∆ 2SO3, observed pressure) vs. T are mixture at 1000 K on derived in (a) Solving a quartic equation can be avoided in this part of the K°P 0.245 1.99 4.96 9.35 0, and xSO3 !of0.440. 0.200 mol of N2, 0.300 mol of H2, and 0.100 mol ndependent T problem.) (b) ideal gases. (b) Find 7.8 (a) For cind556 and f if we574 con485water, calculate 534 of NH3. T/Kpure liquid ! # ossible phases are sider that the chemical species present are H2O, H , OH , and (a) Using only these data, findformed #H°, #S° at 534 for ssume For the gas-phase NF2#G°, " the 3Hand ∆ 2NH , aKclosed O) by hydrogen-bonded dimers (Hreaction value ofideal-gas the num- 6.29 2association 3reCHEM 211 of A and 18.0 mmol this reaction. (b) Repeat 2for2574 K.of Nto, c4.20and What happens f ifof weH2, and action 2H of degrees enumber expression for system initially contains mol 2O ∆ (H 2O) 2. (b)4.50 Problem Sheet for Assignment-‐3 2 ind mol d to 600 K, and the add hydrogen-bonded to the list species? possible trimers (Hmaximum ded to specify for the andofminimum of the NHideal-gas 2O)3 PCl 6.14molFor reaction 3. Give the Dn isexpression established. The 1.00 5(g) ∆ PCl3(g) " Cl2(g), te K° K to values at equilibrium ofestimate eachf,of the quantities: j; nisN2; at following 400 that #H° Appendix data to K° P at 1000 7.9useFind the relation between cind p ifK; (a)assume rigid, permeure 1085 torr and P, and n independent of T. conducting walls separate all the phases of a the able, H2; nthermally NH3. atsystems, 600 K, find assuming asonable choice of system; (b) movable, impermeable, thermally conducting walls he6.15 standard enthalpy of combustion 25°C of liquid acetone (CH ction A ∆ 2B.1. T6.30 (a) For the ideal-gas reaction A" ∆ reaching equilibH2B ∆ CO(g) "3)2CO to The CHat4(g) 2O(g) all theideal-gas phases ofreaction a system. t consideration of separate 2 and C°P,m,B(b)# eCO and H2at O(l) is -1790 Δ (CH3J/ )2CO(l). (g)constant 600 K has kJ/mol. #H° !Find 217.9 kJ/mol, °$298 !xof 242.5 3H # and [x B#S /(1 )](P/P°), T and P, show thatΔK° 2(g) f H° f U° and 0.01031 mol of rium 2at P 298 B of sucrose. An (molxK), ! 72.4 kJ/mol. Estimate(b) theUse temperature nstants and and these isand the#G° equilibrium mole fraction. the resultatof n the container; olid sucrose anthe where B7.2 Section 1 2 1/2 26 xfor this reaction. made. which K°Por! T2. at (a) e from T1 tosolid # " 4z)State $approximations z], where z! K°P P°/P. to True show that g) wassucrose, established Solid 2 [(z normal 7.10 false? The boiling point is the temB(a) wn. Find an Liqex-torr. sured as 231.2 nd ribose. (e) (c) A reaction system is initially composed of 0.200 mol ofK,O2 perature atFor which the4(g) vapor of2NO a in liquid equals 1 atm. 2. For the O 2NO the range 298 to 900 O4(g) ∆ 6.16 theNthat N2pressure 2reaction 2(g) 2(g) in the range 298 to sideal sucrose solution gases. (Hint: reaches (b)900 At the critical point at of 5000 a pure K substance, thebar. densities and 1.50 Find of thetheequilibK,equilibrium us sucrose solution, rium liquid mole and thefraction vapor areand equal. (c) The possible value P # moles of bminimum O$c>1T>K2 2 and O, given that K° enzene (these two 49.3 K° ! a1T>K 2 e of f infor the O phase rule is 1. P(d) The normal boiling point of pure $6 at 4000 2(g) ∆ 2O(g) at 5000 K. (d ) Find the equilibrium ! 3 %of10 water is precisely xture the vapors 100°C. (e) The enthalpy of vaporization a NO 13, b ! $1.304, and fractions in an10equilibrium mixture of NO2 of 2 4 and c ! 7307. (a) where a ! 1.09 % tial pressures PN2 ! mole liquid becomes zero at the critical point. ( f ) Along a line in Find gases at 25°C and 2.00 atm. Use Appendix data. as functions of T for expressions for #G°, #H°, #S°, and #C° orr. Is the mixture in a one-component phase diagram, f " 1. (g) P At the solid– mponents, what is this reaction. (b) Calculate #H° at 300 K and at 0.600 K. unt of N(g) increase 6.31 liquid–gas pointK°of # a one-component (h) CO2SO At triple 727°C, 3.42 for 2SOsystem, (g) " fO"2(g) ∆ (g). 2 ist in equilibrium? P 2 ibrium at 4000 K in has no normal boiling point. (i) Ice melts above 0.00°C if the 3 3.10 of mmol of O and 1.446.2mmol of6.3 SO3 of SO 6.17 mmol Complete the part (b) of2,Example in Sec. H. Hildebrand and If 2.65 2, work pressure is 100 torr. 3 empty vessel6thheld at 727°C, find hotograph is assumed independent of T, thenthe asplaced follows. that if185-cm #C°PChemistry, roblem 6.32 in of Show Lan evine Physical Edition: ¢n>molof a sys-3. Pare What must be true equilibrium 7.11 For each of the following conditions, which amounts of all species andstate find the phase equilibrium $ 1T 2 2 ¢H°1T K° 1 1 P P 2 1 ts in this system? pressure. (solid, liquid, or gas) ln of H2O!has the lowest $ bpotential. a chemical (a) 25°C and 1 atm; K° (b) 25°C and 0.1 R torr; (c) T10°C Tand 2 500 atm; P 1T 12 4, write down the Forand the10ideal-gas reaction B ∆ C, a mixture with (d) 100°C atm; (e) 100°C andA 0.1"atm. in- 6.32 hen K°P must roneutrality condihe ideal-gas reaction 1T 2 # T2.000 ¢C° T1mol is at P 1n 2 A # 1.000 mol, nB # 3.000 mol, and ction, !H° must n7.12 or the independent For the H2O phase diagram " of Fig. 7.1a,Castate ln the"num-$ 1 b at 300 K and 1.000 bar.RSuppose the pressure is 2 ution of KBr and equilibrium ber of degrees of freedom (a) along the line AC; (b) Tin1 the Tliqincreased to 2.000 bar; find the new equilibrium s? (a)between K°P is always ions ion isothermally uidUse area;this (c) at the triple point A. equation and Appendix data to estimate K°P,600 for less. (c) Kgive condition an amounts. P is never ∆ 2NO N2OThe pressure 4(g) vapor 2(g). of water at 25°C is 23.76 torr. (a) If on is the negative of 7.13 as the following 0.360 gFor ∆rigid PCl3container (g) " Clat2(g), use data reaction PCl of Hthe placed in an5(g) empty 25°C 2O is e reverse reaction is 6.33 by T and considering T as a fixed 6.18 (a) Replacing T 2K° 1 AssumetemP(CO) # 342.0the in give reasonable with " 10.0 L, state what phase(s) present at equilibrium atChemistry, 25°Careand at 500 K. idealtheV Appendix to find th E P on. ( f )a Doubling 4. Problem 7 .14 o f L evine P hysical 6 dition: perature, we can write the approximate equation (6.39) in the les: (a) a gaseous O in each phase. (b) The same as (a), except and the mass of H ressure is 439.5 behavior and 2 neglect the temperature variation in !H°. If coefficients squares gasform ! $#H°/RT " C, where the constant C equals ln20.0 K°P(T) present that∆ the we that V " L. State any approximations you make. rction CO of"(so Cl , calculate the equilibrium mole fracstart with pure PCl temperature 2 ln K°P(T1) " #H°/RT1. 5Derive the following exact equation: ure gas of Nin 2, H 2, and on World of all species at 500 K and 1.00 bar. nitial composition of tions action equilibrium; 7.14 Ar has normal melting and boiling points of 83.8 and ! $¢H° ¢S° ln K°Pis1Tat2 83.8 87.3 K; its triple point K and 0.7 " atm, and T>RT T>Rits critical n that all the N2 and 6.34 At 400 K, K° # 36 for N (g) " 3H ∆ 2NH 3(g). P 2 2(g) whether temperature and pressure are 151 K1 and 48 atm.3 State eolNH ; (d) A gasof3 COF2 are Find 400 or K gas forunder (a) each " following ∆ NH 3(g); 2 N2(g) 2 H2(g) condiP at liquid, Ar is aK° solid, of the rium with the conalyst for the gas- (b) (g) atm ∆ and N2(g) (g).atm and 80 K; (c) 0.8 atm 2NH tions: (a) 30.9 90 " K; 3H (b) 20.7 ; (e) a iation of N 2 . Use data in the and 88 K; (d) 0.8 atm and 84 K; (e) 1.2 atm and 83.5 K; ( f ) 1.2 atm o partially decom- 6.35 Given the ! G°1000 gas-phase values 84.31 kcal/mol for and 86 K; (g) 0.5 atmf and 84 K. addition, some of n-pentane, 83.64 kcal/mol for isopentane, and 89.21 kcal/mol med to vapor. 7.15neopentane, Figure 3.7 shows a reversible isobaric present path frominliquid 2C " 2D, it(No is for find the mole fractions an equilib water mixture at #10°Cofand 1 atm to ice at #10°C and 1 atm. 00 mol of A and rium these gases at 1000 K and 0.50 bar. Use Fig. 7.1 to help devise a reversible isothermal path between K P isnheld ! theand relation H " Use ! f G° data in the NIST-JANAF tables (Sec. 5.9) to these two states. nts. (b) Ifrelation. 1.000 6.36 neutrality
osel beata 500 stoichiomeK and
m amounts.
find K°P at 6000 K for N(g) ∆ N"(g) " e$(g).
7.16 For each pair, state which substance has the greater at its normal point: (a) Ne or Ar; (b) H2O $vap Hm Suppose 6.37 thatboiling for a certain ideal-gas reaction, theorerror in
7.22 The normal boiling point of diethyl ether (“ether”) is 34.5°C, and its !vapHm,nbp is 6.38 kcal/mol. Find the vapor pressure of ether at 25.0°C. State any approximations made. 7.23 Use the Clapeyron equation and data from Prob. 2.49 to find the pressure at which water freezes at (a) $1.00°C; (b) $10.00°C. The experimental values these pressures 5. Problem 7.24 of L(c) evine Physical Chemistry, 6th of Edition: are 131 atm and 1090 atm. Explain why the value you found in (b) is greatly in error.
7.24 The heat of fusion of Hg at 291 its normal lev38627_ch09.qxd 3/14/08 1:31 PM Page
melting point, $38.9°C, is 2.82 cal/g. The densities of Hg(s) and Hg(l) at $38.9°C and 1 atm are 14.193 and 13.690 g/cm3, respectively. Find the melting point of Hg at (a) 100 atm; (b) 500 atm.
(a) Find the average !Hm of sub range. (b) Find the vapor pressu
7.31 Use Trouton’s rule to show boiling point Tnbp due to a sm roughly !T ! Tnbp !P/(10 12 atm
7.32 (a) At 0.01°C, !vap Hm !fus Hm of ice is 6.01 kJ/mol. Fi at 0.01°C. (b) Compute the slo lines at the H2O triple point. S State any approximations made.
7.33 Vapor-pressure data vs. 7.25 (a) Repeat the ethanol example of Sec. 7.3 using the av289 sented by the Antoine equation erage of the 25°C and 78.3°C !vap Hm values instead of the 6. Problem .13 of LCompare evine Physical Chemistry, 6thexperimental Edition: 78.3°C9value. the result with the 25°C A$ and1P>torr2 b, each"comp 9.36 Find !mixG, !mixV, !mixS, and !mixH for mixing 100.0 g 9.46 Let phases a ln vapor pressure. (b) The actual molar volumes of ethanol vapor equilibrium with each other. Show of benzene with and 100.0 gatm, of toluene atPM20°C and 1328 Assume be inwhere andless 9.13 25°C 1and a 1:07 solution of Page 72.061 gatm. of H lev38627_ch10.qxd 3/14/08 2O are A, B, and C are constants c in theAttemperature pressure ranges of this example 3 ideal solutions, then x a1 " x b1 and an ideal solution. 2 form OH has a volume of 307.09 cm . In this solug of CH ution-composition 192.252 3 kelvin. The Antoine equation is than"those predicted by PV " RT. " Will inclusion of nonideal3/mol.mFind V two phases have the same compositio cm in this solution. V H2O ! 16.488 tion, CH 3OH H ) and toluene (C H CH ) form nearly 9.37 vapor-pressure typically ity ofBenzene the vapor(Cimprove or worsen the agreement of the result 6 6 6 5 3 phase. Hence liquidsrange, that form ideal 1s ideal solutions. At 20°C the vapor pressure of benzene is 74.7 the temperature range 11°C to 16 of (a)The with the experimental 25°C vapor pressure? density of a methanol–water solution that is 12.000 all proportions. b. 9.1 change if T 9.14 3 torr, and that of toluene is 22.3 torr. (a) Find the equilibrium par18.3036, B " 3816.44, C " $46 weight percent methanol is 0.97942 g/cm at 15°C and 1 atm. tial (s) (buckmin7.26 The average enthalpy ofsolution sublimation of C 60 vapor pressures above a 20°C of 100.0 g of benzene For a solution that is 13.000 weight percent methanol, the dention to Section 9.7find vapor pressures of roblem 9.38 of toluene. Levine Physical Chemistry, 6thwas Edition: sterfullerene) over the range 600 to 800 K determined by 328 solute HCl in each7. Psity 3 plus 100.0 g of (b) Find the mole fractions in the vapor is 0.97799 g/cm at this T and P. Since the change in solu- 9.47 compare withthetheconstant-T-andexperimental v Consider "ofthe allowing vapor in equilibrium withV solid at a fixed mL of a solution tion phase thatUse isthe inthe equilibrium with theestimate solution part (a). composition isDavies small, we can by 10.37 equation to estimate (a) g for 0.02 (b) Use the Antoine equation t Section A nA,2 # n10.9 ! adding A,1 moles of solvent A g of a 10.0 weight temperature to leak into a mass spectrometer and measuring the 100°C. State any approximations 25°C;pressures (b) g! for an aqueous mol/kgAtCaCl 10.48 Use (10.83) and the &o 1) that contains ni moles 100°C theatvapor of CaCl hexane octane are25°C 2(aq) 2 inand " tion (solution whose HCl molal- 9.38 # The graph of ln (IT/K) verintegrated V intensity I of the C60 peaks. " 1 0V> 0n 2 ! 1 ¢V> ¢n 2 A A T,P,n A T,P,n sults, seeanProb. 8.43.) B B mixture mol/kg, solution that 10.9 example to find S °298(s to give ideally dilute solution 1836 and 354has torr,CaCl respectively. A0.02 certain liquidCuSO of 4 of ASec. 2 molality 4 molality $1 sus T was found to have an average slope of $2.18 % 10 K of A. Experimental vapor-pressu these compounds has a3vapor pressure of 666 torr at (c) 100°C. )3 molality 0.005 mol/kg; g" and 0.01 two mol/kg, " and Al(NO moles7.34 OH) for a methanol–water solution at 15°C V Calculate (CH Show that $ T1 [C. K. Mathews et al., J. Phys. Chem., 96, 3566 (1992)]. The 10.49 Use in 2proces 3 is 30.00% CH3OH Find thatdata !G when forthe thisTAppend thethe mole fractions in the liquid mixture and in the vapor solutions show solution of1 part (a). g# for " OHshown by weight. Then calculate 1 Assume atm thatan isideal 122% CH3be placed with (7.24). Hints: In#(7 solid’s vapor pressure can to be proportional to IT &S° 1 atm is 8.911 mol/ and phase. solution. 298 for (a) H (aq) " OH (a " ¢G " n RT 1ln x i,2 # ln xi i " for this (H2O) and (aq) use (8.36). C60(s)CaCl in this temperature (see Prob. Find !mol/kg solution,range. what 2H (a)14.36). Forsolution. a 0.001 → H2O(l) " CO subHm of25°C 2(aq) and 1 atm. (b) Find V10.38 2(g). 9.39 A solution of hexane and heptane at 30°C with hexane to "is required $ RT 1nA,2 ln xA,2 # value of a in the Debye–Hückel equation (10.64) ass concentration. 9.15 Use Fig.0.305 9.3 tohas finda(a) the molality atofwhich ! a0; MgSO mole fraction vapor pressure 95.0 Vtorr and 4 10.50 (a) Use Appendix data of Table 10.2? give agreement with the experimental g th ! the limit of(b)anUsewhere x , x , x , and x are the fin the partial molar volume of MgSO roblem 10.39 of Levine Physical Chemistry, 6Find Edition: 4(aq) in vapor-phase hexane mole fraction of 0.555. the vapor ion in an aqueous8. P(b) (b) Use 25°C " " i,2 for i,1 Cu(NO A,2 A,1 the value of a from part (a)Vand (10.64) estimate 3)2(aq). and to of Hany inga! oftions of the solute and VState of Eq. MgSO infinitely 2O appressures dilute of puresolution; hexane (c) and heptane at 430°C. the solvent i ght. for NaCl(s) → NaCl(aq). (aq). 0.01 mol/kg mol/kgMgSO 25°C CaCl 2 (aq) solution. 0.05 proximations made.4 Eq. (9.23) to show that for this process n 450 mL of water 10.51 The & in a 0.0200 mol/kg HCl solution in 10.39 Calculate g ! law to At Use infinite dilution, theshow ionsthat of for an electrolyte are infi¢G " n i 1NBS m i,2 #tables m i,1 2 give $ nA,2 9.40 (a) Raoult’s an ideal solution of ume of 1.0000 L at 9.16 # 25°C and 1not atm. For atanother. 25°C and 1 atm, the NaSO4 (aq). With the aid of Ap CH 3OH 3OH far apart dofraction interact with one Therefore, B and C, at the B and mole in theCH vapor phase in equilibrium ty of 1.2885 g/cm3. nitely "(2 " " 1nA,2 #Na nA,1 q q reaction dielectric constant and theis density g/cm3. ion-pair formation# V values V strong electrolyte in solution the sum is of 0.787 with thea solution is is 32.6 i of " Assume a$ 3 Å.V q for the ions. Some for at 25°C and where mi,2, mi,1, mA,2, and mA,1 are the f l aqueous i values x *>PC* solutions 10.52 The NBS tables (Sec. B PB 3 th molality 1.506 1 atm are 16.6 cm3/mol v for NaCl, 38.0 cm /mol for KNO3, and potentials of the solute and the so xB "aqueous 10.40 For a 25°C solution of a single strong elec" values: #108.74 kJ/mol for NO l nd the KI molarity. 27.8 cm3/mol for NaNO1. $ *V * # 1KCl >Pq 2 in water at 25°C Comparison of the coefficient of ni in ( (a)xFind B 1P B i C for 3 trolyte, the Meissner equation is HNO3(ai). Without looking up 1 atm. (b) Find 1 0mi> 0P 2 q at 25°C. gives T,nj for KCl in water density r with sol- and (b) At 20°C the vapor pressure of benzene (C6H6) is 74.7 torr one of these numbers must be in molar concentra- and that of toluene (C H CH ) is 22.3 torr. I1>2For solutions of benm i,2 # m i,1 " RT 1ln xi,2 # ln xi,1 2 6 5 3 9.17 log Prove that the internal energy of a phase satisfies U ! 10 g! $ #0.5107z" 0 z# 0 ! xi /MA and that zene plus 1>2 10.53 Find the conventional toluene (assumed ideal) in equilibrium with vapor at " cIshort. %i ni mi .l The proof is1very "PV $ TS $ v The only way (9.68)Consider can hold isthe if two 25°C. (Hint: 20°C, plot x B versus x B for benzene. Repeat for toluene. q " z 0 z 0 log 3 1 # b " b11 " 0.1I 2 4 9.18 Write the defining for the partial molar # equation 10 the ionizationm of"water: 2Of i∆ ol/kg, where mB is 9.41 At 20°C and 1 "atm, RT ln xHi $ 1 the density of benzene is 0.8790 i " # Helmholtz energy of substance i in a solution and state fully 3 H O " OH .) 3 3 #0.023I 3 cular weight (rela- g/cm and that of toluene is definition 0.8668 cg/cm Find b! 0.75 #in0.065q, !stands 1. " 0.055qe what every symbol your for.the density of a where f i (T, P) is some function of T solution of 33.33 g" of benzene and 33.33 g of toluene at 20°C m # 10.54 (10.92) " Na "SO mi,1 at Derive constantEqs. T and P. (b) and Use where I ! Im /m°. Hian Ui $ 9.19 Show that !For P2V i. 4(aq), q $ #0.19. Calculate i,2 and 1 atm. Assume ideal solution. that the Meissner-predicted g! of Na2SO4(aq) at 0.1 mol/kg andshow10.55 (a) The solubility of O2 % n m , m ! m ° $ RT ln (P /P°) [Eqs. (9.23) 9.20 (a) Use G ! an ideal 9.42 Show that i!mix i C i P " i 0 for i isolution. (b) At m #OnA,1above m A,1 "the n A,2 1m*A $ n 1 mol/kg and compare with the values in Table 10.2. A,2 A,2 solutio pressure of . (b) The volume and 2 Eq.CP,m (4.65) applied to pure i to show " 136 J/(mol K) forgas benzene (C6that H6) G andof 25°C(6.4)] and 1and atm, #i O2A,1 in1m wat *A the volumes of its an *(T, ni), 0.1 water. Find & f G°298 for#n ideal gas J/(mol mixture Ttoluene is given " 156 K)atfor (Cby H5G CH! Find ofPai ,the soC Table data: (a) 10.41 For the CaCl i G iCPuse P ,m 610.2 3). % 2(aq) . state is used for the solute O olution must equal where and nigare the partial pressure number of25°C moles Pig100.0 lution of of benzene and 100.0 gand toluene andof 2 ( a spreadsheet Solver tooffind the atMeissner q. (q mol/kg ! and
