Physical Pharmacy Notes

Lorenzo Dominick Cid 2015

Physical Pharmacy • application of physical chemistry in pharmacy • study of physiochemical properties of substances used in drug

formulation

FORCES OF ATTRACTION Intramolecular Forces • forces of attraction within the molecule • Types – Ionic & Covalent Bonds

o Ionic Bond § Transfer of electrons between a non metal

& a metal § observed in formation of salts

o Covalent Bond § sharing of electrons between two non

metals § observed in organic compounds

Intramolecular Forces • forces of attraction between molecules • Types – Binding & Attractive Forces

o Binding Forces § Cohesion – similar molecules § Adhesion – different molecules § Repulsive – prevent molecules from

annihilating each other o Attractive Forces

§ Van der Waals § Hydrogen Bond § Ion-Dipole § Ion-induced Dipole

Van der Waals Forces • weak forces that involve the dispersion of charge across a

molecule called a dipole o Keesom Forces (orientation effect)

§ Dipole-dipole § molecules are polar with permanent polar

dipoles § Ex. water, HCl, ethanol, acetone, phenol

o Debye Forces (induction effect) § Dipole-induced dipole § transient dipole induced by a permanent

dipole § polar molecules produces temporary

electric dipole in nonpolar molecules § Ex. Ethyl acetate, methylene chloride, ether

o London Forces (dispersion effect) § Induced dipole- induced dipole § induce polarity between non polar

molecules

§ responsible for liquefaction of gases § Ex. Carbon disulfide, CCl2, hexane

Hydrogen Bond • electrostatic interaction of H with highly electronegative

atoms (S,N,Cl,F,O) • accounts for unusual properties of water

Ion-Dipole Interaction • polar molecules are attracted to either positive or negative

charges • occurs when salt is dissolved in a polar solvent • solubility if crystalline substances in H2O • quaternary ammonium + tertiary amine

Ion-Induced Dipole • induced by close proximity of a charged ion to a non polar

molecule • responsible for the solubility of non polar molecules • Ex. Iodine complex with salts

PHYSICAL PROPERTIES OF MATTER Additive • depends on the total contribution of the atoms in the

molecules • Ex. MW, Mass • ↑ atoms = ↑MW = ↑Mass

Constitutive • depends on the arrangement of the number & kind of atoms

within a molecule • Ex. Refactive Index, Optical Rotation

Colligative • function of the number of species or particles present in a

given solution • Ex. Osmotic pressure elevation, Vapor Pressure lowering,

Freezing Point Depression, Boiling Point Elevation

TYPES OF PROPERTIES Intensive • independent of the amount of the substance in the system • Ex. Temperature, Pressure, Density, Viscosity, Surface

tension, Specific Gravity

Extensive • depends on the quantity of substance in the system • Ex. Mass, Length, Volume


STATES OF MATTER The Gaseous State Gas Laws • refers to an ideal situation where no intermolecular

interactions exist and collisions are perfectly elastic • there is no energy exchanged upon collision • Boyle’s Law

o relates volume and pressure o constant temperature o PV = k

• Gay-Lussac and Charles’ Law o states that the volume and absolute temperature of

a gas at constant pressure are directly proportional o V = kT

• Ideal Gas Law o PV = nRT o R = 0.08205 liter.atm/mole.K or 8.314 joules/mole.K

or 1.987 cal/mole deg o n = number of moles

Kinetic Molecular Theory • Gases are composed of particles called atoms or molecules,

the total volume of which is so small as to be negligible in relation to the volume of the space in which the molecules are confined

• The particles of the gas do not attract one another, but instead move with complete independence

• The particles exhibit continuous random motion owing to their kinetic energy

• The molecules exhibit perfect elasticity

The Liquid State • Critical temperature – temperature above which a liquid can

no longer exist • Critical Pressure

o pressure required to liquefy a gas a critical temperature

o highest vapor pressure of a liquid • Boiling Point – the temp at which the vapor pressure of the

liquid equals the external and atmospheric pressure • Latent Heat of Vaporization

o the quantity of heat taken up when a liquid vaporizes

o it is liberated when a vapor condenses with a liquid

Clausius-Clapeyron Equation • relationship of vapor pressure and absolute temperature of

a liquid

logP1P2

= ∆Hv (T2-T1)2.303 RT1T2

P1 & P2 = vapor pressures at T1 & T2 ∆Hv = molar heat of vaporization R = 1.987 cal/mole deg

The Solid State • have fixed shapes • nearly incompressible • have strong intermolecular forces • very little kinetic energy • atoms vibrate fixed positions about an equilibrium position, &

so there is very little transitional motion

Crystalline Solids • Solids whose structural units are arranged in a fixed geometric

pattern or lattices • definite shape • orderly arrangement of units • definite and sharp melting points • 6 Distinct Critical Systems Based on Symmetry

o Cubic – Sodium Chloride o Tetragonal – Urea o Hexagonal – Iodoform o Monoclinic – Sucrose o Rhombic – I2 o Triclinic – Boric Acid

Amorphous Solids • glasses or supercooled liquids • molecules are arranged in a random manner • no definite melting points • faster dissolution rate

Polymorphism • condition where substances can exist in more than 1

crystalline form • polymorphs have different melting points, x-ray crystals and

diffraction patterns and solubility • Theobroma Oil Polymorphs (Melting Points)

o Unstable γ form à 18°C o α form à 22°C o β prime form à 28°C o Stable β form à 34°C

• Types of Polymorphism o Enantiotropic – reversible o Monotropic – unidirectional transition

Freezing Point • temperature at which liquid à solid • melting point of a pure crystalline compound


Latent Heat of Fusion • Energy absorbed when 1g of a solid melts • Heat liberated when it freezes

Liquid Crystalline State • liquid crystals à intermediate between liquid and solid states • may result from the heating of solids (thermotropic) or from

the action of certain solvents on solids (lyotropic liquid crystals)

Two Main Types of Liquid Crystals • Smectic

o Soaplike or greaselike o molecules are mobile in 2 directions o rotates in 1 axis

• Nematic o threadlike o molecules are mobile in 3 directions o rotates in 1 axis o Cholesteric – special type of nematic

Supercritical Fluids • properties intermediate between those of liquids and gases • formed from the gaseous state where the gas is held under a

combination of temperatures and pressures that exceed the critical point of a substance

THE PHASE RULE (GIBB’S PHASE RULE) • relates the effect of the least number of independent variables

(T, P & C) among the various phases (S,L & G) that can exist in an equilibrium system containing a given number of components

𝐹 = 𝐶 − 𝑃 + 𝑋

F = no. of degrees of freedom C = no. chemical components P = no. of phases X = variable dependent upod considerations of the phase diagram • F – least number of intensive/independent variables that must

be fixed to describe the system completely • C – smallest number of constituents by which the composition

of each pase in the system at equilibrium can be expressed in the form of a chemical formula or equation

• P – number of homogenous physically distinct portion of a system that is seperated from other portions of the system by bounding surfaces

• 1 Phase – F=2 – Bivariant • 2 Phases – F=1 – Univariant • 3 Phases – F=0 – Invariant

THERMODYNAMICS • deals with the quantitative relationships of interconversion of

the various forms of energy • System – a well defined part of the universe under study • Surroundings – the rest of the universe from which the

observations are made • Boundaries – physical or virtual barriers that separate a

system from the surroundings

Types of Systems • Open – energy and matter can be exchanged with the

surroundings • Closed – energy can be exchange with the surroundings but

not matter • Isolated – neither matter not energy can be exchanged with

the surroundings

First Law of Thermodynamics • Energy cannot be created nor destroyed, it can only be

transformed into a different form • Adiabatic – constant heat • Isothermic – constant temperature • Isochoric – constant volume • Isobaric – constant pressure

Second Law of Thermodynamics • Refers to the probability of the occurrence of a process based

on the tendency of a system to approach a state of energy equilibrium

• Entropy

Third Law of Thermodynamics • The entropy of a pure crystalline substance is zero at absolute

zero because the crystal arrangement must show the greatest orderliness at this temperature

CONDENSED SYSTEMS • S & L phases only • the vapor state is disregarded with an assumption of working

at a pressure at 1atm o 2 Components – liquid phases o 2 Components – S & L – eutectic mixtures o 3 Components

Two Component System Containing Two Liquids • Binodal Curve – area within the curve which represent a 2

phase system • Upper Consolute/Critical Solution Temperature – max.

temperature at which two phase region in the phase diagram of a two-component system containing two liquids will exist


• Tie line o line from which a system seperates into phases of

constant composition o approximates proportion of components in a

particular temperature • Conjugate Phases

o phases of constant composition that separate when a mixture is prepared within the boundary of the 2-phase system

Two Component System Containing Solid and Liquid • Eutectic Point

o minimum temp. where both exist in liquid form o point where solid A, solid B & the liquid phase co-

exist

Three Component System • Ternary system • 2 liquids that are miscible + 3rd component (co-solvent) with

affinity to both layers • has 4 degrees of freedom

MICROMERITICS • study of small particles • Fundamental properties

o defined individually o Ex. particle size & shape, particle size distribution,

surface area • Derived properties

o computed o dependent on fundamental properties o Ex. Porosity, Density, Flow properties, Packing

arrangement

Particle Size Determination Optical Microscopy • microscope • individual particles can be seen • tedious and 2D image is only seen • Ferret Diameter – measure of the distance between tangents

parallel to some fixed directions • Projected Area Diameter – diameter of a circle with the same

area of the particle • Martin Diameter – length of the line that bisects the particle

Sieving • use of sieves • official method – USP Method • mesh number refers to number of openings per inch • ↑ Mesh Number = ↓ Particle Size (inverse proportionality)

Sedimentation • Andreasen apparatus • ↑ Sedimentation rate = ↑ Particle size (direct proportionality) • follow the Stoke’s Law

Particle Size Determination • Coulter Counter • HIAC/Royco • Gelman Counter

Derived Properties Porosity of Voids • Porosity – measure of a void volume in a powder material • Bulk Volume – total volume of the material • Void Volume – difference between bulk and true volume

Density • True Density – density of actual particle • Granule Density – volume of particles together with

intraparticulate spaces • Bulk Density

o mass of powder divided by the bulk volume o USP Method 1 – Graduated Cylinder o USP Method 2 – Scott Volumeter o USP Method 3 – Vessel

Flow Properties • Angle of Response

o maximum angle possible between the surface of a pile of power and the horizontal plane

𝑡𝑎𝑛𝜙 = ℎ𝑟

h = height of cone r = radius of base cone

o ↑ AOR = ↑ Flow Property • Tapped Density

o measured using a tapped density tester by repeated tapping until a consistent tapped volume is achieved

LIQUIDS • less kinetic energy than gases • occupy definite volume • take the shape of contaniners • denser than gases • not compressible

Solutions of Electrolytes & Non-Electrolytes True Solutions • molecular dispersions


• particle size = <1nm

Electrolytes • form ions in solution • electrical conductance

• Strong Electrolytes

o completely ionized in solution o NaCl, HCl, H2SO4

• Weak Electrolytes o partial ionization o CH3COOH and most drugs

Non-Electrolytes • do not form ions in solution • no electrical conductance • sucrose, glycerin, urea

Colligative Properties of Solutions Vapor Pressure Lowering • pressure of saturated vapor above a liquid à escape of liquid

molecules • non volatile solute + volatile solvent à decreased escape

tendency • vapor pressure is lowered proportional to relative number of

added solutes • Ex. Dextrose + Water à ↓VP of water

Boiling Point Elevation • temperature where VP of liquid = external atmospheric

pressure • ↑ non volatile solute in solution = ↑ BP of solution

Freezing Point Depression • Melting or Freezing Point

o temp at which S & L phases are at equilibrium under 1 atm

o indicator of purity • Solutions have ↓ FPD than pure substances

Osmotic Pressure • pressure required to prevent the movement of water through

a semipermeable membrane from region of high to low concentration

Tonicity of Solutions Isotonic Solutions • living cell does not gain or loss water • same osmotic pressure with body fluids • 0.9% NaCl solution, normal saline, D5W

Hypertonic Solutions • more solutes compared to cell concentrations • freeze lower than -0.52°C • causes creanation of the cell • 5% NaCl solution

Hypotonic Solutions • less solutes compared to cell concentrations • freeze higher than -0.52°C • causes lysis of the cell • distilled water

Methods of Adjusting Tonicity and pH • Class I Methods

o NaCl or some other subtance is added to the solution of the drug to make it isotonic

• Freezing Point Depression/Crysoscopic Method o FPD used to calculate the amount of solute to add in

making an isotonic solution • Class II Methods

o water is added to the drug à isotonic solutions § White Vincent Method – V = w x E x 111.1 § Sprowls Method – V = 0.3g x E x 111.1

Theories of Acid & Bases

Theory Acid Base Arrhenius Liberates H3O in aq.

soln Liberates OH in aq. soln

Bronsted-Lowry Proton donor Proton acceptor Lewis Electron acceptor Electron donor

Classification of Solvents • Protophillic (Basic Solvents) – capable of accepting protons

from solute • Protogenic (Acidic Solvents) – proton donating • Aprotic – neither accepts nor donates

Ionization of Weak Acids & Bases • Ionization – complete separation of ions in a crystal lattice

when a salt is dissolved • Dissociation – separation of ions in solution when the ions

are associated by interionic attraction

Henderson-Hasselbalch Equation • aka pH or buffer equation • preparation of drug solutions at a desired pH using both the

neutral and the salt forms of a drug • determine percentage of neutral and ionized forms at a given

pH • determination of pKa of an acid or a base


• For acid and its salt :

𝑝𝐻 = 𝑝𝐾𝑎 + log[𝑠𝑎𝑙𝑡][𝑎𝑐𝑖𝑑]

• For base and its salt :

𝑝𝐻 = 𝑝𝐾𝑎 + log[𝑏𝑎𝑠𝑒][𝑠𝑎𝑙𝑡]

Buffers • compound or a mixture of compounds which has the ability to

resist changes in pH when small amounts of acids and bases are added

Buffer Capacity • buffer efficiency or buffer index

𝛽 = ∆𝐵∆𝑝𝐻

∆B = represents the small increment in gram equivalents per liter

of strong base or acid added to the buffer solution to produce a change in pH

Solubility • concentration of a saturated solution in which the dissolved

solute is in equilibrium with its solid phase at constant • Intrinsic Solubility • Apparent Solubility • Kinetic Solubility • Thermodynamic Solubility

Factors Affecting Solubility • Dissolution Rate of Solute • Temperature • Addition of Salt • Complex Formation • Salt Formation • Amorphous Form Descriptive Term Parts of Solvent for One Part of

Solute Very soluble <1 Freely Soluble 1-10 Soluble 10-30 Sparingly Soluble 30-100 Slightly Soluble 100-1000

Interfacial Phenomenon • attributed to the effect of the properties of molecules located

or close to the boundary between immiscible phases • Interface – boundary between 2 distinct phases

Surface & Interfacial Tension • Surface Tension

o force that pulls molecules of the interface together & contracts the surface

• Interface Tension o force per unit length excisting at the interface

between 2 immiscible liquids

Wetting Phenomenon • contact angle that a droplet of the liquid makes with the solid

surface at the point of contact • ↑ Contact Angle θ = ↓ wetting • 180° = complete non wetting

SURFACTANTS (SURFACE ACTIVE AGENTS) • long chain molecules • affinity for both polar and non polar solvents • reduces interfacial tension • based on Hydrophile –Lipophile Balance (HLB) Values

Type Description Examples Anionic Long chain molecules of

carboxylates, sulfates or sulfonates

Sodium lauryl sulfate

Cationic Interactions with negatively charged surfaces such as cell membranes; cytotoxic – antimicrobial preseratives

Benzalkonium chloride

Amphoteric Naturally occuring surfactants Zwitterions

Polypeptides, Proteins Alkyl bentanes Lecithin, Cephalins

Non-Ionic Long but contains a small alcohol base (eg. propylene glycol), sorbitan or glucerol to which fatty acids are attached to form fatty acid esters

Fatty alcohols (lauryl, cetyl, stearyl) Steroid alcohols Glyceril esters

HLB Values Utilities Examples 1-3 Antifoaming agent Mineral Oil

Fatty Alcohol Wax

3-6 W/O Emulsifying Agents Span 80 Lanolin

7-9 Wetting & Spreading Agents Brij 30 Docusate sodium

8-18 O/W Emulsifying Agents Twean 20 Cremophor A25

13-16 Detergents Alkyl Benzenes Sulfonates

15-20 Solubilizing Sodium Lauryl Sulfate


Electric Properties of Interfaces • Nerst Potential – Electrothermodynamic • Zeta Potential – Electrokinetic

COLLOIDAL DISPERSIONS Lyophillic • Solvent loving • dispersed phase consists generally or large organic molecules

lying within a colloidal range • Molecules of the dispersed phase are solvated – they are

associated with the molecule comprising the dispersion medium

• Spontaneously disperse to form colloidal dispersion • thermodynamically stable

Association • Ampiphillic • dispersed phase consists of micelles or small organic

molecules or ions whose size individually is below the colloidal range

• Hydrophillic or lipophillic portion is solvated – depending on whether the dispersion medium is aq. or non aq.

• colloidal aggregates are formed spontaneously when the concentration of the ampiphile exceeds critical micelle concentration

Lyophobic • solvent hating • dispersed phase consists of materials that have little

attraction for the dispersion medium • material does not spontaneously form a dispersion

Properties of Colloids Kinetic Properties • Brownian Movement – particles appear as tiny points of light

in constant motion • Diffusion – movement of particles from high to low

concentration until equilibrium is achieved

Optical Property • Tyndall Effect – ability to scatter or disperse light • Faraday Effect

Electrokinetic Effect • Electrophoresis – movement of a charged particle through a

liquid • Electroosmosis – movement of a liquid through plug or

membrane across which a potential is applied • Sedimentation – creation of a potential when particles

undergo sedimentation

• Streaming potential -- potential created by forcing a liquid to flow through a plug or bed of particles

COARSE DISPERSION • Emulsion • Suspensions • Semisolid preparations – gels, jellies, suppositories &

ointments

Instability of Coarse Dispersion Emulsions • Creaming – upward movement of internal phase • Sedimentation – downward movement of internal phase • Flocculation – reversible aggregation of droplets • Coalescence/Cracking/Breaking – complete fusion of

droplets (irreversible) • Inversion – change in the type of emulsion (W/O à O/W or

O/W à W/O)

Suspension • Caking – compaction of suspended particles at the bottom of

the container

Gels, Jellies, Suppositories & Ointments • Syneresis – shirking of gel structure caused by loss of liquid • Bleeding – liberation of liquid from the base • Swelling/Imbibition – absorption of liquid into the structure • Swelling – increase in volume • Imbibition – no increase in volume

RHEOLOGY • study of the flow of liquids • viscosity is the expression of the resistance of a fluid to flow

𝜂 =𝐹𝐺

F = shearing stress (dyne/cm2) – amount of force per unit area required to cause a liquid to flow

G = rate of shear (rev/min) – velocity of the system that leads to the deformation of the liquid

Viscosity Units of Measurement • Absolute viscosity – centipoise/poise • Kinematic viscosity – centistoke/stoke • Relative viscosity – unitless


Measurement of Viscosity • Capillary Tube Viscometers

o measure the time required for a given volume of liquid to flow through a capillary

o ↑ Time = ↓ Viscosity o Ex. Ostwald & Ubbelohde viscometers o Follows Poiseulle’s Law :

𝜂 = 𝜋𝑟! 𝑡∆𝑃8𝑙𝑣

r = radius of capillary t = time to flow P = pressure in dyne/cm2 l = length of capillary v = volume of liquid flowing

• Rotational Viscometers o makes use of a bob or spindle w/c is immersed in the

in the liquid whose viscosity is to be determined o Rotating Bob – Brookfeil, Rotovisco, Stormer o Rotating Cup – MacMichael

Factors Affecting Viscosity • Temperature

o ↑T = ↓viscosity in liquids ; ↑ in gases • Shear Rate • Time • Concentration of Solution

Newtonian Systems • direct relationship between shearing stress & rate • constant viscosity with increasing rate • eg. water, ethanol, acetone, glycerine, benzene

Non-Newtonian Systems Plastic Flow • bingham bodies • curve does not pass through the origin but rather intersects

the shearing stress axis at a particular point (yield value) • a yeild value must be overcome before the system begins to

flow • Ex. Flocculated suspension, gels, ointments, pastes,

surfactants, polymeric substances

Pseudoplastic Flow • shear thinning systems • curve begins at the origin • no yeild value • viscosity decreaes w/ increasing shear rate • Ex. Polymer solution, Na alginate, Perityl cellulose, PEG

Dilatant Flow • shear thickening systems • reverse effects of pseudoplastic flow • viscosity increases with increases shear rate • Ex. starch in H2O, conc. suspension of inorganic pigments in

H2O, Zinc Oxide, Barium sulfate or Titanium oxide in H2O

Thixotropy • decrease in viscosity with time when flow is applied to a

sample previously at rest and the recovery of viscosity in time when flow is continued

• Ex. aq. bentonite magma

Rheopexy • refers to the phenomenon that the gel formation of a system

may be facilitated by tapping or low shear compared to keeping the sample at rest

• time dependent increase in viscosity during flow • Ex. Bovine synovial fluid, serum albumin due to protein,

Sodium hyalorunate

Antithixotropy • time dependent increase in viscosity during flow caused by

reversible aggregation of particles • reversed hysteresis loop • Ex. magnesia magma

GASES • have kinetic energy that produces rapid motion • held together by weak intermolecular forces • capable of filling all available spaces • easily compressible

Gas Laws Gas Law Equation Constant

Variable

Boyle’s Law 𝑃!𝑉! = 𝑃!𝑉! Temperature

Gay-Lussac’s Law 𝑃!𝑇!=𝑃!𝑇!

Volume

Charles’ Law 𝑉!𝑇!=𝑉!𝑇!

Pressure

Combined Gas Law 𝑃!𝑉!𝑇!

=𝑃!𝑉!𝑇!

Ideal Gas Equation 𝑃𝑉 = 𝑛𝑅𝑇

Avogadro’s Principle • equal volume of gases at constant temperature & pressure

contain the same number of molecules • N – 6.02 x 1023 molecules/mole


Ideal Gas Law • no molecular interactions • elastic collisions • no exchange of energy

PV = nRT

n = number of mole/s (n = g/MW) R = molar gas constant 0.08205 L.atm/mole.K 1.987 cal/mole.K

Van der Waals Equation

(P + 𝑎𝑛!

𝑣! )×( 𝑉 − 𝑛𝑏) = 𝑛𝑅𝑇

a = force of attraction between molecules b = size of molecules

Henry’s Law • effect of pressure in solubility of a gas in liquid • in dilute solution, the partial vapor pressure of a solute is

proportional to the mole ratio of the solute to that of the solvent in solution

𝑉2𝑉1

=𝑘𝑃!𝑃!

P2 = partial vapor pressure of the has PT = total vapor pressure k = solubility coefficient

Graham’s Law • speed of diffusion of 2 different gases is inversely

proportionality to the square root of their densities

Raoult’s Law • vapor pressure lowering due to effects of electrolytes or

solutes in solution • the partial vapor pressure of the solvent of an ideal solution is

equal to the product of the mole fraction of the solvent and its vapor pressure in pure state

𝑃 = 𝑃! + 𝑃!

PA = Vapor pressure x mole fraction of component A PB = Vapor pressure x mole fraction of component B MF of A + MF of B = 1

DRUG PRODUCT STABILITY • extent to which a preparation retains the same properties that

it had at the time of formulation • It is concerned with :

o Physical Properties

o Chemical Properties and Composition o Microbiological Sterility o Therapeutic Activity

Photodegredation • sensitivity of drug to UV light • prevention à light resistant / opaque containers

Hydrolysis & Acid-Base Catalysis • degredation of esters, amindes, lactams to carboxylic acid

CHEMICAL KINETICS Reaction Rates • may refer to the rate of degredation or formation of a product

from a given reaction • velocity with which the reaction occurs • Influenced by:

o Concentration o Temperature o Change in pH o Presence of additives o Presence of solvents o Radiation o Catalytic Agents or Enzymes

Order of Reactions Zero Order • concentration independent kinetics • elimination of a reactant will be linear with time • Ex. suspension •

First Order • concentration dependent reaction • rate of reaction is proportional to the first power of the

concentration of a single reacting species • most drugs follow such order of reaction

Second Order • amount of drug is decresing at a rate proportional to the

square of the amount of drug remaining • uncommon Order Zero Order First Order Second Order

Integrated Rate Law

𝐴

= 𝐴 𝑜 − 𝑘𝑡

𝑙𝑛 𝐴 = 𝑙𝑛 𝐴 𝑜 − 𝑘𝑡 1[𝐴]

=1𝐴 𝑜

+ 𝑘𝑡

Half Life

𝑡!/! = 𝐴 𝑜2𝑘 𝑡!/! =

0.683𝑘 𝑡!/! =

1𝑘 𝐴 𝑜

Unit of K

𝑐𝑜𝑛𝑐.𝑡𝑖𝑚𝑒 1

𝑡𝑖𝑚𝑒 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛!! 𝑡𝑖𝑚𝑒!!


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Physical Pharmacy Notes