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All Textbook Solutions for Physical Chemistry

A bomb calorimeter is a study metal vessel in which samples can be ignited and the amount of heat given off can be measured as the heat warms up surrounding water. Draw a rough sketch of such an experimental setup and label a the system and b the surroundings.Difference between the system and the surroundings. Give examples of both.1.3E 1.4E 1.5E 1.6E 1.7E A pot of cold water is heated on a stove, and when the water boils, a fresh egg is placed in the water to cook. Describe the events that are occurring in terms of the zeroth law of thermodynamics.hat difference is necessary for heat to flow between two systems? Can you think of an exception to your answer?What is the value of FT for a sample of gas whose volume is 2.97 L and pressure is 0.0553 atm? What could the volume of the gas be if the pressure were increased to 1.00 atm?What is the value of FP for a sample of gas whose temperature is -33.0 C and volume is 0.0250 L? What temperature is required to change the volume to 66.9 cm3?1.12E Hydrogen gas is used in weather balloon because it is less expensive than Helium. Assume that 5.57 g of H2 is used to fill a weather balloon to an initial volume of 67 L at 1.04 atm. If the ballloon rises to an altitude where the pressure is 0.047 atm, what is its new volume? Assume that the temperature remains constant.1.14E A 2.0 L soda bottle is pressurized with 4.5 atm of CO2 at 298 K. If the temperature is increased to 317 K, what is the pressure of the CO2?The Mount Pinatubo volcano eruption in 1991 released an estimated 1.82 x 1013g of SO2 into the atmosphere. If the gas had an average temperature of -17.0 C and filled the troposphere, whose approximate volume is 8 x 1021L, what is the approximate partial pressure of SO2 caused by the eruption?1.17E Scottish physicist W. J. M. Rankine proposed an absolute temperature scale based on the Fahrenheit degree, now called degree Rankine abbreviated R and used by some engineering fields. If a degree Rankine is 5/9 of a degree Kelvin, what is the value of the ideal gas law constant in L. atm/mol. R?Use the two appropriate values of R to determine a conversion between L. atm and J.1.20E Pressures of gases in mixtures are referred to as partial pressures and are additive. 1.00 L of He gas at 0.75 atm is mixed with 2.00 L of Ne gas at 1.5 atm at a temperature of 25.0 C to make a total volume of 3.00 L of a mixture. Assuming no temperature change and that He and Ne can be approximated as ideal gases, what are a the total resulting pressure, b the partial pressures of each component, and c the mole fractions of each gas in the mix?Earths atmosphere is approximately 80 N2 and 20 O2. If the total atmospheric pressure at sea level is about 14.7 lb/in2. where lb/in2 is pounds per square inch, a common but non-SI unit of pressure, what are the partial pressures of N2 and O2 in units lbs/in2?The atmospheric surface pressure on Venus is 90 bar and is composed of 96 carbon dioxide and approximately 4 various other gases. Given a surface temperature of 730 K, what is the mass of carbon dioxide present per cubic centimeter at the surface?1.24E 1.25E In the anaerobic oxidation of glucose by yeast, CO2 is produced: If 1.56 L of CO2 were produced at 22.0 C and 0.965 atm, what mass of C6H12O6 is consumed by the yeast? Assume the ideal gas law applied.What are the slopes of the following lines at the point x = 5? At x = 10? a y = 5x 7 b y = 3x2 5x 2 c y = 7/x.For the following function, evaluate the derivatives in a-f below. F(w,x,y,z)=3xy2+w3z332yxy2z3w a.(Fx)w.y,zb.(Fw)x,y,zc.(Fy)w.x,zd.[ z(Fw)w.y,z ]w,y,ze.[ z(Fw)w.x,y ]w,y,zf.{ [ z(Fw)w.x,y ]w,y,z }x,y,z Determine the expressions for the following, assuming that the ideal gas law holds.Determine the expressions for the following, assuming that the ideal gas law holds.1.31E 1.32E 1.33E 1.34E What properties of a nonideal gas do the Vander Waals constants represent?1.36E 1.37E Calculate the Boyle temperatures for carbon dioxide, oxygen, and nitrogen using the van der Waals constants in Table 1.6. How close do they come to the experimental values from Table 1.5?1.39E 1.40E Table 1.4 show that the second virial coefficient B for He is negative at low temperature, seems to maximize at a little over 12.0 cm3/mol, and then decreases. Do you think it will become negative again at higher temperatures? Why is it decreasing?1.42E What is the van der Waals constant a for Ne in units of bar.cm6/mol2 1.44E Under what conditions would the van der Waals constant b be negative? Do you think there are any gases for which this occurs?By definition, the compressibility of an ideal gas is 1. By approximately what percentage does this change for hydrogen upon inclusion of the second virial coefficient term? How about for water vapor? Give the conditions under which you make this estimate.The second virial coefficient B and the third viral coefficient C for Ar are -0.021 L/mol and 0.0012 L2/mol2 at 273 K, respectively. By what percentage does the compressibility change when you include the third virial term?Use the approximation 1 x-1 1 x x2 to determine an expression for the virial coefficient C in terms of the van der Waals constants.Why is nitrogen a good choice for the study of ideal gas behavior around room temperature?Evaluate for a gas following the Redlich-Kwong equation of state? pV Numerically evaluate for one mole of methane acting as a van der Waals gas at a T = 298 K and V = 25.0 L and b T = 1000 K and V = 250.0 L. Comment on which set of conditions yields a number closer to that predicted by the ideal gas law. pVT,n Under what conditions of volume does a van der Waals gas behave like an ideal gas? Use the van der Waals equation of state to justify your answer.At high temperatures, one of the van der Waals constants can be ignored. Which one? Justify your choice and write a high temperature version of the van der Waals equation of state.Under what conditions of temperature does a Redlich-Kwong gas behave like an ideal gas? Use the Redlich-Kwong equation of state to justify your answer.The Berthelot equation of state for one mole of gas is p=RTV-b-aTV2 Where a and b are constants determined experimentally. For NH3g, a = 741.6 atm. L2. K and b = 0.0139 L. Calculate p when V=22.41L and T = 273.15K. How much does the pressure vary from p as predicted by the ideal gas law?1.56E Referring to exercises 1.6 and 1.7, does it matter if the pressure difference is caused by an ideal gas or a non-ideal gas? Explain your answer.1.58E Use Figure 1.11 to construct the cyclic rule equivalent of Does the answer make sense in light of the original partial derivative?1.60E 1.61E Calculate for one mole of an ideal gas at STP and SATP.1.63E Show that = T/p for an ideal gas.Determine an expression for V/T p, n in terms of and . Does the sign on the expression make sense in terms of what you know happens to volume as temperature changes?1.66E 1.67E Perform a units analysis on the exponent of the barometric function and verify that the overall exponent is unitless.Using the barometric formula, calculate the expected air pressure in Colorado Springs, Colorado, which is 1840 meters above sea level. Assume a temperature of 26.0 C.The barometric formula can also be used for elevations below sea level. In such cases, h is negative. Calculate the expected air pressure at the shore of the Dead Sea in the Middle East, which is 432 meters below sea level. Assume a temperature of 39.0 C.1.71E 1.72E 1.73E 1.74E 1.75E 1.76E 1.77E 1.78E 1.79E Use the ideal gas law to symbolically prove the cyclic rule of partial derivatives.1.81E Calculatethe work performed by a person whoexertsa force of 30 NN = newtonstomove abox 30metersif the force were a exactly parallel to the directionofmovement, and b45to thedirection of movement. Do the relative magnitudesmakesense?Explain inyour own words why work done by the system is defined as the negative of pV, not positive pV.Calculate the work in joules when a piston moves from a volume of 50.00 mL to a volume of 450.00 mL against a pressure of 2.33 atm.Calculatethe work on the system whena piston is compressed by a pressure of 1780torr from 3.55 L to1.00 L.Calculatethe work in joules needed to expanda balloon from5mL to 3.350 L against standard atmosphericpressure. Your lungsprovide that work if you are blowingit up yourself.Consider exercise 2.5. Would the workbe more or less if it were performedagainstdifferent external pressures found a at the top of Mount Everest, b at the bottomofDeathValley,c in space?Apistonhaving0.033 mol ofgas at 35.0Cexpands from0.77 Lto 2.00L.Calculate the work performed if theexpansion occurs a against an externalpressure of 0.455atm,andbreversibly.A bottle of soda has a head space containing 25.0 mL of CO2 gas at 4.2 atm pressure when the soda is at 4.4C. The bottle is opened slowly, letting the excess pressure escape. Howmuch work does the escaping CO2 do if the ambient pressure is 1.0 atm? Assume that the temperature remains constant.2.9E Calculate the specific heat of a material if 288J of energy were required to heat 50.5g of the material from 298K to 330K. What are the units?There is 3930 J of energy added to a 79.8-g sample of H2 gas. By how much doesthe temperature change?If the heat capacity varies withtemperature, abetter form ofequation 2.9 isto solve q=TiTfnCT-t A 50.0-g sample of white phosphorus is heated from 298 K to 350K. If its molar heat capacity is CT- = 56.990.1202T J/mol.K, how much heat is needed?Liquid hydrogen fluoride, liquid water,and liquid ammonia all have relatively high specific heats for suchsmall molecules. Speculate asto whythis might be so.A 5-mmdiameter hailstone has a terminal velocity of10.0m/s. Assuming its mass is6.031025 kg and all of its kinetic energy turns into heat, calculate the temperaturechangeof the hailstone when it hits the ground and stops. The heat capacity of ice is 2.06J/g.K.A7.50-gpiece of iron at 100.0C is dropped into 25.0g of water at 22.0C. Assuming that the heat lost by the iron equals the heat gained by the water,determine thefinal temperature of the iron/watersystem. Assume a heat capacity of water at 4.18 J/g.K and of iron at 0.452J/g.K.With reference to Joules apparatus inFigure2.6, assuminga massof 100.Kg ofwater about100L,a weight witha massof 20.0kg, anda dropof 2.00meters,calculate howmany drops it wouldtake toraise the temperature of the water by1.00C. The acceleration dueto gravityis 9.81m/s2.Hint: See Example2.5.2.17E True or false: Althoughwork done bya free expansion is zero for an ideal gas, it is nonzero for a real gas. Explain your answer.What arethe differencesbetween an open, a closed, and an isolated system?Describe an example of each.The statement Energycan beneithercreatednor destroyedis sometimes used as an equivalent statement of the first law of thermodynamics. There areinaccuracies to the statement, however. Restate it tomake it less inaccurate.2.21E What is the change in internal energy when a gas contracts from 377mL to 119mLundera pressure of 1550 torr, whileat the same time being cooled by removing 124.0J ofheat energy?Calculate the work for the isothermal, reversible compressionof 0.245 moleof an idealgas going from 1.000L to 1.00 mL if the temperature were 95.0C.Calculate the work donewhen 1.000 mole of an ideal gas expands reversiblyfrom 1.0L to 10L at 298.0K. Then, calculatethe amount ofwork done when the gasexpands irreversibly against aconstant external pressure of 1.00 atm. Compare thetwovaluesand comment.Apistonhaving0.033 mol of gas at 35.0C expands from 0.77L to 2.00 L and the systemsimultaneously absorbs 155J of heat.Calculate U if the expansion occursa againstan external pressure of 0.455atm, and b reversibly.2.26E Indicate which state function is equal to heat, q, for each process described. a. The ignition of a sample in a bomb calorimeter, an unyielding, heavy metal chamberin which samples are burned for heat content analysis b.The melting of an icecube in a cup c.The cooling down ofthe inside of arefrigerator d.A fire in a fireplace The distance between downtown San Francisco and downtown Oakland is 9 miles. However, a car driving between the two points travels 12.3miles. Of these distances, which one is analogous to a state function? Why?Is temperature astate function?Defend your answer.A piston reversibly and adiabatically contracts 3.88 moles of ideal gas to one-tenth of its original volume, thenexpands back to the original conditions. It does thisa total of five times. If the initial and final temperatures both are 27.5C, calculatea thetotal work andb thetotal U forthe overall process.Calculate U when 1.00 mol of H2 goes from 1.00 atm, 10.0 L, and 295 K to 0.793 atm, 15.0 L, and 350 K.Many compressed gases come in large,heavy metal cylindersthat are so heavy that they need a special cart to move them around. An80.0-Ltank ofnitrogen gas pressurized to 172 atm is left in the sun and heats from its normal temperature of 20.0C to 140.0C. Determine a the final pressureinsidethe tank and b the work, heat, and U of the process. Assume that behavior is ideal and the heatcapacity of diatomic nitrogenis 21.0J/mol.K.Under what conditions will U be exactly zero for a process whose initial conditions are not thesame as its final conditions?Aballoon filled with 0.505 mole of gascontracts reversibly from 1.0L to 0.10 L ata constant temperature of 5.0C. In doing so, it loses 2690J of heat. Calculate w, q, U, and H for the process.A piston having 7.23 g of steam at 110 C increases its temperature by 35 C. At the same time, it expands from a volume of 2.00 L to 8.00 L against a constant external pressure of 0.985 atm. Calculate w, q, U, and H for the process.It takes 2260 J to vaporize a gram of liquid water to steam at its normal boiling point of 100C. What is H for this process?What is the work, given that the water vaporexpands against a pressure of 0.988atm? What is U for thisprocess?True or false: Any process for which H is negative is exothermic. Explain your answer.2.38E A refrigerator contains approximately 17cubic feet, or about 480 liters, of air. Assuming it acts as an ideal gas with a molar CV of 12.47 J/mol.K, what is the change in U in cooling the air from normal room temperature 22C to refrigerator temperature 4C? Assume an initial pressure of 1.00 atm.In a constant-volume calorimeter, 35.0g of H2cools from 75.3C to25.0C. Calculate w, q, U, and H for the process.A 2.50-mol sample of gas is compressed isothermally from 20.0 L to 5.00 L under a constant external pressure of 10.0 atm. Calculate w, q, U, and H for the process.A 244-g amount of coffee in an open plastic cup cools from 80.0C to 20.0C. Assuming no loss of mass and a heat capacity of liquid water, determine w, q, U, and H for the process. The densities of water are dH2O, 80.0C = 0.9718g/cm3 and dH2O, 20.0C =0.9982 g/cm3.2.43E Starting with equation 2.27 andthe original definitionof enthalpy, derive the fact that Cp-=Cv-+R Derive the fact that HpT is also zero for an ideal gas.Define isobaric,isochoric, isenthalpic,and isothermal. Can achangein a gaseous system be isobaric, isochoric,and isothermal at the same time? Why or why not?Starting from the cyclicrule involvingthe Joule- Thomson coefficient, derive equation 2.35 The ideal gas law is theequation of state for an ideal gas. Why cantit be used to determine TpH?2.49E Estimatethe final temperature of a mole of gas at 200.00 atmand 19.0C as it is forced through a porous plugto a final pressure of 0.95 atm. The UJT of the gas is 0.150K/atm.With regard to exercise 2.50, how accurate do you think your answer is, and why?Use the data in Table 2.2 to determine Hp T for Ar at 0C and 1atm. Make any reasonable assumptions necessary.Use the data in Table 2.2 to determine PH T for N2 at 50C and 20atm. Make any reasonable assumptions necessary.Someone proposes thatthe Joule-Thomson coefficient can also be defined as UJT = UPTcv Is this definition valid? Whyor whynot?Why is equation2.37 written interms of CV and Cp and not c-v and c-p ?What are the numerical values of the heat capacities c-v and c-p of a monatomic ideal gas,in units of cal/mol.K and L.atm/mol.K?In a constant-pressure calorimeter that is, one that expands or contracts if the volume of the system changes, 0.145 mole of an ideal gas contracts slowly from 5.00 L to 3.92 L. If the initial temperature of the gas is 0.0 C, calculate the U and w for the process.What is the finaltemperature of0.122 mole ofmonatomic ideal gas that performs 75J of work adiabatically if the initial temperature is 235C?2.59E Show that =5/3 for a monatomic ideal gas.2.61E 2.62E A 1.00 mol sample of H2 is carefully warmed from 22 K to 40 K at constant volume. a What is the expected heat capacity of the hydrogen? b What is q for the process?Asampleof a monatomic ideal gas doubles itsvolume reversibly and adiabatically. By what percentage does its absolute temperature change?A sample of an ideal diatomic gas is compressed adiabatically and reversibly to double its initial pressure. By what percentage does its absolute temperature change in a the low-temperature limit and b the high-temperature limit?In orbit about Earth, a weather balloonjettisons a weight andascends to a higher altitude. If the initial pressure inside the balloon is 0.0033 atm and it ascends to an altitude where the pressure is 0.00074 atm, by what fraction does the absolutetemperature change? Assumethat the balloon is filled with helium, a good approximation of an ideal gas, and that the change is adiabatic.2.67E 2.68E If pumping up an automobile tire is assumed to be adiabatic and reversible, what is the new temperature of the air if a tire is pumped from 14.7 psi to 46.7 psi using air whose initial temperature is 22 C? Use = 7/5.2.70E Take the volume change into account and calculate H and U for exactly 1 g of ice melting into 1 g of water at standard pressure. The density of ice at 0 is 0.9168 g/mL; the density of water at 0 is 0.99984 g/mL.How much work is performed by 1 mole of water freezing to 1 mole of ice at 0C at standard pressure? Use the densities from the previous exercise.Why are steam burns so much worse than water burns even if the H2O is at the same temperature for both phases? Hint: Consider the heat of vaporization of water.How many grams of water at 0C will be melted by the condensation of 1 g of steam at 100C?Draw a diagram like Figure 2.11 that illustrates the change in enthalpy for the chemical reaction C s 2H2 g CH4 g Which is exothermic by 74.8 kJ/mol.Determine the rxnH(25C) of the following reaction: H2(g)+I2(s)2HI(g)Determine rxnH 25 C for the following reaction: NO g O2 g NO2 g This reaction is a major participant in the formation of smog.The enthalpy of combustion of buckminsterfullerene, C60, is -26,367kJ/mol. C60(s)+60O2(g)60CO2(g) Determine the fHofC60..The enthalpy of combustion of diamond is -395.4 kJ/mol. C s, dia O2 g CO2 g Determine the fH of C s, dia.Using Hesss law, writeout allof the formation reactions that add up to, and calculate rxnH(25C) for, the following reaction: 2NaHCO3(s)Na2CO3(s)+CO2(g)+H2O(l) This reactionoccurswhen one usesbakingsoda tosmother a firein the kitchen.Sublimation is the phase change from solid to gas without going through a liquid phase. Solid CO2, called dry ice, is an example of one substance that sublimed. Use Hesss law to show that the enthalpy of sublimation, subH, is equal to fusH vapH.The thermite reaction combines aluminum powder and iron oxide and ignites the mixture to make aluminum oxide and iron. So much energy is given off that the iron productfrequently is molten. Write a balanced chemical reaction for the thermite process and determine its H(25C).Benzoic acid, C6H5COOH, is a common standard used in bomb calorimeters, which maintain a constant volume. If 1.20 g of benzoic acid gives off 31, 723 J of energy when burned in the presence of excess oxygen and in a water bath having a temperature of 24.6 C, calculate q, w, H, and U for the reaction.Assume that 1.20 g of benzoicacid, C6H5COOH, is burned in a porcelain dish exposed to the air.If 31, 723 J of energy is givenoff andthe surrounding temperature is 24.6C, calculate q, w, H,and U. Compare your answers to those from the previousproblem.Natural gas is mostly CH4. When it burns, the chemical reaction is CH4 g 2O2 g CO2 g 2H2O g The H of combustion of one mole of CH4 at 25.0 C is -890.9 kJ. Calculate q, w, and U under these conditions, assuming an external pressure of 1.07 atm.Assuming constant heatcapacities for products and reactants,determine the H(500C) for 2H2(g)+O2(g)2H2O(g) g. Hint: Becarefulwhichdata you use for water Use the heat capacities of the products and reactants of the thermite reaction and the calculated H of the process to estimate the temperature of the reaction. Assume that all of the heat generated goes to increasing the temperature of the system.The following are values of heat capacity for nitrogen gas; Temp K Cv J/mol. K 300 20.8 400 20.9 500 21.2 600 21.8 700 22.4 800 23.1 900 23.7 1000 24.3 1100 24.9 Using the general formula Cv = A BT C/T2, find values of A, B, and C that fit the given data.2.89E 2.90E The Dieterici equation of state for one mole of gas is p=RTe-aVRTV-b Where a and b are constants determined experimentally. For NH3g, a = 10.91 atm. L2 and b = 0.0401 L. Plot the pressure of the gas as the volume of 1.00 mol of NH3g expands from 22.4 L to 50.0 L at 273 K, and numerically determine the work done by the gas by measuring the area under the curve.2.92E Find the enthalpies of the combustion reactions for methane through n-octane. Plot them versus the number of carbon atoms in the molecule, and determine an equation that gives H for the combustion of a given hydrocarbon. Then use the equation to predict the enthalpy of combustion for n-C12H26 and compare it to experimental values.Decide whether the following processes will be spontaneous, and why. The why can be general, not specific. a Ice melting at 5C b Ice melting at +5C c KBr(s) dissolving in water d An unplugged refrigerator getting cold e A leaf falling from a tree to the ground f The reaction Li(s)+12F2(g)LiF(s) g The reaction H2O(l)H2(g)+12O2(g)Try to find one additional example of a spontaneous process that is in fact endothermic that is, it occurs with an absorption of heat.Consider the following quantities for a Carnot-type cycle: Step 1: q=+850J,w=850J. Step 2: q=0,w=155J. Step 3: q=623J,w=+623J. Step 4: q=0,w=+155J. Calculate the efficiency of the cycle.Consider the following quantities for a four-step cycle: Step 1: q=+445J,w=445J. Step 2: q=0,w=99J. Step 3: q=360J,w=+360J. Step 4: q=0,w=+99J. Under what additional conditions for each step will this be a Carnot-type cycle? What is the efficiency of this process?What is the temperature of the low-temperature reservoir of a process that has an efficiency of 0.440(44.0) and a high-temperature reservoir at 150C?What is the temperature of the high - temperature reservoir of a process that has an efficiency of 44.0(0.440) and a low - temperature reservoir at 150C?3.7E Explain why the high-temperature reservoir of a heat engine must, indeed, be higher in temperature than the low-temperature reservoir. Can it ever be the other way around?Superheated steam is steam with a temperature greater than 100C. Explain the advantages of using superheated steam to run a steam engine.3.10E The Carnot cycle is defined as having a certain specific first step, the isothermal expansion of a gas. Can a Carnot cycle start at step 2, the adiabatic expansion? Why or why not? Hint: See Figure 3.2.In thermodynamics, the pathway in a pressure-volume diagram for an adiabatic change is called an adiabat, while the pathway for an isothermal change is called an isotherm. Identify the adiabats and isotherms in Figure 3.2.A refrigerator is the reverse of an engine: Work is performed to remove heat from a system, making it colder. The efficiency of a refrigerator often termed the coefficient of performance is defined as q3/wcycle=Tlow/(ThighTlow). Use this definition to determine the efficiency needed to halve the absolute temperature. What does your answer imply about attempts to reach absolute zero?Efficiency is given by equations 3.5, 3.6, and 3.10. Although we deal mostly with ideal gases in the development of thermodynamics, experimentally we are confined to real gases. Which of the definitions of e are strictly applicable to processes involving real gases as well as ideal gases?What is the entropy change for an ideal Carnot cycle? Explain your answer.What is the entropy change for the melting of 3.87moles of bismuth at its melting point of 271.3C? The heat of fusion of solid Bi is 10.48kJ/mol. Bismuth is one of the few materials, including water, that is less dense in solid form than in liquid; therefore, solid Bi floats in liquid Bi, like ice floats in water.What is the entropy change for the solidification of 1.00oz.(28.3g) of liquid gold at 1064C? The enthalpy of fusion of Au is 12.55kJ/mol.Explain why the statement No process is 100 efficient is not the best statement of the second law of thermodynamics.What is the change in entropy of 1.00mole of water as it is heated reversibly from 0C to 100C? Assume that the heat capacity is constant at 4.18J/gK.3.20E One mole of He warms up irreversibly at constant volume from 45C to 55C. Is the change in entropy less than, equal to, or greater than 0.386J/K? Explain your answer.Consider a monatomic ideal gas in a piston chamber, where the initial volume is 2.00L and the initial pressure is 8.00atm. Assume that the piston is moving up that is, the system is expanding to a final volume of 5.50L against a constant external pressure of 1.75atm. Also assume a constant temperature of 25.0C for the process. Calculate Ssys,Ssurr, and Suniv for the process.A 0.500-mol sample of an ideal gas has an initial temperature of 298K. It is compressed from an initial volume of 13.00L to 5.00L by an external pressure of 2.45atm, at which point the internal and external pressures are equal. Calculate Ssys,Ssurr, and Suniv for the process.SO2 in a piston chamber kept in a constant-temperature bath at 25.0C expands from 25.0mL to 75.0mL very, very slowly. Assume SO2 behaves as a van der Waals gas, and its van der Waals parameters are a=6.714atmL2/mol2 and b=0.05636L/mol. If there is 0.00100 mole of ideal gas in the chamber, calculate Ssys,Ssurr, and Suniv for the process.A normal breath has a volume of about 1L. The pressure exerted by the lungs to draw air in is about 758torr. If the surrounding air is at exactly 1atm(=760torr), calculate the change in entropy exerted on a breath of air due to its being inhaled into the lungs. Assume a temperature of 22.0C. Hint: You will have to determine the number of moles of gas involved.An automobile tire contains 15.6L of air at 46.0psi absolute and 22.0C. What is the entropy change of the air when it is released from the tire as it delfates to 14.7psi?An automobile tire contains 15.6L of air at 46.0psi absolute and 22.0C. After driving around a while, the tires temperature warms to 85.0C. What is the entropy change of the air? Assume a constant-volume heat capacity of 20.79J/molK for air.A sample of ideal gas from a compressed gas cylinder goes from 230atm to 1atm, with a concurrent change of volume wherein 1cm3 expands to 230cm3 in volume. Assume that the temperature remains or becomes the same for the initial and final states. Calculate the change in entropy for 1mole of the gas undergoing this process. Does your answer make sense? Why or why not?3.29E In Example 3.5, a heat capacity of 20.78J/molK was used, which is 5/2R. Is this value of heat capacity justified? Why?3.31E 4.00L of Ar and 2.50L of He, each at 298K and 1.50atm, were mixed isothermally and isobarically. The mixture was then expanded to a final volume of 20.0L at 298K. Write chemical processes for each step, and determine the change in entropy for the complete process.Dentists might use a mixture of 40N2O and 60O2 as an initial anesthetic of nitrous oxide although the exact proportions may vary. Determine the entropy of mixing for 1mole of such a mixture. Assume ideal gas conditions.A 5.33-g piece of Cu metal is heated to 99.7C in boiling water, then dropped into a calorimeter containing 99.53g of H2O at 22.6C. The calorimeter is sealed to the outside environment, and temperature equalizes. Cp[Cu(s)]=0.385J/gK, Cp[H2O]=4.18J/gK. a Discuss the process that occurs inside the calorimeter in terms of the zeroth and first laws of thermodynamics. b What is the final temperature inside the system? c What is the entropy change of the Cu(s)? dWhat is the entropy change of the H2O(l)? e What is the total entropy change in the system? f Discuss the process that occurs inside the calorimeter in terms of the second law thermodynamics. Do you expect it to be spontaneous?A sample of 1.00mol of silver at 150C is placed in contact with 1.00mol of silver at 0C. Calculate a the final temperature of both silver samples; b The S for the hot Ag sample; c the S for the cold Ag sample; and d the total S of the system. e Is the process spontaneous? How do you know? Assume a constant heat capacity for Ag of 25.75J/molK.3.36E What is the change in entropy when 2.22mol of water is heated from 25.0C to 100C? Assume that the heat capacity is constant at 4.18J/gK.Estimate the entropy change of an 800-lb engine (1lb=0.455kg) that goes from normal environmental temperature, about 20C, to an average operational temperature of 650C. The heat capacity of iron the major component of most engines is 0.45J/gK.Calculate the molar entropy change of the gas that accompanies the bursting of a balloon if the initial pressure is 2.55atm and the external pressure is 0.97atm.A normal breath is about 1L in volume. Assume you take a breath at sea level, where the pressure is 760mmHg. Then you instantly this is a thought experiment, after all go to Los Alamos, New Mexico, located in the mountains where the normal atmospheric pressure is 590mmHg, and you exhale. Assuming ideal gas behavior, whats the change in entropy of the air? Assume a temperature of 37C.The first law of thermodynamics is sometimes stated You cant win and the second law is stated similarly as You cant even break even. Explain how these two statements can be considered apt though incomplete viewpoints for the first and second laws of thermodynamics.Troutons rule states that the entropy of boiling at the normal point is 85J/molK. a Does the data from Example 3.2 support Troutons rule? b H2O has a heat of vaporization of 40.7kJ/mol. Does the vapS for H2O at its normal boiling point support Troutons rule? Can you explain any deviation? c Predict the boiling point of cyclohexane, C6H12, if its vapH is 30.1kJ/mol. Compare your answer to the measured normal boiling point of 80.7C.3.43E Argue from Boltzmanns definition for entropy that S can never have a negative value. Hint: See equation 3.26.3.45E Which system has the higher entropy? a A clean kitchen or a dirty kitchen? b A blackboard with writing on it or a completely erased blackboard? c 1g of ice at 0C or 10g of ice at 0C? d 1g of ice at 0K or 10g of ice at 0K? e 10g of ethyl alcohol, C2H5OH, at 22C roughly room temperature or 10g of ethyl alcohol at 2C the approximate temperature of a cold drink?Which system has the higher entropy? a 1g of solid Au at 1064K or 1g of liquid Au at 1064K? b 1 mole of CO at STP or 1 mole of CO2 at STP? c 1 mole of Ar at a pressure of 1atm or 1 mole of Ar at a pressure of 0.01atm?The absolute entropy of He at 298.15K is 126.04J/molK. What is its absolute entropy at 1000.00K? Assume that the heat capacity is constant.The absolute entropy of Kr at 298.15K is 163.97J/molK. What is its absolute entropy at 200.00K if the volume remains unchanged? Assume that the heat capacity is constant.The element helium is thought to remain a liquid at absolute zero. Solid helium can be made only by exerting a pressure of about 26atm on a liquid sample. Is the entropy of liquid helium at absolute zero exactly zero? Why or why not?Order the following substances in order of increasing entropy: NaCl(solid), C(graphite), C(diamond), BaSO4(solid), Si(crystal), Fe(solid).The molar entropy change for a process is 1.00J/molK. By what percentage has the number of possible distributions changed when going from reactants to products? You will need to use the relationship in equation 3.26.What is the entropy change of a process if doubles in the course of the process? You will need to use the relationship in equation 3.26.One mole of ideal gas expands isothermally and reversibly by 1.00L. In one case, the expansion starts at 1.00L, and in a second case, the expansion starts at 10.00L. Calculate the entropy changes for both expansions and justify the relative values in terms of the change in for each expansion.Why isnt the entropy of elements in their standard pressure at normal that is, room temperatures equal to zero?Determine the entropy of formation, fS, of the following compounds. Assume 25C. a H2O(l) b H2O(g) c Fe2(SO4)3 d Al2O3 The thermite reaction has solid aluminum powder reacting with iron (III) oxide to make aluminum oxide and iron. The reaction is so exothermic that the iron product is usually molten initially. Write the balanced chemical reaction for the thermite reaction and determine the rxnS for the process. Assume standard conditions.3.58E Determine the differences in the rxnS under standard conditions for the two following reactions: H2(g)+12O2(g)H2O(l)H2(g)+12O2(g)H2O(g) and justify the difference.Calcium carbonate has two crystalline forms, called aragonite formed by mollusks for their shells and calcite formed in sedimentary rocks. The enthalpy change for the reaction calcitearagonite at 1atm is 0.20kJ/mol at its transition temperature of 380C. Calculate S for this phase change.The chemical formula for gasoline can be approximated as C8H18. The chemical reaction for the combustion of gasoline is 2C8H18(l)+25O2(g)16CO2(g)+18H2O(l) If S(C8H18)=361.2J/molK, calculate the entropy change that accompanies the combustion of 2653g(=1.00gal) of gasoline.3.62E 3.63E Plants take in CO2(g) and H2O(l) and make glucose, C6H12O6(s), and O2(g). Determine the standard entropy change for the overall reaction.3.65E 3.66E Plots of Cp/T versus T are used to determine the entropy of a material, as the entropy value would be the area under the curve. For sodium sulfate, Na2SO4, the following data are available: T(K) Cp(cal/K) 13.74 0.171 16.25 0.286 20.43 0.626 27.73 1.615 41.11 4.346 52.72 7.032 68.15 10.48 82.96 13.28 95.71 15.33 Source: G.N. Lewis and M.Rabdall, Thermodynamics, rev. K. Pitzer and L.Brewer, McGraw-Hill, New York, 1961. Extrapolate to 0K using a function f(T)=kT3, where k is some constant. Using your plot, numerically evaluate the experimental entropy of Na2SO4 at 90K.List the sets of conditions that allow dS, dU, and dH of a process in a system act as a spontaneity condition.Explain why conditions for using S>0 as a strict spontaneity condition imply that U and H both equal zero.Explain how the equation dU+pdVTdS0 is consistent with the idea that spontaneous changes occur with a decrease in energy and an increase in entropy.Explain why the spontaneity conditions given in the equation 4.3 and 4.4 are in terms of the general derivatives dU and dH and not some partial derivative of U and H with respect to some other state variable.Prove that the adiabatic free expansion of an ideal gas is spontaneous.Derive equation 4.6 from equation 4.5.Derive equation 4.8 from equation 4.7.The third part of equation 4.9 mentions a condition called equilibrium, in which there is no net change in the state of a system. What are the equilibrium conditions for dU, dH, and dA?Calculate A for a process in which 0.160mole of an ideal gas expands from 1.0L to 3.5L against a constant pressure of 880mmHg at a temperature of 37C.What is the maximum amount of non-pV work that can be done by the reaction 2H2+O22H2O If fG(H2O)=237.13kJ/mol, and fG(H2)=fG(O2)=0?Consider a piston whose compression ratio is 10:1; that is, Vf=10Vi. If 0.0200mole of gas at 1400K expands reversibly, what is A for one expansion of the piston?When one dives, water pressure increases by 1atm every 10.55m of depth. The deepest sea depth is 10, 430m. Assume that 1mole of gas exists in a small balloon at that depth at 273K. Assuming an isothermal and reversible process, calculate w, q, U, H, A, and S for the gas after it rises to the surface, assuming the balloon doesnt burst Calculate G(25C) for this chemical reaction, which is the hydrogenation of benzene to make cyclohexane: C6H6(l)+3H2(g)C6H12(l) Would you predict that this reaction is spontaneous at constant T and p? Use data in Appendix 2.Thermodynamic properties can also be determined for ions. Determine H,S,andG for the following two reactions, which are simply reactions of dissolution: NaHCO3(s)Na+(aq)+HCO3(aq)Na2CO3(s)2Na+(aq)+CO32(aq) Assume standard conditions standard concentration is 1M for ions in aqueous solution, and consult the table of thermodynamic properties in Appendix 2. What similarities and differences are there?Calculate G in two different ways for the dimerization of NO2: 2NO2(g)N2O4(g) Are the two values equal?Calculate G in two different ways for the combustion of benzene: 2C6H6(l)+15O2(g)12CO2(g)+6H2O(l) Are the two values equal?For the reaction C(graphite)C(diamond) at 25C, H=+1.897kJ and G=2.90kJ. What is S for the reaction? From what you know about the structures of graphite and diamond, does the value of S make sense?Determine G for the following reaction at 0C and standard pressure: H2O(l)H2O(s) Is the reaction spontaneous? Why are the thermodynamic values from Appendix 2 not strictly applicable to this reaction under these conditions?What is the maximum amount of electrical that is, non-pV work that can be obtained by reacting 1.00molCH4 in a fuel cell whose reaction is CH4(g)+2O2(g)2H2O(l)+CO2(g) at 25C?When a person performs work, it is non-pV work. Energy to do work typically comes from the metabolism of glucose in the cells: C6H12O6(s)+6O2(g)6CO2(g)+6H2O(l) If jogging involves 2090kJ of work per hour, how much time is needed to burn off 120g of glucose, a typical amount in a medium candy bar?Can non-pV work be obtained from a process for which G=0? Explain.Can pV work be obtained from a process for which G=0? Explain.Batteries are chemical systems that can be used to generate electrical work, which is one form of non-pV work. One general reaction that might be used in a battery is M(s)12X2(s/l/g)MX(crystal) Where M is an alkali metal and X2 is a halogen. Using Appendix 2, construct a table that gives the maximum amount of work that a battery can provide if it uses different alkali metals and halogens. Do you know if any of these types of batteries are actually produced?The value of G for any phase change at constant p is exactly 0. Knowing this, determine S for the process Au(1mol,s)Au(1mol,l) at 1064C and constant pressure. The enthalpy of fusion of Au is 12.61kJ/mol.The value of G for any phase change at constant p is exactly 0. Knowing this determine S for the process Au(1mol,l)Au(1mol,g) at 2808C and constant pressure. The enthalpy of vaporization of Au is 343kJ/mol. Explain why this value is so much larger than the value of S calculated in the previous exercise.Under what conditions is A=0 for a phase change? Is this likely to be useful under real conditions?Example 4.2 calculated A for one step of a Carnot cycle. What is A for the entire Carnot cycle?Can CV and Cp be easily defined using the natural variable expressions for dU and dH? Why or why not?Analogous to equation 4.26, what is the expression for U, assuming one knows the behavior of A as it varies with respect to temperature and volume?4.30E 4.31E 4.32E Although ideally, U=H=0 for a gas-phase process at constant T, A and G are not. Explain why this is so.Use equations 4.21 and 4.25 to explain why H and G vary much more with pressure for a gas than they do for a solid and a liquid.4.35E Which of the following functions are exact differentials? a dF=1xdx+1ydy b dF=1ydx+1xdy c dF=2x2y2dx+3x3y3dy d dF=2x2y3dx+2x3y2dy e dF=xndx+yndy,n= any integer f dF=(x3cosy)dx+(x3siny)dy 4.37E 4.38E 4.39E Equation 4.19 says that (UV)S=p If we are considering the variation of U, the change in the change of the internal energy, we can write that as see the previous problem for an analogous argument ((U)V)S=p Show that this is entirely consistent with the first law of thermodynamics.For an isentropic process, what is the approximate change in U if a system consisting of 1.0mole of gas goes from 7.33atm and 3.04L to 1.00atm and 10.0L? Hint: See the previous problem.Use the ideal gas law to demonstrate the cyclic rule of partial derivatives.4.43E 4.44E Evaluate (U/V)T for an ideal gas. Use the expression from Example 4.11. Does your answer make sense?Evaluate (U/V)T for a van der Waals gas. Use the third expression from Example 4.11 and compare your answer to the answer from the previous exercise.Repeat the previous exercise for a gas that follows the Berthelot equation of state see exercise 1.55.Determine an expression for (p/S)T for an ideal gas and for a van der Waals gas.Determine the value of the derivative {[(G)]/T}p for the solid-state reaction 2Al+Fe2O3Al2O3+2Fe Hint: See exercise 3.57.4.50E 4.51E A 0.988-mole sample of argon expands from 25.0L to 35.0L at a constant temperature of 350K. Calculate G for this expansion.A 3.66-mol sample of He contracts from 15.5L to 2.07L at a temperature of 188C. Calculate G for the process.4.54E 4.55E Use the Gibbs-Helmholtz equation to demonstrate that C(diamond) is unstable with respect to C(graphite) at any temperature. See exercise 4.17 for H and G data.For the equation 2H2(g)+O2(g)2H2O(g) H(25C)=241.8kJ and G(25C)=228.61kJ. Use the Gibbs-Helmholtz equation to estimate the temperature for which G=0.Use equation 4.46 as an example and find an expression for A as the volume varies.What is the value of G when 1.00mol of water at 1.00atm is compressed isothermally to a pressure of 100.0atm? Assume a constant molar volume of 18.02cm2.

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