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