states of matter. states of matter gases, liquids, and solids are the three states of matter....

States of Matter

States of matter

• Gases, liquids, and solids are the three states of matter.

• Certain asymmetric molecules (surfactants) commonly exhibit a fourth phase called the mesophase which is between the liquid and solid state. Therefore the fourth state of matter is the Liquid Crystalline state.

Gas State

• Gases are described as molecules that have kinetic energy that produces rapid motion.

• Gas molecules exert relatively small forces on each other (molecules try to act independently of one another).

• A gas mixes completely with any other gas.

• They move in random and vigorous motion bouncing of the walls of the container. This constant motion produces a pressure called vapor pressure. It is measured in atm, mm (cm) of mercury or dyne/cm2.

Gas State

• Gas is the only state that is compressible.

• A gas uniformly fills any container and assumes its shape (volume).

• It is important to understand gas laws in the development of pharmaceutical aerosols, anesthetics, and inhalers.

The Ideal Gas Law PV=nRT

• The ideal gas law shows the relation between the volume, pressure, temperature, and the number of moles of the gas.

• R is the gas law constant (1.98717 cal.K-1.mol-1, 8.3143 J .K-1.mol-1, or 0.082 L.atm.K-1mol-1, to be selected based on the other units in the equation).

• The ideal gas law is an equation of state for a gas, where the state of the gas is its condition at any given time. A particular state of a gas is described by its pressure, volume, temperature, and number of moles. Knowledge of any three of these properties is enough to completely define the state of a gas, since the fourth property can then be determined from the equation for the ideal gas.


• To obtain the numeric value of R, the following procedure is followed. If 1 mole of an ideal gas is chosen, its volume under standard temperature and pressure (STP) (i.e. at 0ºC (273.15 K) and 760mmHg (1 atm) has been found to be 22.4 liters. When P is 1 atm, V=22.4 L (volume of 1 mole of an ideal gas), and T is 273.15 K, the gas constant is 0.082 L.atm.K-1mol-1.

• See example 2-2 page 25 and solve problem 2-3 page 50 – fourth edition of Martin. If you have the fifth edition, see example 2-2 page 28 and solve problem 2-3 page 685. If you have the sixth edition see example 2-2 page 23.

Example:

One mole of water is converted to steam at 100 oC at 1 atm. What is the volume of the steam? T(K) = T(C)+273 = 100+273 =373

V = n RT/P

= 1 mol x 0.082 LatmK-1mol-1373 K / 1 atm = 30.6 L


• The ideal gas law can be very useful when one needs to find the approximate molecular weight of a gas. The n is substituted for g/M, which is grams of the gas/ molecular weight.

• See example 2-3 page 26 in the fourth edition (if you have the fifth edition see example 2-3 page 28. If you have the sixth edition see example 2-3 page 24).

• Solve problem 2-4 page 50 in the fourth edition (if you have the fifth edition solve problem 2-4 page 685. If you have the sixth edition solve problem 2-3).


Kinetic Molecular Theory

• The kinetics molecular theory was developed to explain the behavior of gases and to lend additional support to the validity of the ideal gas law.

• Some of the important statements include:

1- Gases are composed of particles called molecules, the total volume is so small as to be negligible in relation to the volume of the space in which the molecules are confined. This condition is approximated in actual gases only at low pressures and high temperatures, in which case the molecules of the gas are far apart.

Kinetic Molecular Theory

2- The particles of the gas do not attract one another but rather quickly move with complete independence; again, this statement only applies at low pressures.

3- The particles exhibit continuous random motion owing to their kinetic energy.

4- The molecules exhibit perfect elasticity, that is, there is no net loss of speed or transfer of energy after they collide with one another and with the molecules in the walls of the confining vessel, which latter effect accounts for the gas pressure.

The Liquid State

. • The liquid state is defined in comparison to the gaseous

and solid states:• A liquid occupies a definite volume and takes the shape

of the container required to hold it.• Liquids are denser than gases, are not compressible and

possess less kinetic energy than do gases.• Liquids flow readily and the flow is influenced by friction.• Liquids can be frozen, have boiling points and have

vapor pressure and surface tension.

Liquification of Gases:

Cooling of the gas loss of kinetic energy reduction in velocity.

Applying pressure intermolecular forces liquid state.

Transition from gas to liquid and from liquid to solid depends on temperature and pressure.

Critical temperature: The temperature above which it is impossible to liquefy a gas irrespective of the pressure applied.

Critical Pressure: The pressure required to liquefy a gas at its critical temperature. (Also it is the highest vapor pressure a liquid can have).

The Liquid State

The critical temperature: serves as a rough measure for the attractive forces:

E.g. Water: C.T. is 647°K; C.P. is 218 atm. {dipolar forces, H-bonding}.

Helium: C.T. is 5.2°K; C.P. 2.26 atm {London Forces}.

The Liquid State

Vapor Pressure of Liquids

• Molecules in the liquid state vary in the level of kinetic energy they possess: – Translational– Vibrational– Rotational

• When a liquid is placed in a container at a constant temperature, molecules with the highest energy break away from the liquid and pass into the gaseous state (evaporate).

• On the other hand subsequently return to the liquid state (condense).


• When the rate of evaporation is equal to the rate of condensation at a definite temperature, an equilibrium is established and the vapor is said to be saturated.

• Equilibrium vapor pressure is the pressure of a saturated vapor above a liquid.

The effect of external pressure on the equilibrium vapor pressure


• Factors affecting the vapor pressure:

– The nature of the attractive forces in the liquid e.g. water < ethyl alcohol < diethyl ether.

– The effect of temperature: vapor pressure increases with raising temperature.

• Not affecting: the vapor pressure of a liquid is independent of the volume of the container, provided that there is some liquid present so that equilibrium can be established.

The liquid state-the Vapor pressure of liquids


Raoult’s law:

• In an ideal solution, the partial vapor pressure of each volatile constituent is equal to the vapor pressure of the pure constituent multiplied by its mole fraction in the solution.

PA= PA°XA PB=PB°XB

• PA, PB: Partial vapor pressure of the constituents. XA, XB: Molar fraction.

Heat of vaporization

• The relationship between the vapor pressure and the temperature (absolute) of the liquid is expressed by the Clausius-Clapeyron equation.

• P1 and P2 are the vapor pressures at absolute temperatures T1 and T2

• ΔHv is the molar heat of vaporaization (the heat absorbed by 1 mole of liquid when it passes into the vapor state).

21

12

1

2

303.2

)(log

TRT

TTH

P

P V

Heat of vaporization• ΔHv varies with temperature, however over a short range it may be

considered constant. For water at 100oC ΔHv is 539 cal/g while at 180oC it is 478 cal/g.

• The Clausius-Clapeyron equation can be written in a more general form,

or in natural logarithms,

from which it is observed that a plot of the logarithm of the vapor pressure against the reciprocal of the absolute temperature results in a straight line, enabling one to compute the heat of vaporization of the liquid from the slope of the line.

tconsTR

HvP tan

1

303.2log

tconsTR

HP v tan

1ln

Heat of vaporization

• See example 2-7 page 29 – fourth edition (if you have the fifth edition see example 2-7 page 33. If you have the sixth edition see example 2-7 page 28).

• Solve problem 2-13 page 50 and problem 2-14 page 51 in the fourth edition (if you have the fifth edition solve problems 2-13 and 2-14 page 686. If you have the sixth edition solve problem 2-9).

Boiling Point• If a liquid is placed in an open container and heated until

the vapor pressure equals the atmospheric pressure, the vaporization process will be at its highest rate.

• The vapor will form bubbles that rise rapidly through the liquid and escape into the gaseous phase.

• The temperature at which this happens is called the boiling point.

The boiling point is the temperature at which vapor pressure of the liquid equals the external (atmospheric pressure).

Boiling Point• The boiling point may be considered as the temperature

at which thermal agitation overcomes the intermolecular interactions of the molecules of the liquid.

• The boiling point of normal hydrocarbons, simple alcohols and carboxylic acids increases with increased molecule weight.

• Branching of the chain reduces the points of interaction between molecules and reduces intermolecular interactions and boiling point.

Boiling Point

Compound Boiling Point (oC)

ΔHv

(cal/g)

Helium -268.9 6

Propane -42.2 102

Methyl Chloride -24.2 102

Butane -0.4 92

Isobutane -10.2 88

Ethyl ether 34.6 90

Ethyl alcohol 78.3 204

Water 100 539

Aerosols

• Gases can be liquefied under high pressure in closed chambers as long as the chamber is maintained below the critical temperature.

• When the pressure is reduced, the molecules expand and the liquid reverts to gas.

• This reversible change of state is the basic principle involved in the preparation of pharmaceutical aerosols.

Aerosols

• In an aerosol, a drug is dissolved or suspended in a propellant.

• A propellant is a material that is liquid under the pressure conditions existing inside the container but forms a gas under normal atmospheric conditions.

• The container is designed so that by depressing the valve, some of the drug-propellant mixture is expelled because of the excess pressure inside the container.

Aerosols

• Propellants: Florinated hydrocarbons: such as Trichloromonofluoromethane,

and dicholorodifluoromethane Hydrocarbons: such as propane, isobutane. Compressed gas: such as CO2, N2, and N2O

Aerosols

Aerosols

• If the drug is nonvolatile, it forms a fine spray as it leaves the valve orifice, the liquid propellant vaporizes off.

• Chlorofluorocarbons (CFCs) and hydrofluorocarbons (HFCs) have been most commonly used (Ozone depletion).

• Alternate fluorocarbons propellants that do not deplete the ozone layer of the atmosphere are under investigation, in addition, an increase in the use of other gases such as nitrogen and carbon dioxide is observed during the last decade.

Aerosols

• The containers are filled either by: – Cooling the propellant and drug to low temperature within the

chamber which is then sealed by the valve.– Sealing the drug in the container at room temperature and then

forcing the required amount of the propellant into the container under pressure.

• Aerosols are used for the delivery of antiseptic and local anesthetics onto injured skin (ethylchloride effect !!).

• Exubera® inhaled insulin approved in 2006 by the FDA.


Calculate the vapor pressure at 298 K above an aerosol mixture consisting of 30% w/w of aerosol propellant 114 (mol.wt = 170.9) with vapor pressure of 1.90x105 Nm-2 and 70% w/w of propellant 12 (mol.wt. =120.9) with a vapor pressure of 5.85x105 Nm-2. Assume ideal behaviour.

Amount of a in mixture = 30/170.9=0.1755 molesAmount of b in mixture = 70/120.9=0.5790 molesXa =0.1755/ (0.1755+0.5790)= 0.2326Xb =0.5790/ (0.1755+0.5790)= 0.7674

P (total)=(1.90x105 x 0.2326)+(5.85x105 x 0.7674) = 4.492x105 Nm-2

Solid State

• Solids are characterized as having a fixed shape and being incompressible.

• Molecules in the solid state have strong intermolecular forces and therefore very little kinetic energy.

• In solids there is very little translational and rotational kinetic energy, however atoms vibrate around a fixed equilibrium position.

• Very few solids are volatile enough to have a sublimation point (nitroglycerin solid below 14oC).

Solid State

• Solids are usually characterized by:– Shape– Particle size– Melting point– Surface energy– Hardness– Elastic properties– Compaction– porosity

Solid State

• There are three main types of solids:– Crystalline– Amorphous– Polymeric

Crystalline Solids

• The molecules of a crystalline solid are arranged in repetitious three-dimensional lattice units.

• Crystalline solids show definite melting points, passing rather sharply from the solid to the liquid state.

• These three dimensional lattice units may assume different shapes:– Cubic as in sodium chloride– Tetragonal as in urea– Hexagonal as in iodoform– Rhombic as in iodine– Monoclinic as in sucrose– Triclinic as in boric acid

Crystalline Solids

Crystalline Solids

• Different types of bonding may be involved in crystal formation.

Unit Example Bonding Physical Characteristics

Atom to atom Carbon, diamond, graphite

Strong carbon covalent bonds

Hard large crystals

Metallic Silver Strong metal bond Positive ions in a field of free moving electrons

Molecular Menthol Van der Waals forces

Close packing, weakly held together, low melting point

Ionic NaCl Electrostatic ionic bonds

Hard, close packing, strongly held together, high melting

point

Crystalline Solids

• Crystallization from solutions occurs as a result of three successive procedures:– Supersaturation of solution.– Formation of crystal nuclei.– Crystal growth round the nuclei.

Crystalline Solids

• Some materials may exist in more than one crystalline form.

• Polymorphism is the property of having more than one crystalline form.

• These different crystalline forms of the same material are called polymorphs.

Crystalline Solids

• Polymorphs generally have different melting points, stabilities, density, hardness, crystal shape, optical and electrical properties, vapor pressure, and solubilities even though they are chemically identical.

Crystalline Solids

• Crystalline solids may change its crystal system reversibly with changes in temperature (enantiotropic change)

• Changing the crystal form irreversibly is called a monotropic change.

Crystalline Solids

• Theobroma oil (cocoa butter) is a triglyceride that is used in pharmacy as a suppository base.

• Suppositories must be solid at room temperature but melt at body temperature.

• The melting point of the most stable polymorph of cocoa butter is approximately 35oC.

• If cocoa butter is overheated (>40oC) and cooled quickly in the mold during the preparation of the suppository, it will solidify in a less stable polymorphic form that melts at lower temperature (15-28oC).

Crystalline Solids

• Many pharmaceutical solids are synthesized by an organic chemical process, purified and then crystallized out of different solvents.

• Residual solvents might get trapped in the crystalline lattice, creating a cocrystal or a solvate.

• Solvates may be referred to as pseudopolymorphs.

Crystalline Solids

• A solvate may be defined as a molecular complex that has incorporated the crystallization solvent molecules into specific sites within the crystal lattice. When the incorporated solvent is water the complex is called Hydrates.

• Anhydrous compound, that doesn’t include water in its structure.

• The hydrous and anhydrous forms of a drug differ greatly in their solubility and melting points.

Crystalline Solids

Amorphous Solids• These are solid materials where a long range order or

individual units is absent.

• Amorphous solids are referred to as glasses or supercooled liquids because of the random order of arrangement.

• Characterized by higher thermodynamic energy than crystalline solids

• Usually the temperature of transition from an amorphous solid into a liquid is a range of several degrees.

• The solubility of amorphous solids is more than that of crystalline solids.

Amorphous Solids

• Prepared by: – Rapid precipitation– Lyophilization– Rapid cooling of molten material– Grinding

Amorphous Solids

• Anisotropy is the property of being directionally dependent.

• Something which is anisotropic may appear different or

have different characteristics in different directions.

• An example is the double refraction of light coming through a polarizing lens (Birefringence).

• Anisotropy is characteristic of most crystalline solids.

Amorphous Solids

• Isotropy is the property of being independent of direction.

• Isotropy is characteristic of cubic crystals and

amorphous materials.

Polymeric Solids

• Polymeric solids are made up of long chain molecules, wrapped around each other. The polymer chains are made up repeated monomers.

• Better flowability, elastic deformability.

• Polymeric materials may contain both crystalline and

amorphous domains.

Melting Point and Heat of Fusion

• The melting point or freezing point of a pure crystalline substances: is the temperature at which the pure liquid and solid exists in equilibrium.

• Usually it is reported as the temperature of the equilibrium mixture at an external pressure of 1 atm (Normal freezing point).

• Latent heat of Fusion: the heat absorbed when a gram of solid change melts or the heat librated when it freezes.


• The heat added during the melting process does not bring about a change in temperature until all the solid had disappeared.


• Changes in the freezing point or the melting point with pressure can be obtained using the following form of the Clapeyron equation:

• Where Vl and Vs are the molar volumes (cm3/mole) of the liquid and solid respectively.

• ΔHf is the molar heat of fusion.

• ΔT is the change in melting point brought about by a pressure change of ΔP.

f

sl

H

VVT

P

T


• The molar volume is calculated by dividing the gram molecular weight on the density of the compound.

Normal melting points and molar heats of fusion of some compounds

Substance Melting Point K

ΔHf

H2O 273.15 1440

CH4 90.5 226

C2H6 90 683

n-C3H8 85.5 842

C6H6 278.5 2348

C10H8 353 4550


• Water is unusual in that it has a larger molar volume in the solid state than in the liquid state (VlVs) at the melting point.

• Because of that, {∆T/∆P } is negative this means that the melting point is lowered by an increase in pressure.

• This phenomenon is rationalized in terms of the Le Chatelier’s Principle which states that a system at equilibrium readjusts so as to reduce the effect of the external stress.

• Solve problem 2-18 part (b) page 51 in the fourth edition, if you have the fifth edition solve problem 2-18 part (b) page 687. If you have the sixth edition solve problem

2-12 part (b).



• Heat of fusion: the heat required to increase the inter atomic or intermolecular distances in crystals , thus allowing melting to occur.

• Weaker bond---lower heat of fusion--- lower melting point.

– The melting point of saturated hydrocarbons increase with molecular weight because of Van der Waal forces.

– Carbons of even no. of atoms has higher melting point than those with odd no. of atoms ( odd no. has lower efficiency in arrangement)

– Carboxylic acid: they crystallize more symmetrically than odd ones. Reason: the carboxyl groups are joined at two points compared to odd which are joined at one point


• How to measure melting point:– Capillary melting– hot stage microscopy– Differential scanning calorimetry

Characterization of the Solid State

• Thermals analysis (TA):– Methods used to characterize the physical and

chemical alterations in material due to temperature effect.

• TA is used for:– Characterization and identification of drugs– determination of purity– Polymorphism– solvent and moisture content– stability and compatibility with excipients


• Heat absorbing (endothermic) processes:– Fusion, boiling, sublimation, vaporization, desolvation, solid-solid

transition and chemical degradation.

• Heat generating (exothermic) processes:– Crystallization and degradation.

• The major use of DSC for:– Quantitative measurement for: purity, polymorphism, solvation,

degradation and excipients compatibility.

• Thermogravimetric Analysis or TGA is a type of testing that is performed on samples to determine changes in weight in relation to change in temperature.


• Vapor sorption/desorption analysis is a technique similar to TGA.

• It measures weight changes in solids as they are exposed to different solvent vapors and humidity and/or temperature conditions.

• A positive change in the weight of the solid would indicate that the solid material is absorping/adsorping (sorping) the solvent.


• The ability of the solid to continuously absorb water until it goes into solution is called deliquescence.

• A weight loss could also be measured under low relative humidity (desorption).


The Liquid Crystalline State

• It is a meso-phase (prefix meaning middle or intermediate). – Liquid-like: intermediate mobility and rotation.

– Crystal-like: being birefringent.

• Molecules that can form mesophase should be: Organic, elongated and rectilinear in shape, rigid, possess strong dipoles and easily polarizable groups.

• Liquid crystals are either thermotropic (the order of its components is determined or changed by temperature) or lyotropic (the ordering effects in it are induced by changing its concentration within a solvent) .

The Liquid Crystalline State

• Types of liquid crystals: smectic, nematic and , cholestric.

• According to the shape of the crystalline structure.

states of matter. states of matter gases, liquids, and solids are the three states of matter....

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