Review P i - University of California, San Diegoruben.ucsd.edu/20/r08.pdf · Henry’s Law (gas in...
32
Review • The chemical poten1al of component J: – Gas – Liquid mixture – ΔG and entropy of mixing. • The chemical equilibrium – K via concentra1ons and reac1on stoichiometry – From K, to ΔG o – From K at T 1 and T 2 , to ΔH o and ΔS o , Van’t Hoff ln K = − Δ r G o RT ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − Δ − = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 2 1 2 1 1 1 ln T T R H K K o 0 ln 0 c c RT i c i i + = μ μ ] ][ [ ] [ . . , 1 B A B A K g e a K n i i i • = = ∏ = ν μ i g = μ i P 0 + RT ln P i P 0 a i below may also be molar frac1on x i or concentra1on c i depending on the standard state and ideality R S RT H K o r o r Δ + Δ − = ln
Transcript of Review P i - University of California, San Diegoruben.ucsd.edu/20/r08.pdf · Henry’s Law (gas in...
Review• Thechemicalpoten1alofcomponentJ:– Gas– Liquidmixture– ΔGandentropyofmixing.
• Thechemicalequilibrium– Kviaconcentra1onsandreac1onstoichiometry
– FromK,toΔGo
– FromKatT1andT2,toΔHoandΔSo,Van’tHoff lnK = −
ΔrGo
RT
⎟⎟⎠
⎞⎜⎜⎝
⎛−
Δ−=⎟⎟
⎠
⎞⎜⎜⎝
⎛
212
1 11lnTTR
HKK o
0
ln0
ccRT ic
ii += µµ
]][[][..,
1 BABAKgeaK
n
iii
•==∏
=
ν
µig = µi
P0 + RT ln PiP0
aibelowmayalsobemolarfrac1onxiorconcentra1oncidependingonthestandardstateandideality
RS
RTHK
or
or Δ
+Δ
−=ln
Gas-Solu1onEquilibriumforEachSolu1onIngredient
• imaybewaterordrug
• xi-Solute(orsolvent)molarfrac1on
• *-pure(saturated)ingredient
µi,liq = µi,vap ; µi,liq* = µi,vap
*
µi,liq* + RT ln ci
ci*
⎛
⎝⎜
⎞
⎠⎟= µi,vap
* + RT ln pipi*
⎛
⎝⎜
⎞
⎠⎟
RT ln cici*
⎛
⎝⎜
⎞
⎠⎟= RT ln
pipi*
⎛
⎝⎜
⎞
⎠⎟
cici*
⎛
⎝⎜
⎞
⎠⎟i
=pipi*
⎛
⎝⎜
⎞
⎠⎟
Raoult’sLaw
• Solvent(egwater)pressurevsmolarfrac1onofnon-vola+lesolute
• Vaporpressureofasolu1onisdecreasedasthesoluteconcentra1onisincreased
• P*water=0.23barat20oC(100C?)
P = xw P*w= (1- xsolute) P*
w
P*w-P=ΔP = xsolute P*
w
FrenchphysicistFrançois-MarieRaoult
• Waterpressurewillbelowerasyouaddsalt• Saltywaterwillboilathighertemperature
xwi ≡ nwi / ntotal
w = pgi / pi*g pure i iswater
Henry’sLaw(gasinsolvent)• Gasdissolvesinliquidpropor1onallyto
itspressure.Example:Oxygeninblood
• HereKisanempiricalconstant,slopeofthetangenttotheexperimentalcurve.
• Pi=xiP0-Dalton’slaw
Pi,gas = xi,sol⋅KxH
Henry’s Law
Raoult’s Law for xsolvent→1 Henry’s Law for xsolute→0 Mixtures that obey
and are called ideal-dilute solutions.
xliqi = pgi / pi
*g pure i isgascomponent(egoxygen)
AirPressurevsO2inBlood• oxygen(O2):KH=769.2L·atm/mol• carbondioxide(CO2):KH=29.4L·atm/mol• hydrogen(H2):KH=1282.1L·atm/mol
8,848m(M.Everest)4,421m(M.Whitney)
Temp(C)P(kPa) P(mmHg) 0 0.6 4.5 3 0.8 6.0 5 0.9 6.8 8 1.1 8.3 10 1.2 9.0 12 1.4 10.5 14 1.6 12.0 16 1.8 13.5 18 2.1 15.8 19 2.2 16.5 20 2.3 17.5 21 2.5 18.7 22 2.6 19.8 23 2.8 21.1 24 3.0 22.4 25 3.2 23.8 26 3.4 25.2 27 3.6 26.7 28 3.8 28.4 29 4.0 30.0 30 4.2 31.5 32 4.8 36.0 35 5.6 42.0 40 7.4 55.5 50 12.3 92.3 60 19.9 149.3 70 31.2 234.1 80 47.3 354.9 90 70.1 525.9 100 101.3 760.0
WaterpressurevsT
Ph=P0•e-Mgh/RT
Classifica:onofMembranes
Permeable impermeable semi-permeableCellularplasmamembraneissemi-permeable
Osmosis• Thebiologicalmembraneisnotpermeableforelectrolytes
Osmosis• Differen1allypermeablemembrane• Osmo:cpressureisthehydrosta1cpressureproducedbyasolu1oninaspacedividedbyadifferen1allypermeablemembraneduetoadifferen1alintheconcentra1onsofwater(orothersolute).
Osmo1cPressure
• Colliga+veproperty.Osmo1cpressuredependsonthenumberofsolutemolecules,notontheiriden1ty
• Waterflowstotheareawheretherearemorenon-watermolecules
• Osmo1cpressurelookslikethegaslawformula,wherenisthetotalnumberofmolesofthesolutepar1cles
• ForV=1L,Δn/VbecomesΔM
• Posm=ΔP=Phigher-Plower PosmV = ΔnsoluteRTPosm = ΔMsoluteRT
Higherpressure:lowerpressure
P1V = n1,soluteRTminusP2V = n2,soluteRT
Derivingvan’tHoff’sequa1onforOsmo1cPressure
• DecreaseinFreeenergyinthe“polluted”chamberiscompensatedbyextraworkPosmV.V=1L=10-3m3
atT=36oC• Mismolarity(molarconcentra1on),notmass!• ThetotalMcanbecalculatedviavan’tHoff’s
factors,i,i.e.M →i�M
GP =GP0+VΔP
PosmV = −nwRT ln xw= −nwRT ln(1− xstuff ) ≈ nwRTxstuff
Posm = (nstuff /V )RT = ΔMRTPosm[bar]= ΔMRT ≈ 25.7ΔM[bar]
Van’tHofffactor,i• Thenumberofmolesofpar1clespermoleofsoluteisthevan'tHofffactor,i.
• HowmanymolesofALLDERIVATIVEFORMSareinsolu:onuponadding1moleofsolidsolute?
• E.g.NaClresultsinNa+andCl-,x1=0, x2=1 i=2• Examplewithpar1aldissolu1on:
– 50%undissociated,30%in2par1cles,20%in3par1cles:i = 0.5 + 2*0.3 + 3*0.2 = 1.7; P=25.7*i*M [bar]
€
i = x1 + 2x2 + 3x3 + ..
Posm=ΔM RT i
Examples• Theobservedlowervan’tHofffactorsillustratethedifferencesbetweenac1vi1esandconcentra1ons.Ionsarenotfullyindependentoneachother.
Tonicity
Isotonic,Hypotonic,Hypertonicenvironments(plantcells)
Normal Turgid Plasmolysis
MolarityvsMolality
• Molarity M≡ n/literofsolu+on• Molefrac1on x≡ n/Σni• Molality m≡ n/kgofsolvent
1molalsolu1on:1moleofsoluteper1kgofsolvent
x=nsolute/nwater=Msolute/55.5Oneliterofwatercontains55.5Molesofwatermolecules.
Tonicityofintravenousfluids• Osmolality: total soluteconcentra1on inafluid
compartment.• Tonicity: the combined ability of solutes to
produce a osmo1c driving force that causeswater to move from one compartment toanother.– Solutes that are capable of moving water are
called“effec1veosmoles”.– These are solutes that are unable to cross from
the ex t race l lu la r to the in t race l lu la rcompartment: sodium, glucose, mannitol,sorbitol.
– Thecontroloftonicitywilldeterminethenormalstateofcellularhydra1onandcellsize.Thisisofpar1cularconcerninthecaseofbraincells.
• Pharmaceu1callabelingregula1onsmayrequireastatementontonicity.
Non-polarmoleculescrossmembranes:oxygen,carbondioxide,ethanolWater,ureausesomeassistance
Fas1ngglucose:4.4to6.1mmol/L(79.2to110mg/dL)Urea:~3to7mmol/L
Examples
• Osmolali1esofsomeintravenousfluids
• Hightonicityofenteralfeedingofprematureinfantshasbeenimplicatedinnecro1singenterocoli1s(NEC)
WhatOsmolarityisNormal?• Osmolarityofplasmais285-295milli-osmoles/L• I.V.:anyfluid>550mOsm/Lshouldnotbeinfusedrapidly• Thehigherthetonicity,thelowershouldbetherateofinfusion.
• CalculatedosmolarityinmMunits=2[Na+]+(2[K+])+[Glucose]+[Urea]+[Ethanol](allinmmol/L) (glucoseMM=180g/mol:3.5–6.5mmol/L)
• Alterna1veformulawith[Conc]inmg/dL(correctedbyMM):2[Na+]+[Glucose]/18+[BUN]/2.8+[Ethanol]/3.7– BUNmeansBloodUreaNitrogen:6to20mgofureaper100mlofblood(6–20mg/dL,2to7mmol/L)
– Na+~11g/mol;glucoseMM=180g/mol
Howtomeasureosmolari1es?
• Osmolari1esofIVororalmedica1onscanbemeasuredbyfreezingpointdepression
• Why?
BoilingandFreezingPoints
• Addingsolutemakestheliquidstatemoredesirablebecauseoftheentropyincreasesandthechemicalpoten1albecomeslower.Ifxwisequalto1inpurewater:
€
Δµwater = RT ln(1− xsolutes) ≈ −RTxsolutesΔSwater _ in _ solution = Rxsolutes
€
µw = µwpure + RT ln xw
Boilingpointeleva1onofasolu1on
• Asolu1onexhibitsahigherboilingtemperaturethanthatofpuresolvent
ΔTboiling=Kbx
Pure solvent: xw = 1, boiling temperature T*
0=Δ−Δ ∗ STH vapvap
Solute added: xw < 1, boiling temperature T
€
Δ vapH −T(Δ vapS + Rxsolute ) = 0
€
ΔT⋅ Δ vapS = ΔT⋅ Δ vapH /T = TRxsolute
ΔT = T −T∗ ≈ xsoluteRT∗2
Δ vapH
'
( ) )
*
+ , ,
Pure solvent: xw = 1, freezing temperature T*
Solute added: xw < 1, freezing temperature T
Freezingpointdepressionofasolu1on
• Asolu1onexhibitsalowerfreezingtemperaturethanthatofpuresolvent
ΔTfreezing=Kfx
€
ΔT = T −T∗ ≈ xsoluteRT∗2
Δ fusH
&
' ( (
)
* + + €
Δ fusH −T∗Δ fusS = 0
€
Δ fusH −T(Δ fusS + Rxsolute )
Review• Chemicalpoten1alofthesamemoleculein
differentphasesorcompartments(osmosis)mustbeequal
• Chemicalpoten1alofwaterislower(beyer)insolu1onIfxsolutesissmall:
• Osmo1cpressure:Posm=ΔMRT,whereΔMismolaritydifferencecorrectedbydissocia1on,i,ΔM=iΔM0
• Osmosis:semipermeablemembranes.• OsmolarityandTonicity:coun1ngsolutes
thatcannotcrossthemembraneandtakingdissocia1onintoaccount(i,van’tHoff’sfactor).
• Boilingpointeleva1on• Freezingpointdepression(Kfdoesnotdepend
onsolutes!).Kf=1.858Kkg/mol• Waterpressurereduc1on:Raoult’slaw• Gasdissolu1oninwater:Henry’slaw• Theeffectsareentropicandtothefirst
approxima1ondonotdependonthenatureofsolutes(colliga1veproper1es)
€
µw _ in _ solution = µw _ pure + RT ln(xw )Δµw = RT ln(1− xsolutes) ≈ −RTxsolutesΔSw ≈ Rxsolutes
Posm =ΔnsolV
RT = iΔMRT
ΔTboiling = KbxsolutesΔTfreezing = K f xsolutesPw_ vap_ solution = Pw_ vap_ purexwaterPsolute_ in_ gas = KHenry
solutexsolute_ in_water
Osmo1cPumpsforDrugDelivery
Semi-permeable
OROS(Osmo1c[Controlled]ReleaseOral[Delivery]System)isacontrolledreleaseoraldrugdeliverysystemintheformofatablet.Thetablethasarigidwater-permeablejacketwithoneormorelaserdrilledsmallholes.Asthetabletpassesthroughthebody,theosmo1cpressureofwaterenteringthetabletpushestheac1vedrugthroughtheopeninginthetablet.
Name(Genericname)Acutrim(phenylpropanolamine)AdalatOROS(nifedipine)AlpressLP(prazosin)CarduraXL(doxazosin)Concerta(methylphenidate)CoveraHS(verapamil)DitropanXL/LyrinelXL(oxybutynin)DynacircCR(isradipine)Efidac24(pseudoephedrine,..)Exalgo/Jurnista(hydromorphone)GlucotrolXL(glipizide)Invega(paliperidone)MinipressXL(prazosin)ProcardiaXL(nifedipine)Sudafed24(pseudoephedrine)TegretolXR(carbamazepine)Volmax(salbutamol)
SomeProblems:§ P~25atm•ΔM§ Subjecttodose
dumpingifmembranebreakse.g.someonechewsit
§ Slightlymoreexpensivetoformulatethancoa1ngtablets
§ Possibleholeplugging
Asimplemodelofapa1ent
• TwoCompartmentModel– Intracellular=Cytoplasmic(insidecells)
– Extracellular(outsidecells)ECFICF
TotalBodyWater=WEIGHTx0.5(women)or0.6(men)
Homeostasis
• Defini:on:Processesbywhichbodilyequilibriumismaintainedconstant.
• ExamplesofBodilyhomeostasis:• temperature• bloodpressure• heartrate• bloodglucoselevel• bodyfluidcomposi1on• Osmolarity• Extracellularfluid(ECF)volume• Acid-Basebalance
Osmo1cpressureofdrugsolu1onsFreezingPointdepression
• Reminder:theosmolarityofserumis~290mOsm/L(notlowerthan210).
• Dominatedby[Na+]andtheassociatedanions.~2*[Na]
• IsotonicosmolaritytranslatesintoΔTf_depr=0.52o.
• IfweknowtheΔTf_deprforthedesireddrugconcentra1on,onecanaddNaCltomatchΔTf_deprtomakethesolu1onisotonicwithblood(ormakenetosmolarityequalto290mOsm/L
Distribu1onofSolutesinthreefluids
K+incells
Cells
Noalbumininlympth
Na+influids
PlasmavsLymph:Edema• Edemaisdefinedasso~1ssueswelling
duetoexpansionoftheinters11alvolume.Edemacanbelocalizedorgeneralized.
• Someextracellularfluidcompartments,a.k.a.transcellularfluids(cerebrospinalfluid,intraocularfluidandjointfluid)donotcommunicatefreelywiththerestofthebody.
Waterflow
Albumin+bloodproteins
LessProtein
Cells
Mechanismsmaintaininginters11alfluidvolume
• PlasmavsLympth,theroleofalbumin:70%ofPoncisduetoalbumin.Albuminsize:~10nM(100Å)
• Onco1cpressureisaformofosmo+cpressurecreatedbyplasmaproteinmoleculesthatareimpermeableacrossthecapillarymembrane.
• Starling'sLaw:Hydrostatic Pressure-Oncotic pressure = net fluid movementoutofcapillaryintointers11um.
• P=120mmHgsystolicpressure(+Patm).Thesmallestpressureincapillaries~20mmHg
60-80nm• endocrineglands• intes1nes• pancreas• glomeruliofkidney
30-40μmAllowcellstopass• Bonemarrow• Lymphnodes• Adrenalglands
• <10nM• Regularcapillaries• CNS(1ghter)
HumanSerumAlbumin&Drugs• HSAmaintainsosmo1c/onco1cpressure• C=35-50g/L=3.5-5.0g/dL=0.5-0.75mM• Transportsmanydrugs• Transportsthyroidhormones,T3andT4• Transportsotherhormones,par1cularlyfatsolubleones
• Transportsfayyacids("free"fayyacids)totheliver
• Transportsunconjugatedbilirubin(hemecatabolism,yellowbruisesandbrownfeces)
• Compe11velybindscalciumions(Ca2+)• BufferspH
RenaltoxinCMPFindrugsite1StephenCurry
AlbumincarriesBilirubinfromdestroyedhemesinthespleentoliver
15-20%ofT3andT4->HSA(majoritybyTBG)[]
31
Albuminandotherdrugbindingproteins
• HSAMW67kDa,609aminoacids• Halflife20days(drughalflife
extension)• Likestobinddrugswithcarboxyls
and/orhydrophobicareas• Otherproteinsbindingdrugs
– Lipoprotein– Glycoprotein– α,ß‚andγglobulins.
• Theboundpor1onmayactasareservoirordepotfromwhichthedrugisslowlyreleasedinfreeform.
Hypoalbuminemia• Liverdisease(egcirrhosis)• Excessexcre1onbythekidneys• Excesslossinbowel(e.g.,Ménétrier's
disease)• WoundsandBurns(plasmaloss)• Increasedvascularpermeability• Acutediseasestates(‘nega1veprot.’)• Muta1onscausinganalbuminemia• Malnutri:on(starva1on)
HSAloadedwithmul1pleligands
