第5章 相平衡

1(1)(2)(3)(4)(5)(6)(7)(8)(9)5.15.1.1αβγ…πi=1,2NπβαTTT=⋅⋅⋅==i=1,2N5-1πβαppp=⋅⋅⋅==i=1,2N5-22πβαµµµiii=⋅⋅⋅==i=1,2N5-3πβαiiifffˆˆˆ=⋅⋅⋅==i=1,2N5-45.1.2F2+−=πNF5-5FNπ5.2TpyixiTpyixi5-4liviffˆˆ=i=1,2N5-6iviivipyfφˆˆ=i=1,2N5-7iviiviyffγΘ=ˆi=1,2N5-8liilipxfφˆˆ=i=1,2N5-93iliilixffγΘ=ˆi=1,2N5-105-8viγliγiγlifˆ5.2.1EOS5-65-75-9liiviipxpyφφˆˆ=iliivixyφφˆˆ=i=1,2N5-11viφˆliφˆi4-88viφˆTpyiliφˆTpxiEOSEOS5-11viφˆliφˆ4-88iviφˆliφˆ5.2.2lifˆiiiviixfpyγφΘ=ˆi=1,2N5-12ΘifiLewis-RandallTpiliiff=Θi=1,2N4-964()⎟⎟⎠⎞⎜⎜⎝⎛−=RTppVxppysiliiisisiviiexpˆγφφi=1,2N5-13pyiiviφˆipisTisiφiTpisiγixiiViliRT5-13piγ5-135-131)5-13Vilm3·mol-1-5ppisPap-pisR=8.314m3·Pa·mol-1·K-1T2()1exp≈⎟⎟⎠⎞⎜⎜⎝⎛−RTppVsili2)Lewis-Randalliviφφ=ˆ1=iγ3)1ˆ=viφ1=siφ—1)iisisiviixppyγφφ=ˆi=1,2N5-14—1)+2)isisiviixppyφφ=i=1,2N5-15viφTpi4.5.45—1)+3)iisiixppyγ=i=1,2N5-16—1)+2)+3)isiixppy=i=1,2N5-17RaoultRaoult5.2.35-15-11.2.EOS3.4.1.2.filγi3.1.EOS2.3.1.2.3.5.35-14iisisiviixppyγφφ=ˆi=1,2N65-145-145.3.15.3.1.1Tp-x-y5-1KMNKGNMGGMpyixi5.3.1.2Raoult121==γγ()12122211xpppxpxppsssss−+=+=5-15Tsp1sp25-25-1Tp-x-y5-275.3.1.311γ12γ11γ12γpRaoultCH3OH-H2O5-3pRaoultCH2Cl2-CH3OCH35-45.3.1.4p-xp5-5(a)x=yazT-x-y5-5(b)y-x5-5(c)5-35-48CH3CH2OH-H2OCH3CH2OH-C6H5CH312p-x5-6(a)azT-x-y5-6(b)y-x5-6(c)HNO3-H2OCH3OCH3-CHCl35.3.1.55.6.2--5-75-55-65-79--5.3.2N2NTpy1y2···yN-1x1x2···xN-1F=N-2+2=NNN5-14viiisisiipxpyφγφˆ=i=1,2N5-14∑==Niiy11()Tfpsi=5-16()Tgsi=φ5-17()NixxTK⋅⋅⋅=1,γ5-18()NviyypTF⋅⋅⋅=1,,ˆφ5-191)BUBLPTx1x2···xNpy1y2···yN5-16~5-19Tx1x2···xN5-14viφˆpy1y2···yN∑iy1101∑iy∑1iy∑=1iy5-85-82)BUBLTpx1x2···xNTy1y2···yN5-16~5-195-14sipsiφiγTviφˆTT5-9I.Tviφˆyi1ˆ=viφII.AntoniesipEOSsiφiγIII.5-14yi∑iyIV.yiTpviφˆVIV.viφˆsipsiφiγpxi5-14yi∑iy11VI.∑iyyiTpviφˆVVIIVII.∑iy1∑≠1iyTII∑=1iyTyi∑1iyT∑1iy5-93)DEWPTy1y2···yNpx1x2···xN5-14isisiviiippyxγφφˆ=i=1,2N5-205-16~5-19TsipsiφpTyiviφˆxi125-10I.piγxi1=iγII.AntoniesipEOSsiφIII.EOSviφˆIV.5-20xi∑ixV.xiTiγVIIIVI.iγviφˆsipsiφyip5-20xi∑ixVII.VVIII.∑ixxiTiγVIIXIX.∑ix1∑≠1ixpIII∑=1ixpxi∑1ixp∑1ix135-104)DEWTpy1y2···yNTx1x2···xN5-11145-115.3.35-20iisiixppyγ=i=1,2N5-161ˆ=viφ1=siφ5.3.2p1p2py1111xppypisiγ==5-2122222xppypsγ==5-2222211121xpxppppssγγ+=+=5-23152221111111xpxpxpysssγγγ+=5-24α2121//xxyy=α5-25y1+y2=1x1+x2=1()11111xxy−+=αα5-265.3.1y-x5-26αα5-215-252211γγαsspp=5-27αTxiαxiαα5-265.3.4K5.3.4.1KKKiiixyK=5-28K165-115-13viliiiixyKφφˆˆ==5-29()visiliisisiiiipRTppVpxyKφγφˆexp⎥⎦⎤⎢⎣⎡−==5-305-16~5-19KiTpyixi5-135-11iiixKy=5-315-31K5.3.4.2KK1=iγLewis-Randalliviφφ=ˆisisiiiippxyKφφ==5-32KTpyixiKTp-De-Priesterp-T-KK5-32p-T-K5-125-13atm17KKTpyixiyixiTpKi5-12776kPa27.4atmCH4C2H6C3H6C3H8-C4H10-C4H100.050.350.150.200.100.151.00xiCH4C2H6C3H6C3H8-C4H10-C4H10xi0.050.350.150.200.100.151.00Ki6.01.30.470.430.200.381-24yi0.300.4550.07050.0860.020.02070.952Ki6.21.370.510.450.2120.147-26yi0.3060.4800.07650.0900.02120.02200.996yi0.3070.4820.07680.09040.02130.02211.0005.3.4.3p-T-KKii=1,2…6xiyii=1,2…6∑iy=1end≠1tp=27.4atmt5-12p-T-K5-13p-T-K18Kz1z2…zNTpy1y2···yNx1x2···xN5-14FVLe=V/Fl=L/F1=+leLVF+=5-33iiiLxVyFz+=i=1,2N5-34iiixKy=i=1,2N5-35()11+−=iiiKezxi=1,2N5-36()11+−=iiiiKezKyi=1,2N5-37yixi∑=1iy∑=1ixKip-T-Kzi1)Tplyixip-T-KKii=1,2…N(5-43)xii=1,2…N∑ix=1≠1lpTziliiixKy=∑iyi=1,2…Nlyixi5-14192)Tlpyixi3)plTyixi5-2(1)(2)0.30.73445.05kPa115l=80%T=388.15Kp=3445.05kPaKiK1=1.45K2=0.845-432752.01=x7231.02=x∑=9983.0ix∑1ixl=68%2622.01=x7377.02=x∑=9999.0ix68%3802.01=y6198.02=y5.4MPap-T-KKii=1,2…N(5-43)xii=1,2…N∑ix=1≠1TTiiixKy=∑iyi=1,2…NTyixiplzip-T-KKii=1,2…N(5-43)xii=1,2…N∑ix=1≠1ppiiixKy=∑iyi=1,2…NpyixiTlzi205.4.1F=25.4.1.1p-x-yT-x-y5-15(a)(b)p-x-yT-x-yp-x-ypc2pc1Tc2Tc1I.ppc2pc2II.pc2ppc122212III.ppc1(a)TaTc2TbTc1Td(b)papc2pbpc1pd5-15p-x-yT-x-y21p-x-yT-x-y5-16y-xp4p5pc2y-xp2p3pc22p1pc11y-x5.4.1.2p-T5-17p-Tx2=1KC2C22LC1C11z1z2z35-17p-T5-16y-xp5p4pc2p3p2pc1p122z=xz=yABCBp0T0z3z3z2z2p0T0z3z2p-TABC5-17C1C2z1C1C25.4.1.3CC5-17z15-18CFCE1GMGMJJMJMMJ5-182312CJFMC3DLDLKKLKLLK32EKCLEC100MPaMPa-5-181-2JJ5.4.25-45.2.1EOS5-11K5.4.2.1EOSiliivixyφφˆˆ=i=1,2N245-114.5.4ZdVnpVRTRTVnVTiijln1ˆln,,−⎥⎥⎦⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛∂∂−⎟⎠⎞⎜⎝⎛=∫∞φ4-895-11SRKPRBWR4-89iφˆ()illixVTpf,,,ˆln=φi=1,2N()ivviyVTpf,,,ˆln=φi=1,2NliφˆliVxiviφˆviVyi5.4.2.2KKiiixKy=5-31K5.3.4.2Kviivipyfφˆˆ=iililixffγ=ˆ5-4viiliiiipfKxyφγˆ==i=1,2N5-3225lilipfφ=5-32viiliiiiKxyφγφˆ==i=1,2N5-33liφiTpviφˆiiγiliφviφˆRKiγK1961ChaoSeaderChao-Seader5.5TpxyTpxyTpxyGibbs-DuhemGibbs-DuhempRTVTRTHxxEEddlndlnd22211−=+γγ5475.5.11.RTVE0lndlnd2211=+γγxx548Herington19471x=01x=1548∫∫====[phone]lndlndxxxxxxγγ[]∫∫======−−=1011210221111110dlndlndlnxxxxxxxγγγγ55055021lnγγ~1x26()()()()100---×+++=D2D2.∫∫=====102101121111ddlnxxExxTRTHxγγ552HeringtonDminminmax150TTTJ−×=maxTminT()10−JD5.5.21959vanNess1γ2γ2211lnlnγγxxRTGE+=553RTGERTGE~1x5201x=11x=0()12d/dxRTGxRTGaEE+=554a()11d/dxRTGxRTGbEE−=554b5531x554βγ21lnxa+=557aβγ12lnxb−=557b271ddxpRTVE⎟⎟⎠⎞⎜⎜⎝⎛=β12ddxTRTHE⎟⎟⎠⎞⎜⎜⎝⎛−=β557ababRTGE~1xvanNess21xRTxGE~1xRTGE~1x21xRTxGE~1x5.6TQTQSsurrsurrsurrddd−==558surrSsurrQddQsurrTT280ddd≤−+tttSTVpU561561561()0d,≤ttVStU562()0d,≥ttVUtS563561()0d,≤−+pTtttTSpVU564()0d,≤pTtG565565TpGibbsTpGibbs()0d,=pTtG566565TpGibb