outline of the course - chemistry at uoft 6 fall 2010.pdf · outline of the course 1) review and...

Outline of the Course

1) Review and Definitions

2) Molecules and their Energies

3) 1st Law of Thermodynamics

4) 2nd Law of Thermodynamics

5) Gibbs Free Energy

6) Phase Diagrams and REAL Phenomena

7) Non-Electrolyte Solutions

8) Chemical Equilibrium

9) Kinetics

Phase Diagrams and Real Phenomena :Bringing It All Together

PHYSICAL CHEMISTRYApply toolbox of conceptsand functions (H, S, G) toproblems in pharmaceutical science.

Section 6.0. Phase Diagrams and Real Phenomena

6.1. Phase Diagrams

6.2. Sample Applications of Thermodynamics/Phase Diagramsin Pharmaceutical Science

Section 6.1. Phase Diagrams

Goals

(1) To understand phase equilibria and phase diagrams

(2) To review phase diagrams of water and CO2 (as examples)

(3) To review the dependence of G on pressure and temperature

Phase Equilibria and Phase Diagrams

Phase diagram = map of the pressures and temperaturesat which each phase of a substance is the most stable

Examples of phase transitions(with no change in chemical composition):

Melting, Vaporization and conversion of diamond to graphite

In our discussion we will consider pure substances:

so remember G =

- the spontaneous direction of change will always betowards decreasing G ……..thus decreasing

A phase = a form of matter that is completely uniform in termsof both chemical composition and physical state.

Examples: liquid, gas, solid (and for solids there are often various states; e.g. for carbon: graphite and diamond)

A phase transition: spontaneous change of one phase to anotheroccurs at a particular T for a given P

Consider H2O:

ICE Water

At 1 atm, below O°C ice is most stable form of H2O above O°C water becomes most stable form.

T O° C ice water

T O° C water ice

Transition temperature is the temperature at which the two phasesare in equilibrium.( phase 1 = phase 2 )

• phase with lowest chemical potential is themost stable at a particulartemperature

Figure taken from Physical Chemistry by Peter Atkins 6th Edition

Be careful just because a specific state of a substance is knownto be most stable (lowest chemical potential) at a specific T and Pdoesn’t mean substance will exist in this state……..

relationship between thermodynamics and kinetics

For example, at normal temperature and pressure C(graphite) has a lower chemical potential than C(diamond)………..

but the transition from C (diamond) to C (graphite) takesa very very very long time at room temperature……………

We can say there is a “thermodynamic tendency for diamond tochange into graphite” but this process is very slow.


Why is the transition from C (diamond) to C (graphite) so slow ?

…..because the mobility of molecules or atoms in the solid stateis limited (except at higher temperatures).

The rate at which equilibrium is achieved is a KINETIC problem.

• in gases and liquids the mobility of molecules allows transitions tooccur rapidly

• in solids thermodynamically unstable phases may be “frozen in”these are referred to as metastable phases

e.g. Diamond is a metastable phase of carbon.

Phase Diagrams provide a summary of the thermodynamicallystable phases at specific pressures and temperatures.


• lines separating thephases are called phaseboundaries

• the phase boundariesindicate the P and Tunder which phases

coexist in equilibrium

• T3 is the triple pointat which the three phases co-exist inequilibrium

T3 Tc

Vapour Pressure

The vapour pressure of asubstance is the vapourthat is in equilibrium witha liquid or solid

Closed Vial


Liquid – vapour phase boundaryshows how vapour pressure of the liquid varies with Temperature

Solid – vapour phase boundaryshows how sublimation vapourpressure varies with Temperature(vapour pressure of solid phase)

Vapour pressure increases with T T population of molecules in state of higher energy (i.e. state where molecules have

escaped nearest neighbors)

Consider a liquid in an open container…………..

• when the liquid is heated it vaporizesfrom its surface

• vaporization throughout entire liquidoccurs when vapour pressure is equal to external pressure (then vapourcan expand freely into the surroundings)…………this is called BOILING

Boiling Temperature = temperature at whichthe vapour pressure of a liquid is equal tothe external pressure

When a liquid is heated in aclosed vessel boiling cannot occur

………..instead the vapourpressure and density of vapourincrease…….

Consider a liquid in a closed container…………..

Consider a Closed System………

A B C

A – liquid in equilibrium with itsvapour

B - as we heat the liquid in the sealed container……..the density of the vapour phase increases and the density of the liquiddecreases

C – at a specific point the densityof the vapour = density of the liquid

Temperature when the interfacebetween the two phases disappears……is termedthe Critical Point (TC).

T3 Tc

Tc = Critical Temperature

• at the TC and above wehave a single uniformphase called a

Supercritical Fluid

• above the TC the liquidphase does not exist

What is the difference between the normal and the standard boiling point ?

• boiling temperature is the temperature at which the vapourpressure of a liquid is equal to the external pressure

At a pressure of 1 atm the boiling temperature is called the Normal Boiling Point

At a pressure of 1 bar the boiling temperature is called the Standard Boiling Point

(the same convention is used for freezing point i.e. normal vs. standard freezing point)

Let’s Consider a Few Phase Diagrams as Examples……

Phase Diagram of Water• normal boiling pt. of

water isat 373.15 K (and 1 atm)

• normal freezing pt. ofwater is at 273.15 K

• T3 is at 273.16 K and 0.006 atm

• Note: negative slope of S-L phase boundary

- as you P the Tm -- ice has a very open structure …..higher volume than liquid form

(i.e. the liquid is more dense than the solid)

• at higher pressures there are differentstable structural forms of ice…..

Ice I, Ice II, Ice III etc…

• there are actually five other triple pointsin the diagram (besides the one for ice I,vapour and liquid)

More Detailed Phase Diagram for Water

Atkins p. 139 7th Edition

Phase Diagram for CO2

• note difference betweenphase diagram for CO2 andH2O is positive slopefor S - L boundary

V liquid V solid

• liquid CO2 is not stable at pressure 5 atm

so at 1 atm it can only sublime…can’t melt !

………term……”dry ice” …….

Remember that for pure substances: G =

• the spontaneous direction of change will always be towards decreasing G ……..thus decreasing

• at low T the solid phase of a substance usually has the lowestchemical potential

……..as T the chemicalpotential of another phasemay be below that of the solidphase………this phase will now bethe thermodynamically most stable phase at this T

…….a phase transition will occurif “kinetically” possible Figure taken from Physical Chemistry by Peter Atkins 6th Edition

Dependence of G on Temperature:

At constant pressure: dG = -SdT

G = - S T

P

= = - S TP


• as T the chemical potentialof a substance

Slope of plot of vs. T is negative

• as T the since S 0

so we have a negative slope ….

• slope of liquid is steeper than that of solid……..slope of gas

is steeper than that of liquid

•since S(g) S(l) S(s) thenslope is steeper for gas thanit is for liquid and solid

• as T is increased the chemicalpotential of liquid falls below

solid ……and chemical potential of gas falls below liquidFigure taken from Physical Chemistry by Peter Atkins 6th Edition

• in P raises (since V 0)

(A) usually V(l) V(s) so in P will forliquid more than for solid

(B) if V(s) V(l) in P will for

solid more than for liquid (e.g. for H2O)A B

P Tm P Tm

Dependence of G on Pressure

The variation of G with respect to P at constant T:

T

= V P

G = V P

T

Phase Diagram for CO2

Positive slope for S-Lphase boundary……….…. P results in Tm P Tm

Phase Diagram of Water

Negative slope for S-Lphase boundary……….…. P results in Tm

P Tm

in P will forsolid more than for liquid

The Phase Rule

f = c - p + 2

f = degrees of freedom

f gives no. of intensive properties that can be changedindependently without changing the no. of phases in equilibrium

c = no. of components

p = no. of phases

e.g. at point A …f = 1 - 1 + 2 = 2

can change T or P without affecting the # of phases in equilibrium

A

**** on a phase boundaryf = 1-2+2 = 1

so for a value of P can onlybe one value of T

P (a

tm) 2

x 1

043300

Temperature (°C)

Sample Problem:

(a) How many triple points are there ?

(b) What phases coexist at thetriple points ?

(c) Synthetic diamond canbe made from graphite.

Use phase diagram to determine how you would go about making diamond.

Solution

diamond

graphite

vapor

liquid

Sample Problem

1. Use the phase diagram of water to predict the change thataccompanies the following:

a) At the triple point of waterT is lowered at constant P

b) Somewhere along the S-Lcurve of water P is increasedat constant T

Fig. 6.5

6.2. Sample Applications of Thermodynamics/Phase Diagrams in Pharmaceutical Science

6.2.1. Pharmaceutical Aerosols

6.2.2. Polymorphism (of drugs)

6.2.3. Differential Scanning Calorimetry in Drug Analysisand Formulation

6.2.1. Inhaled Pharmaceutical Aerosols

e.g. “ puffer” for asthma

• technical terms for “puffer” are

Pressurized metered dose inhaleror

Propellant metered dose inhaler

pMDI or MDI

MDI……..is a small, pressurizedmultiple dose system…thatdelivers small doses of drug to the lungs.

MDI components:• cannister• drug formulation

(propellant and active ingredient)• metering valve for dose control • actuator

• within cannister we have drug formulation……………….this includes a liquid propellant and the active ingredient.

• when the piston is depressed to release the dose the propellantevaporates creating a mist or drug

• mist of fine particles penetrates into lungs

• initially propellants were chlorofluorocarbons (CFCs)……but thesewere later banned due to concern for ozone depletion…….thusnew propellants were explored……….

DESIRED PROPERTIES of PROPELLANT:- “ appropriate boiling point and vapor pressure” ……..

i.e. must be liquefied in closed cannister and evaporate at normal pressure and temperature

- non-flammable, low toxicity, stability, etc.

MDI continued…………..

•gases can be liquified by P (at T below the Tc)

• when P is reduced liquid then reverts to gas

this “Reversible Change of State”is principle behind Pharmaceutical Aerosols

• in these aerosols a drug is dissolved or suspended in a propellantthat is liquid in the container ….and becomes gas under normalatmospheric conditions

• a valve is depressed and mixture is expelled due to excess P….the drug forms mist and propellant is vaporized……..

(need to know phase diagram for propellant !!!!)

MDI continued………..

Solids and the Crystalline State

• crystalline solids (e.g. ice) have structuralunits with fixed geometric patterns

• the units that constitute the crystal structure can be atoms, molecules or ions

• crystalline solids have definite sharp melting points that characterize thesolid to liquid transition

• some crystalline substances can exist in more than one crystallinestate…………this is known as polymorphism

• Polymorphs are chemically identical but usually have differentmelting points and solubilities.

6.2.2 Polymorphism

The crystal lattice of NaCl

Taken from http://www.iit.edu/~felfkri/report.htm

The Seven Crystal Systems

Taken from : (http://www.people.virginia.edu/~lz2n/mse209/Chapter3.pdf)(http://www.iit.edu/~felfkri/report.htm)

Pictures of the Different Allotropes of Carbon

“An allotrope is the purest form of a polymorphismbecause only contains one element…..”

Polymorphism

polymorphs may differ in terms of the followingproperties: solubility, hardness, melting point, density and rate of dissolution

……..these differences in physical properties can translateinto differences in therapeutic activity or efficacy……….

“Ritanovir: An Extraordinary Example of Conformational Polymorphism”

Bauer et al. Pharm Res. 2001

Ritanovir (Norvir®) Abbott LaboratoriesClassification: protease inhibitor Indication: FDA approved for treatment of HIV infection

• In 1996 marketed as Norvir oral liquid and Norvir semi-solid capsules (both include Ritanovir in ethanol/water base)

• since not bioavailable from solid state by International Conference on Harmonization (ICH) guidelines no crystal form control was required

……………… “for a drug product that is a solution, there is little scientific rationale for polymorph control”……..

Ritanovir continued………

• during development of drug only one crystal form was identified( 240 lots of Norvir capsules produced with no stability issues)

• Mid-1998…….problems were encountered…………..- several lots of capsules Failed dissolution tests- capsules were then analyzed by microscopy and

X-ray powder diffraction- analysis revealed a new polymorph

• original form referred to as Form I, newly identified Form as II

• study of Form II revealed it had reduced solubility (when comparedto Form I)

• Form II found to be “unusually stable” yet “unusually difficult to crystallize”

Photomicrographs for Ritanovir Polymorphs (a) Form I, (b) Form II

(a) (b)

• polarized light microscopy reveals two distinct crystals present


Form II

Form I

X-ray Powder Diffraction Patterns for Form I and Form II


Solubility Study of Ritanovir

• appropriate crystal form added to 100 mL solvent • stirred at 5 or 25°C • aliquots removed and analyzed over time

Form I solution begins to decrease in concentration at approx.7 days…….at this point itis 210 % supersaturatedwith respect to FormII……………..


Solubility Profile of Form I and II in Ethanol/Water Solutions


OTHER examples where polymorphism of active ingredienthas been important……………………

•Zantac® (Ranitidine HCl) Glaxoanti-ulcer drug

• Chloramphenicol – 3- palmitate (CAPP)antibiotic

Others……tamoxifen citrate (breast cancer), cortisone acetate

6.2.3. Differential Scanning Calorimetry (DSC)

• technique that is commonly used to characterize thermal properties of substances

e.g. melting temperature (Tm) of a drug

• polymorphic forms of a compound may have different meltingpoints

(although DSC analysis of Forms I and II of Ritanovirrevealed melting points to be approx. the sameTm = 122°C.)

• also useful for indication of purity

Sample

Differential Scanning Calorimeter

• DSC consists of two separate compartments: sample pan and reference pan

• sample and reference pans are heated at constant rate

• system controls electrical output so to maintain reference andsample at same temperature

• the temperature of sample changes if chemical or physical changeoccurs during scan

• to maintain sample and reference at same T excess heat is transferred to or from sample

DSC Continued………..

The temperature at time (t) during a scan is T = T0 + twhere T0 is the initial temperature and is the scan rate (in K/s).

The system will transfer heat to or from the sample pan if necessaryduring scan so to maintain same T in reference and sample pans.

e.g if sample undergoes an endothermic process this will lower T of sample relative to that of reference……….so sample must beheated more in order to maintain equal T in both pans

If no physical change occurs the heat transferred to the sample isqp = Cp T (where T = T – T0)

…….when a chemical or physical change occurs excess heat must be transferred (qp,ex)

qp + qp,ex = (Cp + Cp,ex) T

qp + qp,ex = (Cp + Cp,ex) T

T = T0 + t

T = T – T0

Therefore,

Cp,ex = qp,ex / T = qp,ex / t = Pex/

where Pex is the excess electrical power necessary toequalize the temperatures of the sample and reference pans.

A plot of Cp,ex or Pex versus T is referred to as a Thermogram or DSC trace.

Cp,ex

or heat flow

DSC Trace or Thermogram

• enthalpy change is the area under the curve of Cp,ex vs. T

Tm

Peak = 173.109°C

Area = 604.667 mJDelta H = 155.043 J/g

Taken from Perkin Elmer Pyris 6 DSC PE-Tech 53

Hea

t Flo

w E

ndo

Up

(mW

)

Peak = 57.534 °CArea = 3.173 mJDelta H = 0.814 J/g

Use of DSC in Pharmaceutical Science

• identification of compounds/substances(i.e. each drug has a characteristic melting point (Tm))

• determine Tm , H of compounds or materials

• determination of compound purity

• differentiation of polymorphic forms of compounds

• stability studies on compounds

• study interactions between drug and material/excipient(i.e. material/excipient used for formulation of drug)

Form 1Form 2

Form 3

Piroxicam

International Journal of Pharmaceutics 2003, 256, 3 – 15.

Hea

t Flo

w E

ndo

Up

The rate of dissolution can vary for the different crystal forms of the same drug

Form 1 Form II

Form III

International Journal of Pharmaceutics 2003, 256, 3 – 15.

DSC Scans of ASA and Excipients

• DSC used to study interaction betweendrug and excipient

• excipient that causesminimal change in thermalproperties of drug is usually the most suitable for formulation

(usually the more an excipient alters thermalproperties the more it

interacts with the drug!)J. Pharm. Biomed. Anal. 2003, 32, 1067-1072

ASA = acetyl salicylic acid … “ aspirin “

ASA

J. Pharm. Biomed. Anal. 2003, 32, 1067-1072

Summary of Degradation/Stability Resultsfrom J. Pharm. Biomed. Anal. 2003, 32, 1067-1072

ASA 0.71 0.27

ASA + Talc 4.89 7.80

ASA + Starch 4.93 2.24

ASA + Lactose 11.26 6.56

ASA + Magnesium Stearate 28.44 57.43

% degradation

2 months at 35°C 2 months at 55°C

outline of the course - chemistry at uoft 6 fall 2010.pdf · outline of the course 1) review and...

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