Problems 29 which gives _ 0.464 x 83144 X 700 os? At their melting temperatures, the coordination numbers of liquid Cd and liquid Ga ae, respectively, 8 and 11. It will thus be assumed thatthe coordination number in the 50-50 solution is the average of 8 and 11, namely, 9.5. The bond energy, Ecs- cue is obtained from the molar enthalpy of evaporation, AH. according to a 10,7953 1 Meapcnca = ~52NoE on cu 270,000 x 2 Tr x 6023 195 7 ~815 x 10-3 and similarly, 100,000 x 2 8 x 6.023 x 10” Ecsca = = 415 x 10°F ‘The bond energy. Ecy-ca is obtained from 1 a= oat Ecaca ~ 7(Ecace + Fexo| 10,795 = 9.5 x 6.023 x 10 [ze = teas x 10° - 815 x 107 as Feags = ~596 x 10-5 PROBLEMS - 9.1 One mole of solid Crz03 at 2500 K is dissolved in a large volume of a liquid Raoultian solution of Al,O5 and Cr,0; in which Xe, = 0.2 end which is also at 2500 K. Calculate the changes in enthalpy and entropy caused by the addi- tion. The normal melting temperature of CrsO, is 2538 K, and it can be as- sumed that the A5y.q,0, = ASy.cr0: 9.2. When I mole of argon gas is bubbled through a large volume of an Fe-Mu melt Of Xun = 0.5 at 1863 K evaporation of Mn into the Ar causes the mass of the melt o decrease by 1.50 g. The gas leaves the melt at a pressure of | atm. Cal- ‘culate the activity coefficient of Mn in the liquid alloy93 94 “98 96 97 98 99 | Chapter9: ‘The Behavior of Solutions ‘The variation, with composition, of G%* for liquid Fe-Mn alloys at 1863 K is listed below. Does the system exhibit regular solution behavior? Calculate GF and Gi at Xyqq = 0.6. Calculate AGY at Xy4q = 04. Calculate the partial pressures of Mn and Fe exerted by the alloy of Xygq = 0.2. Xvg 0.1 02 03 04 05 06 07 09 GFF joules 395 703 925 1054 1100 1054 925 703 395 Calcutate the heat required to form a liquid solution at 1356 K starting with 1 ule of Cu and 1 mole of Ag at 298 K. At 1356 K the molar heat of mixing of liquid Cu and liquid Ag is given by AZ" = ~20,590Xc.Xaq- Melts in the system Pb-Sn exhibit regular solution behavior. At 473°C apy = 0.055 ina liquid solution of Xpp = 0.1. Calculate the value of 9. for the system and calculate the activity of Sn inthe liquid solution of Xsq = 0.5 at 500°C. ‘The activities of Cu in liquid Fe-Cu alloys at 1550°C have been determined as Xe, 09 08 07 06 05 04 03 02 01 005 acy 1.0 0.935 0.895 0.865 0.850 0.830 0.810 0.780 0.720 0.575 0.40 Using. separately, Eqs. (9.55) and (9.61), ealculate the variation of ag. with ‘composition in the system at 1550°C. ‘The activities of Ni in liquid Fe-Ni alloys at 1600°C have been determined as Xw 1 09 08 07 06 05 04 03 02 oO ay, | 089 0.766 062 0489 0.374 0.283 0.207 0.136 0.067 Using, separately, Eqs. (9.55) and (9.61), calculate the variation of ap. with ‘composition in the system at 1600°C. Tin obeys Henry's Law in dilute liquid solutions of Sn and Cd and the Henrian activity coefficient of Sn, yf. varies with temperature as 82 4 138 ny Calculate the change in temperature when { mole of liquid Sn and 99 moles of liquid Cd are mixed in an adiabatic enclosure. The molar constant pressure heat capacity of the alloy formed is 29.5 1/K. Use the Gibbs-Duhem equation to show that, ifthe activity coefficients of the components of a binary solution can be expressed as Vt + degxd Ket Sek + yaa + Inv = and. BiXs +H 0+ th +‘over the entire range of composition, then ez; = By = 0, and that, ifthe varia- tion can be represented by the quadratic terms alone, then az = Bi 9.10 ‘The activity coefficient of Zn in liquid Zn-Cd alloys at 435°C can be repre- sented as In Yzq = 0.875 XBq — 0.30 Xy Derive the corresponding expression for the dependence of In cy on compo- sition and calculate the activity of cadmium in the alloy of Xcq = 0.5 at 438°C. 9.11 The molar excess Gibbs free energy of formation of solid solutions in the sys- tem Au-Ni can be represented by T MS = XyiXnu(24,140 Xau + 38,280 Xyi — 14,230 XpXys){ 1 — 3o—m )I GS = KyiX (24,140 Nay + 38,280 Xyq — 14,230 X, 260 xs) Calculate the activities of Au and Ni in the alloy of Xq, = 0.5 at 1100 K.0 C02, 9 —e Cry, @) + mel rel Mouth DM = Simul * Trait " Clots00) 2538 C4, Cadeatien) amd Denix. 5 Mouth Abts = toys Tell AGA, = 2324 2324 = 13%) deel Win 2 Mitel = Pia # OHM x As i Buy = OS + DSmix Or rvcl = Matt - = et (Ko, Bore? Tralt = M189 $0 B31 Qo " 25% * = 7 = 46% 49 a = te =@ y= Bom mw Xion On * Finn , Pron We = ~ 33440 _ Zordet 4 37.68 = = 33440 — 3.02 MCigesy 4 3168 186 Fw = 06-0443. chm Yon 7 (Xn maw \(R ) . Ge) CA) = 0.0266 1s : (e) +1 Bun = 2066 og SM. 0-048 \n = OBA © lee Os os ~ ImRwy ay b) ¢) 4) CO Q¥o%—% . _ xs Xin = 0-9 Xe = 049 > B= Ge = ¥*S = 4389 Yom OE) MOK GO Lig Xie (6.10.84 - ue = 4393 (0.2008 9 GaBr Samus S b= 2%Q% Dex a Y 4340 1A Begulay Sabatinns Be Axe ~ 5 oF Gen = (io) (049 = 102.4 2, =~ ‘ Ge = (4s09C0.6) = 1980 2) n mid xs OG = nG) 4G FX p Prbnxa + 2% RTE%, + (1054) = CAVES ICED OH (OGD + (0.6) (831 C1BHIM.6) 4 1054 = -4365 3 mel ae Gan a u = 2 FLL = (arto ycoey = eTrmY = Pr ta ( Bom Xr (490.6) =Ceanciessy 0 (Ann (=) Bmmn = 0.240 - x. ttn Fn = Pann Fon 0.080% Bs Fan 0, 249 C0.0483) = 6,0 alm )Ge = SUX, = @Moy2s = sb = PPL = Ord fae me) c5s6 = @anaKes ye (Ae OP & = 6.80%. = te Fre Caf = ge Ye = =O — heater + 25:43 Tv =~ 450 _ 1.94 nC18639 423.45 VEb3, = Fat. -S ¥. = 4,94 xO ’ o eo Fe = Oe Fh, = OAILESSAYIO) = F.684w 12 anCues ame). | 2H ar AM taix Tey Oy real BE K aye DAL = \ (2760 + GaeKD VAT = 22.64 CSE MGT + 6.2 CAST angry 219” AS m = ras oR = \2a0 WB * > 5-2 OW = ( (ai30+ B40 T + LSTRIO TAT is = 2Mdo (1234- mney + e540 Ce aby Sind CL 1) z as kaa ae — 1444 Dig = Noto 5 . Bo Mg = (Gono) a = 30.50 (135-1234) = 312) 94 Diy = C 20H 1S 96037) x@ mel) = - (0245 Dias = DAKE III + Deadd + NAO + 3721 ~ OS = 1331% 3T= 434243 = Mab Ke Xp = 0) Xe, = 04 ~ Om, ~ 0.055" N, ox mw a = AX, = Rr Ba Ye, “Dm Brine, = (Bat rca rBa( 225 ) ma SICH XSn oat = -4515 5 Rus Gen = C4595 C05") = Bancrsy ba ( Se) Mn = AD pusneue 9.47 Ace Mat = on? a(4) Gh Ye = 840 CL) tse eho %, = ~@sncen(hy +198 A Cerin). Ceayyoeoy =~ $e0-4 3 ACh) — oe Want « nat >{(0.01)¢-1a0.49 | pot nadine = ~G4 F a = np) a1 a a Ans nee 0 x 24.5 .6 Gibleg - Onhom Exide =° Exidmt, =o Xad Ory + AMY, =o XpdMYg = + AMR —~ AQ) AbY, = Od¥g + La,Q>xyZdxq + Lol, oxy Ax, +-- - Bots = Bd ke + $A, C2 XadXq tb A GD XAdMy ton - Ma) 5 Xp dxgt Hy %a %ehXq Pa, Xm AX = X56 dX, —P¥e%o4Xp > By XX, Ax, = Xe OX, +h ary Akg +B, X4xe Ax, oe d= Bo =o war a, > AyGo Gibbs - Puhawn Byuatine Kad Ona + %yd On He =e Neg Keg + Kandla, = dM, =~ den 4 dah, Xa db, = ©8919) (29 xy d xg ~ 0.303) Xeq AX, = IAS Xeq dred = 08 X5 Axed hy, = thiy = TNS Xan Xl 4 04 Ha, Keg AKeg = FAS Sy AX, ON CAG AR a, 5 MMe “IV Sy . TA Xed + kay =) = 1.85 4, 408 dK, taly = (08S dn + [oA Sax, = OR x 4 gay? San + 28 Xan a 3 WY, = OA y+ O3x, —— fry cd. AW. Xyroy 2% 0S de FA = gas (oss 4 03 COS ed ay = OST es J