = 1, ms = 0 (c) n = 3, = 1, m = 2, ms = +1/2State which of the following orbitals cannot exist according to the quantum theory: 2s, 2d, 3p, 3f, 4f, and 5s. Briefly explain your answers.State which of the following orbitals cannot exist according to the quantum theory: 3p, 4s, 2f, and 1p. Briefly explain your answers.Write a complete set of quantum numbers (n, , m) that quantum theory allows for each of the following orbitals: (a) 2p, (b) 3d, and (c) 4f.Write a complete set of quantum numbers (n, , and m) for each of the following orbitals: (a) 5f, (b) 4d, and (c) 2s.A particular orbital has n = 4 and = 2. What must this orbital be: (a) 3p, (b) 4p, (c) 3d, or (d) 4d?A given orbital has a magnetic quantum number of m = 1. This could not be a(n) (a) f orbital (b) d orbital (c) p orbital (d) s orbital45PS46PSWhich of the following are applicable when explaining the photoelectric effect? Correct any statements that are wrong. (a) Light is electromagnetic radiation. (b) The intensity of a light beam is related to its frequency. (c) Light can be thought of as consisting of mass- less particles whose energy is given by Plancks equation, E = h.48GQGive the number of nodal surfaces through the nucleus (planar nodes) for each orbital type: s, p, d, and f.What is the maximum number of s orbitals found in a given electron shell? The maximum number of p orbitals? Of d orbitals? Of f orbitals?Match the values of l shown in the table with orbital type (s, p, d, or f).Sketch a picture of the 90% boundary surface of an s orbital and the px orbital. Be sure the latter drawing shows why the p orbital is labeled px and not py, for example.Complete the following table.Excited H atoms have many emission lines. One series of lines, called the Pfund series, occurs in the infrared region. It results when an electron changes from higher energy levels to a level with n = 5. Calculate the wavelength and frequency of the lowest energy line of this series.An advertising sign gives off red light and green light. (a) Which light has higher-energy photons? (b) One of the colors has a wavelength of 680 nm, and the other has a wavelength of 500 nm. Which color has which wavelength? (c) Which light has the higher frequency?Radiation in the ultraviolet region of the electro-magnetic spectrum is quite energetic. It is this radiation that causes dyes to fade and your skin to develop a sunburn. If you are bombarded with 1.00 mol of photons with a wavelength of 375 nm, what amount of energy, in kilojoules per mole of photons, are you being subjected to?A cell phone sends signals at about 850 MHz (where 1 MHz = 1 106 Hz or cycles per second). (a) What is the wavelength of this radiation? (b) What is the energy of 1.0 mol of photons with a frequency of 850 MHz? (c) Compare the energy in part (b) with the energy of a mole of photons of violet light (420 nm). (d) Comment on the difference in energy between 850 MHz radiation and violet light.Assume your eyes receive a signal consisting of blue light, = 470 nm. The energy of the signal is 2.50 1014 J. How many photons reach your eyes?If sufficient energy is absorbed by an atom, an electron can be lost by the atom and a positive ion formed. The amount of energy required is called the ionization energy. In the H atom, the ionization energy is that required to change the electron from n = 1 to n = infinity. Calculate the ionization energy for the He+ ion. Is the ionization energy of the He+ more or less than that of H? (Bohrs theory applies to He+ because it, like the H atom, has a single electron. The electron energy, however, is now given by E = Z2Rhc/n2, where Z is the atomic number of helium.)Suppose hydrogen atoms absorb energy so that electrons are excited to the n = 7 energy level. Electrons then undergo these transitions, among others: (a) n = 7 n = 1; (b) n = 7 n = 6; and (c) n = 2 n = 1. Which of these transitions produces a photon with (i) the smallest energy, (ii) the highest frequency, and (iii) the shortest wavelength?Rank the following orbitals in the H atom in order of increasing energy: 3s, 2s, 2p, 4s, 3p, 1s, and 3d.How many orbitals correspond to each of the following designations? (a) 3p (b) 4p (c) 4Px (d) 6d (e) 5d (f) 5f (g) n = 5 (h) 7sCobalt-60 is a radioactive isotope used in medicine for the treatment of certain cancers. It produces particles and rays, the latter having energies of 1.173 and 1.332 MeV. (1 MeV = 106 electron-volts and 1 eV = 1.6022 1019 J.) What are the wave-length and frequency of a -ray photon with an energy of 1.173 MeV?Exposure to high doses of microwaves can cause tissue damage. Estimate how many photons, with = 12 cm, must be absorbed to raise the temperature of your eye by 3.0 C. Assume the mass of an eye is 11 g and its specific heat capacity is 4.0 J/g K.When the Sojourner spacecraft landed on Mars in 1997, the planet was approximately 7.8 107 km from Earth. How long did it take for the television picture signal to reach Earth from Mars?The most prominent line in the emission spectrum of chromium is found at 425.4 nm. Other lines in the chromium spectrum are found at 357.9 nm, 359.3 nm, 360.5 nm, 427.5 nm, 429.0 nm, and 520.8 nm. (a) Which of these lines represents the most energetic light? (b) What color is light of wavelength 425.4 nm?Answer the following questions as a summary quiz on the chapter. (a) The quantum number n describes the ______ of an atomic orbital. (b) The shape of an atomic orbital is given by the quantum number _______. (c) A photon of green light has _______ (less or more) energy than a photon of orange light. (d) The maximum number of orbitals that may be associated with the set of quantum numbers n = 4 and = 3 is ________. (e) The maximum number of orbitals that may be associated with the quantum number set n = 3, = 2, and m = 2 is _______. (f) Label each of the following orbital pictures with the appropriate letter: (g) When n = 5, the possible values of are _________. (h) The number of orbitals in the n = 4 shell is _______.Answer the following questions as a summary quiz on this chapter. (a) The quantum number n describes the ________ of an atomic orbital, and the quantum number describes its ________. (b) When n = 3, the possible values of are _________. (c) What type of orbital corresponds to = 3? ________ (d) For a 4d orbital, the value of n is _______, the value of is ________, and a possible value of m is _________. (e) Each of the following drawings represents a type of atomic orbital. Give the letter designation for the orbital, give its value of , and specify the number of planar nodes. Letter = ______ ______ value = ______ ______ Planar nodes = _______ ______ (f) An atomic orbital with three planar nodes through the nucleus is a(n) ______ orbital. (g) Which of the following orbitals cannot exist according to modem quantum theory: 2s, 3p, 2d, 3f, 5p, 6p? (h) Which of the following is not a valid set of quantum numbers? (i) What is the maximum number of orbitals that can be associated with each of the following sets of quantum numbers? (One possible answer is none. ) (i) n = 2 and =1 (ii) n = 3 (iii) n = 3 and = 3 (iv) n = 2, = 1, and m = 0For an electron in a hydrogen atom, calculate the energy of the photon emitted when an electron falls in energy from the n = 5 level to the n = 2 state. What are the frequency and wavelength of this electromagnetic radiation?A solution of KMnO4 absorbs light at 540 nm (page 206). What is the frequency of the light absorbed? What is the energy of one mole of photons with = 540 nm?71ILThe spectrum shown here is for aspirin. The vertical axis is the amount of light absorbed, and the horizontal axis is the wavelength of incident light (in nm). (For more on spectrophotometry, see Section 4.9) What is the frequency of light with a wavelength of 278 nm? What is the energy of one mole of photons with = 278 nm? What region of the electromagnetic spectrum is covered by the spectrum above? Knowing that aspirin only absorbs light in the region depicted by this spectrum. What is the color of aspirin?The infrared spectrum for methanol. CH3OH, is illustrated below. It shows the amount of light in the infrared region that methanol transmits as a function of wavelength. The vertical axis is the amount of light transmitted. At points near the top of the graph, most of the incident light is being transmitted by the sample (or, conversely, little light is absorbed). Therefore, the peaks or bands that descend from the top indicate light absorbed; the longer the band, the more light is being absorbed. The horizontal scale is in units of wavenumbers, abbreviated cm1. The energy of light is given by Plancks law as E = hc/; that is, E is proportional to 1/. Therefore, the horizontal scale is in units of 1/ and reflects the energy of the light incident on the sample. (a) One point on the horizontal axis is marked as 2000 cm1. What is the wavelength of light at this point? (b) Which is the low energy end of this spectrum (left or right), and which is the high energy end? (c) The broad absorption at about 3300-3400 cm1 indicates that infrared radiation is interacting with the OH group of the methanol molecule. The narrower absorptions around 2800-3000 cm1 are for interactions with CH bonds. Which interaction requires more energy, with OH or with CH?Bohr pictured the electrons of the atom as being located in definite orbits about the nucleus, just as the planets orbit the Sun. Criticize this model.Light is given off by a sodium- or mercury-containing streetlight when the atoms are excited. The light you see arises for which of the following reasons? (a) Electrons are moving from a given energy level to one of higher energy. (b) Electrons are being removed from the atom, thereby creating a metal cation. (c) Electrons are moving from a given energy level to one of lower energy76SCQWhat does wave-particle duality mean? What are its implications in our modem view of atomic structure?79SCQSuppose you live in a different universe where a different set of quantum numbers is required to describe the atoms of that universe. These quantum numbers have the following rules: N, principal 1, 2, 3,, L, orbital = N M, magnetic -1, 0, +1 How many orbitals are there altogether in the first three electron shells?A photon with a wavelength of 93.8 nm strikes a hydrogen atom, and light is emitted by the atom. How many emission lines would be observed? At what wavelengths? Explain briefly (see Figure 6.10).Explain why you could or could not measure the wavelength of a golf ball in flight.83SCQ(a) What element has the configuration 1s22s22p63s2ps?
(b) Using spdf notation and an orbital box diagram, show the electron configuration of phosphorus.
Write one possible set of quantum numbers for the valence electrons of calcium.Using the periodic table and without looking at Table 7.3, write electron configurations for the following elements: (a) P (b) Zn (c) Zr (d) In (e) Pb (f) U Use the spdf and noble gas notations. When you have finished, check your answers with Table 7.3.7.4CYUWithout looking at the figures for the periodic properties, compare the three elements B, AI and C. (a) Place the three elements in order of increasing atomic radius. (b) Rank the elements in order of increasing ionization energy. (c) Which element, B or C, is expected to have the more negative electron attachment enthalpy value?The most common oxidation state of a rare earth element is +3. a) What is the ground state electron configuration of Sm3+? b) Write a balanced chemical equation for the reaction of Sm(s) and O2(g) to form samarium(III) oxide.1.2ACP1.3ACPUse the atomic radii of scandium, yttrium, lanthanum, and lutetium to answer the questions below.
Explain why lutetium has a smaller atomic radius than lanthanum, even though it has a greater number of electrons.
Do the atomic radii argue for the placement of La or Lu below Y in the periodic table? Explain.
1.5ACP1.6ACPGive the electron configurations for iron and the iron(II) and iron(III) ions.2.2ACP2.3ACP2.4ACPWrite the electron configurations for P and CI using both spdf notation and orbital box diagrams. Describe the relationship between each atom's electron configuration and its position in the periodic table.Write the electron configurations for Mg and Ar using both spdf notation and orbital box diagrams. Describe the relationship of the atom's electron configuration to its position in the periodic table.Using spdf notation, write the electron configurations for atoms of chromium and iron, two of the major components of stainless steel.Using spdf notation, give the electron configuration of vanadium, V, an element found in some brown and red algae and some toadstools.5PS6PSUse noble gas and spdf notations to depict electron configurations for the following metals of the third transition series. (a) Tantalum, Ta. The metal and its alloys resist corrosion and are often used in surgical and dental tools. (b) Platinum, Pt. This metal was used by pre-Columbian Indians in jewelry. Now it is still used in jewelry but it is also the basis for anti-cancer drugs and catalysts (such as those in automobile exhaust systems).The lanthanides, once called the rare earth elements, are really only medium rare Using noble gas and spdf notations, depict reasonable electron configurations for the following elements. (a) Samarium, Sm. This lanthanide is used in magnetic materials. (b) Ytterbium, Yb. This element was named for the village of Ytterby in Sweden, where a mineral source of the element was found.9PS10PSWhat is the maximum number of electrons that can be identified with each of the following sets of quantum numbers? In some cases, the answer may be none In such cases, explain why none is the correct answer. (a) n = 4, = 3, m = 1 (b) n = 6, = 1, m = 1, ms = 1/2 (c) n= 3, = 3, m = 3What is the maximum number of electrons that can be identified with each of the following sets of quantum number? In some cases, the answer may be none. In such cases, explain why none is the correct answer. (a) n = 3 (b) n = 3 and = 2 (c) n = 4, = 1, m = 1, and ms = +1/2 (d) n = 5, = 0, m = 1, ms = +1/2Depict the electron configuration for magnesium using an orbital box diagram and noble gas notation. Give a complete set of four quantum numbers for each of the electrons beyond those of the preceding noble gas.Depict the electron configuration for phosphorus using an orbital box diagram and noble gas notation. Give one possible set of four quantum numbers for each of the electrons beyond those of the preceding noble gas.Using an orbital box diagram and noble gas notation, show the electron configuration of gallium, Ga. Give one possible set of quantum numbers for the highest-energy electron.Using an orbital box diagram and noble gas notation, show the electron configuration of titanium. Give one possible set of four quantum numbers for each of the electrons beyond those of the preceding noble gas.17PSWhich of the following statements correctly describes the value of the effective nuclear charge. Z, felt by (a) the 2s electron at a large distance from a Li atom? (i) Z equals 1. (ii) Z is between 1 and 3. (iii) Z equals 3. (b) the 2s electron at its most probable distance from the nucleus of a Li atom? (i) Z equals 1. (ii) Z is between 1 and 3. (iii) Z equals 3.19PS20PSUsing orbital box diagrams, depict an electron configuration for each of the following ions: (a) Mg2+, (b) K+, (c) Cl, and (d) O2.22PS23PSUsing orbital box diagrams and noble gas notation, depict the electron configurations of (a) Ti, (b) Ti2+, and (c) Ti4+. Is the element or any of the ions paramagnetic?Manganese is found as MnO2 in deep ocean deposits. (a) Depict the electron configuration of this element using the noble gas notation and an orbital box diagram. (b) Using an orbital box diagram, show the electrons beyond those of the preceding noble gas for Mn4+. (c) Is Mn4+ paramagnetic? (d) How many unpaired electrons does the Mn4+ ion have?One compound found in alkaline batteries is NiOOH, a compound containing Ni3+ ions. When the battery is discharged, the Ni3+ is reduced to Ni2+ ions [as in Ni(OH)2]. Using orbital box diagrams and the noble gas notation, show electron configurations of these ions. Are either of these ions paramagnetic?27PSArrange the following elements in order of increasing size: Ca, Rb, P, Ge, and Sr. (Try doing it without looking at Figure 7.5; then check yourself by looking up the necessary atomic radii.)29PS30PSWhich of the following groups of elements is arranged correctly in order of increasing ionization energy? (a) C Si Li Ne (b) Ne Si C Li (c) Li Si C Ne (d) Ne C Si LiArrange the following atoms in order of increasing ionization energy: Li, K, C, and N.Compare the elements Na, Mg, O, and P. (a) Which has the largest atomic radius? (b) Which has the most negative electron attachment enthalpy? (c) Place the elements in order of increasing ionization energy.Compare the elements B. Al, C, and Si. (a) Which has the most metallic character? (b) Which has the largest atomic radius? (c) Which has the most negative electron attachment enthalpy? (d) Place the three elements B, Al, and C in order of increasing first ionization energy.Explain each answer briefly. (a) Place the following elements in order of increasing ionization energy: F, O, and S. (b) Which has the largest ionization energy: O, S, or Se? (c) Which has the most negative electron attachment enthalpy: Se, Cl, or Br? (d) Which has the largest radius: O2, F, or F?Explain each answer briefly. (a) Rank the following in order of increasing atomic radius: O, S, and F. (b) Which has the largest ionization energy: P, Si, S, or Se? (c) Place the following in order of increasing radius: O2, N3, and F. (d) Place the following in order of increasing ionization energy: Cs, Sr, and Ba.Identify the element that corresponds to each of the simplified photoelectron spectral data given below. (Energy data taken from D. A. Shirley, R. L Martin, S. P. Kowalczyk. F. R. McFeely, and L. Ley: Core-electron binding energies of the first thirty elements, Physical Review B, Vol. 15, pp. 544-552, 1977.) (a) There are peaks at energies of 64.8 and 5.4 eV, corresponding to 2 and 1 electrons, respectively. (b) There are peaks at energies of 3614, 384, 301, 40.9, 24.7, and 4.34 eV, corresponding to 2, 2, 6, 2, 6, and 1 electrons, respectively. (c) There are peaks at energies of 4494, 503, 404, 56.4, 33.6, 8.01, and 6.65 eV, corresponding to 2, 2, 6, 2, 6, 1, and 2 electrons, respectively.Identify the element that corresponds to each of the simplified photoelectron spectral data given below. (Energy data taken from D. A. Shirley, R. L. Martin, S. P. Kowalczyk. F. R. McFeely, and L Ley: Core-electron binding energies of the first thirty elements Physical Review B, Vol. 15, pp. 544-552, 1977.) (a) There are peaks at energies corresponding to 1079, 70.8, 38.0, 5.14 eV, corresponding to 2, 2, 6, and 1 electrons, respectively. (b) There are peaks at energies corresponding to 4043, 443, 351, 48.4, 30.1, and 6.11 eV, corresponding to 2, 2, 6, 2, 6, and 2 electrons, respectively. (c) There are peaks at energies corresponding to 5475, 638, 524, 77, 47, 12. and 7.3 eV, corresponding to 2, 2, 6, 2, 6, 3, and 2 electrons, respectively.Explain why the photoelectron spectra of hydrogen and helium each has one peak whereas that for lithium has two peaks. What would be the relative intensity of each of the peaks in these spectra?Sketch the major features (number of peaks and relative intensities for the peaks) of the expected photoelectron spectrum for atoms of nitrogen.These questions are not designated as to type or location in the chapter. They may combine several concepts. The red color of rubies is the result of the substitution of some Cr3+ ions for Al3+ ions in solid Al2O3. (a) Using spdf notation with the noble gas notation, write the electron configuration for the Cr atom and for the Cr3+ ion? (b) Is Cr2+ paramagnetic? Is Cr3+? (c) The radius of the Cr3+ ion is 64 pm. How does this compare with the radius of the Al3+ ion?The deep blue color of sapphires comes from the presence of Fe2+ and Ti4+ in solid Al2O3. Using spdf notation with the noble gas notation, write the electron configuration for each of these ions.Using an orbital box diagram and noble gas notation, show the electron configurations of uranium and of the uranium(IV) ion. Is either of these paramagnetic?44GQ45GQ46GQWhich of the following is not an allowable set of quantum numbers? Explain your answer briefly. For those sets that are valid, identify an element in which an outermost valence electron could have that set of quantum numbers.A possible excited state for the H atom has an electron in a 4p orbital. List all possible sets of quantum numbers (n, , m, ms) for this electron.The magnet in the following photo is made from neodymium, iron, and boron. A magnet mode of on alloy containing the elements Nd, Fe, and B. (a) Write the electron configuration of each of these elements using an orbital box diagram and noble gas notation. (b) Are these elements paramagnetic or diamagnetic? (c) Write the electron configurations of Nd3+ and Fe3+ using orbital box diagrams and noble gas notation. Are these ions paramagnetic or diamagnetic?Name the element corresponding to each characteristic below. (a) the element with the electron configuration 1s22s22p63s23p3 (b) the alkaline earth element with the smallest atomic radius (c) the element with the largest ionization energy in Croup 5A (d) the element whose 2+ ion has the configuration [Kr]4d5 (e) the element with the most negative electron attachment enthalpy in Croup 7A (f) the element whose electron configuration is [Ar]3d104s2Arrange the following atoms in order of increasing ionization energy: Si, K, P, and Ca.52GQAnswer the questions below about the elements A and B, which haw the electron configurations shown. A = [Kr]5s1 B =[Ar]3d104s24p4 (a) Is element A a metal, nonmetal, or metalloid? (b) Which element has the greater ionization energy? (c) Which element has the less negative electron attachment enthalpy? (d) Which element has the larger atomic radius? (e) What is the formula for a compound formed between A and B?