FreeEnergyandStateEquilibria

Gibbs Free Energy (G)

G=H-TS G1 = G2 G→minimum

Objec5ves:•  understandaerosoldispensers•  boilingcondi5ons•  drugcrystalsandcrystaltransi5ons•  mixturesandchemicalpoten5al

Phasesandphasetransi5onsofdrugsubstances

Smole=kBln(Ntotal_nof_states)=Rln(nstates_of_one_molecule)ΔS= nR ln(n1/n2)

PhaseEquilibria•  Tradingenthalpyforentropy•  Theentropiccontribu5on–TSgainsmagnitudewithtemperature.

•  Thetemperatureatwhich

G1=G2,thephasesareinequilibrium,e.g.

0=Δ−Δ

−=−

STHTSHTSH

trstrs

ggll

Clapeyron Equation

dPdT

=Sα − SβVα −Vβ

=ΔStrsΔVtrs

EntropyandPhaseChanges

•  Considerasystemanditssurroundingsatnormaltransi2ontemperatureTtrs

•  Thesystemisinequilibrium⇒anyheattransferisreversible.

•  Entropychange:

Increase in entropy

Increase in entropy

€

Δ trsS =Δ trsHTtrs

trs1 trs2

Ttrs =ΔtrsHΔtrsS

DispensingDrugsasAerosolsforAsthma,COPD,etc.

ThefirstaerosolspraycanpatentwasgrantedinOslo,Norwayin1926toErikRotheim

SalbutamolandBeclometasone:asthmaandallergicrhini5sIpratropiumbromide:COPDoracuteasthmaTolna6ate:forjockitch,athlete'sfootandringworm.Cromoglicicacid:nasalspray,non-steroid,leukotrieneRagonistNedocromil:alsoamastcellstabilizer

metered-doseinhalers

Propellants:FromChlorofluorocarbons(banned)toHydrofluoroalkanes(HFA)

Howdotheywork?HowdoestheoutsidetemperatureaffectitsfuncHon?

(nor)EpinephrineSalbutamolβ2adrenergicreceptoragonist

USAdultswithasthma:18.9million(8.2%)

BoilingLiquidtoGas

•  Bubblescontainsolventingasstate,pressuregrowswithT

•  Whenvaporinbubblesreachesexternalpressure(atmospheric)solventboils.

•  Boilingpointislowerathighal5tudesorlowerpressure.

Pexternal = Pvapor (depends on T)

WaterVaporPressure•  Isonly0.03atm@25degC.•  Reaches1atm@100degC.• 

Pb(Tb)Clausius-Clapeyron

€

ln P2P1

"

# $

%

& ' = −

ΔHvap

R1T2−1T1

"

# $

%

& '

ΔHvap = TΔSvap ≈ −TR ln(Pvap )ln(P) = −ΔHvap / RT

Trouton’srule,BoilingTemperature

•  Liquidssubstancesboilatverydifferenttemperatures

•  ΔH~TB

€

Δ vapS =Δ vapHTBoiling

≈ const

Benzene +30.8 80.1 +87.2 carbon tetrachloride +30. 0 76.7 +85.8 cyclohexane +30.1 80.7 +85.1 hydrogen sulphide +18.7 -60.4 +87.9 methane +8.18 -161.5 +73.2 water +40.7 100.0 +109.1

ΔvapH0BoilingpointoCΔvapS0[J/(molK)]

Trouton’sobserva5on:ΔvapS0iscloseforawiderangeofsubstancesandTvap.Thereforefromaboilingtemperaturewecanes5mateenthalpyloss:ΔvapH0

BoilingT

FrederickThomasTrouton,Physicist,1963-1922

0=Δ−Δ

−=−

STHTSHTSH

trstrs

ggll

Excep5onsfromTrouton’srule

•  Thevaporiza5onentropyranges–  from73J/(Kmol)(CH4)–  to109J/(Kmol)forwater–  normallyΔS=85-89J/(Kmol)or10.5R

•  Waterismoreorderedthanotherliquidsbecauseofthehydrogenbondingstructure

•  Methaneisunusuallyround

Waterismoreorderedthanotherliquids

Therela5veincreaseinanumberofstatespermoleculeingas:

ΔvapS ≈ 4.5R+ R lnT ≈10.5R

ΔvapS = R lnngnl

#

$%

&

'(

lna− lnb = ln(a / b)ln(ng / nl ) =10.5

ng / nl = e10.5 ≈ 36,500 ~ 30•1200

Halothanevapor

•  Halothanevapor(akaFluothane)isaninhala5onalgeneralanaesthe5c(mixedwithO2)

•  Itboilsat50C(s5llaboveroomtemperaturebutenoughforhighconcentra5on)

•  @20CP=244mmHg(~0.3atm)•  Q:ishalothaneagoodpropellant?

DrugDelivery:Aerosols•  Gas is thevaporsofa liquidwithboiling

po int s l ight ly lower than roomtemperature. Thismeans that inside thepressurized can, the vapor can exist inequilibrium with its bulk liquid. As gasescapes it is immediately replaced bymore evapora5ng liquid. Since thepropellant exists in liquid form it isdesirable that it be miscible with ordissolvedinthedrug

•  Medicinalaerosolssuchasasthmainhalersusehydrofluoroalkanes(HFA),food:nitrousoxide(whippedcream).

BoilingT

AerosolPropellants•  Heavypropellants:Deathof21oldArinRugefromaerosol(“Huffing”fromcompressedair)

•  Temperature-sensi5vity–  ToostrongathighT,stopsatlow

Propellants:FromChlorofluorocarbons(bannedduetoozonedepleHon)toHydrofluoroalkanes(HFA)

Tb=8.92°C-26.3°C

TetrafluoromethaneTb=-127.8°C

PhaseTransi5onsinPureSubstances

•  Phaseboundaries–coexistencecurves(twophasescoexist)

•  Triplepoint–3phasescoexist

•  Beyondcri2calpoint,liquidandgasarefusedtoformsupercri2calfluid

•  Solid,Liquid,Gas•  Phases–notonlysolid/liquid/gas,butalsoallotropes,•  Usually,atgivenP,Tonlyonephaseofpuresubstanceis

thermodynamicallystable

water

CrystalsandAllotropes

Graphite Diamond Theenthalpyandentropyofforma5onofallotropes

H,kcal/molS,cal/molK

Graphite0.001.36Diamond0.450.58But:Graphiteislighter

•  Whichformis“forever”?

Crystals

•  MostDrugsinthetabletformaremicrocrystals

•  Crystalsnaturallypurifythedrugfromthemixture

•  Manydrugsorcontrastagentsexcretedintheurinehavethepoten5altoformcrystals.Highconcentra5onanddifferentpHmaybefactors

Crystal-Methmethamphetamine

Purifica5onandslowdeliveryofinsulin

•  Oneofthemostimportanthumanproteintherapeu5cagentisinsulin.

•  Roleofcrystalsforproteins– 3Dstructuredetermina5on– Purifica5onmethod– Slowdelivery(dependsonacrystalform.3formswithdifferentrateofrelease) Insulincrystals

Thekine5csdependsonthesizethetypeofcrystals

TypicalPhaseDiagrams:CarbonDioxide

•  Basicfacts,CO2:0.039%•  DryIce:Cooling(leavesnotrace)•  Blood:

–  70%to80%isconvertedtobicarbonateionsHCO−3bycarbonicanhydraseintheredbloodcells

–  CO2+H2O→H2CO3→H++HCO−3.

–  ~10%dissolvedintheplasma–  ~10%isboundtohemoglobin

•  Solid-liquidboundaryhasaposi2veslope,asformostsubstances

•  Thetriplepoint:P=5bar>1atm⇒–  liquidCO2doesnotexistat1atm⇒

“dryice”–  Phasetransi5on:sublima2on

CarbonMonoxide

•  HemoglobincanexchangeO2andCO2•  CarbonMonoxidebindsTOOTIGHTLYtohemoglobin

17

ImportantPhaseDiagrams:Water•  Waterismoredensethaniceat00C,

•  Tetrahedralarrangementinice

Deriva5on.Vaporpressuresatvarioustemperatures

•  Alongacoexistencecurve:Gα(T,P)=Gβ(T,P)

Gα(T+dT,P+dP)=Gβ(T+dT,P+dP)dGα=dGβ

Vα,⋅dP–Sα,⋅dT=Vβ⋅dP–Sβ⋅dT

•  whichrearrangesto:

Clapeyron Equation

dPdT

=Sα − SβVα −Vβ

=ΔStrsΔVtrs

Theexactslopeofphaseboundaryforanyphaseequilibriumofanypuresubstance!

Note:waterP373K=1atm

α

β

Fromthe1stLawanddefofG,q:dG=V⋅dP–S⋅dT

dGgas

dGliquid

Appendix.Deriva5on

VaporPressurevsTemperatureAnalterna5veformofClausius-Clapeyroneq:where• T1andP1areacorrespondingabsolutetemperatureandvaporpressure,samefortheT2andP2pressure• ΔHvapisthemolarenthalpyofvaporiza5on

€

ln P2P1

"

# $

%

& ' = −

ΔHvap

R1T2−1T1

"

# $

%

& '

dPdT

=ΔStrsΔVtrs

=ΔHtrs

TΔVtrs≈ΔHtrs

TVgas=

ΔHtrs

T RTP

#

$%

&

'(

dPP=ΔHtrs

RT 2 ; ln(P) 21 = −ΔHtrs

R1T#

$%

&

'( 21

ln P2P1

#

$%

&

'(= −

ΔHvap

R1T2−1T1

#

$%

&

'(

dGgas

Deriva5on:TheGaslawfor1mole:

12

Appendix

Mixtures,Equilibrium&ChemicalPoten5alµ

Singlecompartment•  TotalG->minumum

equlibrium

Twocompartments• Chemicalpoten5alµΑofeachcomponentisequalinbothcompartmentsinequilibrium

A(gas)

A(liquid)

•  SoluHons•  Suspensions•  Colloids(milk,

nanopar5cles,colloidalsilver,sulphur,gold)

ChemicalPotenHalµ•  G = H-TSisanextensivevariable•  ForapuresubstanceJthechemicalpoten5al is

defined asmolarGibbs energy: µJ≡Gm= G/n

•  ChemicalPoten7alis molarFreeEnergyof a par7cular chemical ingredient in amixture

•  Inamixtureofn1,n2,..,nJ

JinTpJJ n

G

≠

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂=

,,

µ