Physical Pharmacy I - States of Matter PDF

# Physical Pharmacy I ## Lec (1) ### By: Sanaria Th. Nasser ## Objectives * To understand the application of quantitative and theoretical principles of the physical characters of matter to the practice of pharmacy. * It helps the pharmacist to predict the solubility, compatibility and biologica...

# Physical Pharmacy I ## Lec (1) ### By: Sanaria Th. Nasser ## Objectives * To understand the application of quantitative and theoretical principles of the physical characters of matter to the practice of pharmacy. * It helps the pharmacist to predict the solubility, compatibility and biological activity of drug products. * As a result of this knowledge, it is helpful in the development of new drugs and dosageforms as well as in the improvement of various modes of administration. ## Chapter 2: States of Matter ### Binding Forces between Molecules * All matter is held together by force. * The force between atoms within a molecule is a chemical or intramolecular force. * The force between molecules is a physical or intermolecular force. * Forces can be attractive or repulsive depending on whether like or unlike charges are closer together. * Adhesion is the force of attraction between molecules of different substances while cohesion is the force of attraction between molecules of the same substance ### Repulsive and Attractive forces * On the atomic or molecular scale, all particles exert both attractive and repulsive forces on each other. * If the attractive forces between two or more atoms are strong enough to make them into unit with own observable properties, we call the result a "molecule" and refer to the force as a "chemical bond". * If the attractive forces between two or more atoms are not strong enough to bind them into a new molecular unit, so we call this force a non-bonding attraction. * The shape of the curve shows how repulsive and attractive forces affect the potential energy in opposite ways: repulsions always raise this energy, and attractions reduce it. The curve passes through a minimum when the attractive and repulsive forces are exactly in balance (equilibrium state). As we stated above, all particles exert both kinds of forces on one another. ### Intermolecular Forces: * What determines if a substance is a solid, liquid, or gas? * The state a substance is in at a particular temperature and pressure depends on two factors: * The kinetic energy of the particles * The strength of the attractions between the particles (intermolecular) * Gases: The average kinetic energy of the gas molecules is much larger than the average energy of the attractions between them. * Liquids: the intermolecular attractive forces are strong enough to hold the molecules close together, but without much order. * Solids: the intermolecular attractive forces are strong enough to lock molecules in place (high order). * The strengths of intermolecular forces are generally weaker than either ionic or covalent bonds. * Polarity; the dipoles can be formed as a result of unbalanced distribution of electrons in asymmetrical molecules. This is caused by the location of a few more electrons on one side of the nucleus than on the other. ## 1-VAN DER WAALS BONDING * It is a weak bond, with a typical strength 1-10 Kcal/mole. * It occurs between molecules. * The explanation of these weak forces of attraction is that there are fluctuation in the electron density of all molecules and these cause small dipoles within the molecules. It is these dipoles that attract one molecule to another. They are called van der Waals' forces. ### Types of Van der Waals Forces * dipole-dipole, (Van der Waals-Keesom force) * Force between two permanent dipoles * dipole-induced dipole, (Van der Waals-Debye force) * Force between a permanent dipole and a corresponding induced dipole * dispersion, (London dispersion force or Van der Waals-London force) ## 2-Ion Dipole Forces * The force of attraction between an ion and a polar molecule. * NaCl breaks up because the ion dipole with water is stronger than the attraction of Na+ to Cl- ## 3-Ion- Induced Dipole Forces * The force of attraction between an ion and weak dipole which are induced in non polar molecules. * Example: * An ionic substance in anon polar solvent (NaCl in hexane) * lodine with potassium iodide ## 4-Hydrogen bonding * Hydrogen bond is the attractive interaction of a hydrogen atom with an electronegative atom, such as N, O or F. * The hydrogen must be covalently bonded to another electronegative atom to create the bond. * These bonds can occur between molecules (intermolecularly), or within different parts of a single molecule (intramolecularly). The hydrogen bond is stronger than a van der Waals interaction, but weaker than covalent or ionic bonds. * Hydrogen bonding affects physical properties (mp, bp, solubility) of substance. * About one sixth of the hydrogen bonds of ice are broken when ice convert to liquid state and all are destroyed when it vaporize * Example: water, H-F------H-F, salicylic acid ## Bond & Energy | Bond | Energy | |--------------|------------------------| | Ionic | 100-200 Kcal/mole | | Covalent | 50- 150 Kcal/mole | | H-bond | 2-7 Kcal/mole | | Van der Waals forces | 1-10 Kcal/mole | ## Gases * Because gas particles move at a high velocity and are separated by large distances, the forces acting between gas particles (intermolecular forces) tend to be negligible. It is for this reason that gases are free to expand to fill the volume of any container. Since intermolecular repulsive forces are significant only at very small distances, gases are also highly compressible. * can be compressed * exert pressure on whatever surrounds them * expand into whatever volume is available * mix completely one another * can be described in terms of their temperature, pressure, the volume occupied, and the amount (number of moles) present P, V, T, n ### 1. Ideal Gases * An ideal gas is an imaginary gas which has no intermolecular forces and no molecular volume. ### Ideal Gas Law * When we describe an ideal gas we are interested in four variables. These variables are listed below along with common conversions factors. * P, pressure. (1 atm = 760 mm Hg), (1 atm = 760 torr), (1 atm = I x 10sPa). * V, volume. (1 L = 1000 mL),(I L = 1000 cm³), (1 m³= 1000 L). * n, moles. (# moles = # grams/MW). * T, temperature. (K = ·C+ 273), where K is the temperature expressed in Kelvin. The relationship of the above variables is given in the ideal gas equation below: $PV=nRT$ * where P is in atm, V is in L, T is in Kelvin. R is the molar gas constant which is equal to 0.082 L• atm/mol• K. (When Sl units are used R = 8.3 J/mol• K.) * if 1 mole of an ideal gas is chosen, its volume under standard conditions of temperature and pressure (STP)(0°C and 760 mm Hg) has been found by experiment to be 22.4 L. * PV=nRT * 1 atm x 22.414 liters= 1mole x Rx 273 k * R = 0.082 L. atm/mol• K. * (Other R value = 8.314 joule/ mole. K, R= 1.987 cal/mole. K) * Historically the ideal gas law was derived from a number of simpler relationships which we will explore shortly. * Standard temperature and pressure, STP, is 0°C (273 K) and 1 atm. * Calculate the standard molar volume of an ideal gas at STP. * The standard molar volume is the volume occupied by one mole at 273-K and 1 atm. $V = nRT/P, V = (1)(0:082)(273)/(1) V = 22.4 L$ * Molecular weight calculation using ideal gas law. The number of moles of gas n is replaced by its equivalent g/M, in which g is the number of grams of gas and M is the molecular weight $PV =\frac{g}{M}RT$ $M =\frac{gRT}{PV}$ * When a gas under goes a change from one set of conditions to another set of conditions the ideal gas law may be written in the form shown below: $\frac{P_1V_1}{n_1T_1} = \frac{P_2V_2}{n_2T_2}$ where the subscripts 1 and 2 represent initial and final conditions, respectively. In this form of the gas constant R does not appear. When working with this equation you may use any units which are convenient for P and V, but I must be in Kelvin. ### Boyle's Law Boyle's law states that a sample of gas at a constant temperature will have a volume which is inversely proportional to its pressure. $P\alpha\frac{1}{V}$ $PV = k$ or $P_1V_1 = P_2V_2$ ### The Law of Gay-Lussac and Charles's Law states that a sample of gas at a constant pressure will have a volume which is directly proportional to its temperature. $V α T$ or $V=KT$ $\frac{V}{T}=k$ or $\frac{V_1}{T_1}=\frac{V_2}{T_2}$ * These equations can be combined to obtain the familiar relationship: $\frac{P_1V_1}{n_1T_1}=\frac{P_2V_2}{n_2T_2}$ ### Kinetic Molecular Theory The kinetic molecular theory of gases is a theoretical model of gas behavior which utilizes a number of simplifying assumptions so that real gases may be treated as ideal gases: * Gases are composed of particles in constant random motion. * Because the size of the gas particles is so small, and the distance separating them so great the volume occupied by the gas particles will be negligible when compared to the volume of their container. * No appreciable intermolecular forces occur except during collisions. * All collisions are perfectly elastic. Kinetic energy is conserved when gas particles collide among themselves, or with the walls of the container. * The average kinetic energy of gas particles is directly proportional to their absolute temperature. All gases at the same temperature have the same average kinetic energy. ### 2. Real Gases * One of the assumptions of the kinetic molecular theory of gases is that the gas particles are separated by large distances. Under conditions of high pressure and low temperature this assumption will no longer be true and deviations from ideal behavior will occur. #### Deviations Due to Low Temperature * Under conditions of low temperature gas particles are close enough together so that intermolecular attractive forces become significant. This causes the pressure of the gas to be less than that predicted by the ideal gas law. #### Deviations Due to High Pressure * At high pressure gas particles are close enough together to experience intermolecular attractive forces. This causes the volume of the gas to be less than that predicted by the ideal gas law. * Under high pressures the volume occupied by a real gas will be greater than that predicted for an ideal gas. At high pressures the volume occupied by the gas particles becomes a significant percentage of the total volume. Thus the total volume must be greater than predicted so as to compensate for the excluded volume. ### Van der Waals' Equation The van der Waals' equation is a way of quantifying deviations from ideal gas behavior. $P + \frac{an^2}{V^2}(V - nb) = nRT$ * b= constant representing volume excluded per mole of molecules * a= depends on the strength of attractive forces ### Problem 2-1 A weather balloon rises 2 miles into the upper atmosphere. Its volume at ground level is 2.5 liters at 1 atm pressure and 24 °C. What is its final volume if the atmospheric pressure is equal to 8.77 x10-³ and temperature is -44.7 °C at the 2 mile position? * V1= 2.5L, P1= 1 atm, T1= 24+273=297 k * V2=?, P2=8.77 x10-3 atm, T2= -44.7+273= 228.3 K $\frac{P_1V_1}{n_1T_1} = \frac{P_2V_2}{n_2T_2}$ $\frac{1\times25}{297}=\frac{8.77 \times 10^{-3}\times V_2}{228.3}$ $V_2= 219.6 L$ ### Question: If 0.5 g of drug in the vapor state occupies 100 ml at 120 °C and 1 atm pressure. What is approximate M.wt (assuming that the gas behaves ideally) $PV=nRT$ $PV=\frac{wt}{M.wt}RT$ $M.wt = \frac{wt \times R \times T }{P.V}$ $\frac{0.5 \ g\times0.082 \ L.atm/mol\times K \times 393k}{1 \ atm \times 0.1L}$ $=161.13 \ g/mole$ ### Question: A sample of chlorine gas has a volume of 1.8 L at 1.0 atm. If the pressure increases to 4.0 atm (at constant temperature), what would be the new volume? $P_1V_1=P_2V_2$ $V_2= \frac{(p_1v_1)}{p_2}$ $\frac{(1 \ atm \times 1.8L)}{4 \ atm}= 0.45 \ L$ ### Question: A sample of methane gas that has a volume of 3.8 L at 5.0 °C is heated to 86.0 °C at constant pressure. Calculate its new volume. $\frac{V_2}{T_2} = \frac{V_1}{T_1}$ $\frac{V_1 \times T_2}{T_1} = \frac{3.8 \ L \times 359K}{278K}$ $V_2 =4.9L$ ## Phase Changes * Evaporation: Liquid → Gas * Condensation: Gas → Liquid * Melting: Solid → Liquid * Freezing: Liquid → Solid * Sublimation: Solid → Gas ## THE LIQUID STATE * It can be considered an intermediate state as the matter goes from solid state to the gaseous state. * Liquefaction of Gases * The transitions from a gas to a liquid and from a liquid to a solid depend on the temperature and pressure. * So 2 ways for Liquefaction of Gases: * When a gas is cooled, it loses some of its kinetic energy in the form of heat, and the velocity of the molecules decreases. * If pressure is applied to the gas; the molecules are brought within the sphere of the van der Waals interaction forces and pass into the liquid state. Because of these forces, liquids are considerably denser than gases and occupy a definite volume. ### Critical temperature * Is the temperature, above which a liquid can no longer exist irrespective to the pressure applied. ### Critical pressure * Is the pressure required to liquefy a gas at its critical temperature. The critical temperature of water is 374°C, or 647 K, and its critical pressure is 218 atm, whereas the corresponding values for helium are 5.2 K and 2.26 atm. The critical temperature serves as a rough measure of the attractive forces between molecules because at temperatures above the critical value, the molecules possess sufficient kinetic energy so that no amount of pressure can bring them within the range of attractive forces that cause the atoms or molecules to "stick" together. * The high critical values for water result from the strong dipolar forces between the molecules and particularly the hydrogen bonding that exists. * Conversely, only the weak London force attracts helium molecules. ### Aerosols * Gases can be liquefied under high pressures in a closed chamber as long as the chamber is maintained below the critical temperature. When the pressure is reduced, the molecules expand and the liquid reverts to a gas. This reversible change of state is the basic principle involved in the preparation of pharmaceutical aerosols. In such products, a drug is dissolved or suspended in a propellant, a material that is liquid under the pressure conditions existing inside the container but that forms a gas under normal atmospheric conditions. ### Vapor pressure of liquids * Evaporation is the name of the process by which a liquid becomes a gas. * Evaporation takes place from the surface of a liquid. * If we place a liquid in a sealed container with some empty space above the liquid initially there will be no vapor or gas above that liquid. * Those molecules at the surface of the liquid with sufficient energy will leave the liquid and enter the gas phase (forming a vapor above the liquid). * This vapor exerts a pressure on the surface of the liquid, i.e., Vapor Pressure. Some of the vapor molecules will strike the surface of the liquid and return to the liquid phase. * When the rate at which the liquid is entering the gas phase equals the rate at which the vapor is returning to the liquid phase we say the system is at equilibrium. After this time the liquid level will remain constant. The pressure exerted by the vapor at this time is called the vapor pressure. * We can define the vapor pressure of a liquid as: "the pressure exerted by a vapor that is in equilibrium with its liquid.” * The equilibrium vapor pressure is the vapor pressure measured when a dynamic equilibrium exists between condensation and evaporation. The vapor pressure is physical property of liquid and does not depends on the weight,volume, and surface area of liquid but it depend on kinetic energy of molecule (temperature and intermolecular forces). * Those molecules that have strong intermolecular attractive forces have lower vapor pressures than expected. | Liquid | Molecular weight (u) | Polarity | Vapor pressure (torr) | |-----------------|-------------------|---------------------------------------|-----------------------| | pentane (C5H12) | 72 | Nonpolar | 414.5 | | 1-butanol (C4H9OH) | 74 | Polar (hydrogen bonds) | 7.1 | * At 20°C H²O (MW = 18 gmol-¹) has a vapor pressure of 17.5 torr. While diethyl ether has a vapor pressure of 377 torr. This due to strong hydrogen bonds_between water molecules. * The individual compounds in a mixture each exert its own pressure (partial pressure) * -The sum of the partial pressures equals to the total vapor pressure of the solution * As we increase the temperature the vapor pressure of a liquid increases. | Substance | 20 °C | 25 °C | 50 °C | |---------------|------------------|--------------|----------------| | water | 17.535 torr | 23.8 torr | 92.5 torr | | diethyl ether | 377 torr | 470 torr | 1325 torr | ### Clausius-Clapeyron Equation: Heat of vaporization The relationship between the vapor pressure and absolute temperature of liquid is expressed by the Clausius-Clapeyron Equation. $log\frac{P_2}{P_1} = \frac{\Delta H_v(T_2-T_1)}{2.303 \ RT_1T_2}$ * Molar heat of vaporization (∆Η») is the energy required to vaporize 1 mole of a liquid. ### Example Compute the vapor pressure of water at 120°C. The vapor pressure p1 of water at 100°C is 1 atm, and ∆Hv may be taken as 9720 cal/mole for this temperature range. Thus, $log\frac{p_2}{1} = \frac{9720 \times (393-373)}{2.303 \times 1.987 \times 393 \times 373}$ $p_2 = 1.95 \ atm$ ### Boiling point * if a liquid is placed in an open container and heated until the vapor pressure equals the atmospheric pressure, the vapor will form Bubbles that rise rapidly through the liquid and escape into gaseous state. * The temperature at which the (equilibrium) vapor pressure of a liquid equals the external pressure (atmospheric pressure) is called the boiling point. * The normal boiling point is the temperature at which a liquid boils when the external pressure is 1 atm. Liquids with high vapor pressures (Volatile compounds) require relatively little energy (heat) to increase the vapor pressure to match the applied (atmospheric) pressure, and thus, boil, i.e. they have low_boiling points. * Liquids with low vapor pressures require considerably more energy to increase the vapor pressure to the point where it matches the applied pressure, thus, they have relatively high boiling points ### Factors that affect boiling point: * Atmospheric pressure * The boiling point of liquid increases with the increase of atmospheric pressure (at lower altitude) * Intermolecular forces: * London dispersion forces < Dipole-Dipole interactions < Hydrogen bonds * There is a relationship between attractive forces and boiling point. The stronger the attractive forces, the higher the boiling point. | Compounds with | | Compounds with | | Compounds with | |----------------|---|---|---|----------------| | dispersion forces | | dipole-dipole Interactions | | hydrogen bonding | | | | | | | | Increasing strength of intermolecular forces | | | | | | Increasing boiling point | | | | | * **CH3CH2CH2CH2CH3** **pentane** * **bp = 36 °C** * **CH3CH2CH2CHO** **butanal** * **bp = 76 °C** * **CH3CH2CH2CH2OH** **1-butanol** * **bp = 118 °C** * **Increasing strength of intermolecular forces** * **Increasing boiling point** * **Number of sites for intermolecular interactions (surface area):** * Larger surface (more electrons) → more sites for London → ↑b.f * **Molecular shape: With the same molecular weight.** * Linear CH3-CH2-CH2-CH2-CH3 > branched * **Boiling point of alcohol higher than hydrocarbons of the same molecular weight because the presence of hydrogen bonds between molecules of alcohol.** * **CH3-CH2-OH > CH3-O-CH3** * **Boiling point of carboxylic acid is high because the presence of hydrogen bonds between 2 molecules (dimer).** ## SOLIDS AND THE CRYSTALLINE STATE * The solids can be divided into two groups: * Crystalline-particles are in highly ordered arrangement. ex, crystalline SiO2 * Amorphous—no particular order in the arrangement of particles, not distinct melting point. Ex, amorphous SiO2, rubber, glass, nylon. ### Crystalline Solids * The structural units of crystalline solids, such as ice, sodium chloride, and menthol, are arranged in fixed geometric patterns or lattices. * Crystalline solids have definite shapes and an orderly arrangement of units. Solids, like liquids, are practically incompressible. * Crystalline solids show definite melting points, passing rather sharply from the solid to the liquid state. * The various crystal forms are divided into six distinct crystal systems based on symmetry. They are, together with examples of each, cubic (sodium chloride), tetragonal (urea), rhombic (iodine), monoclinic (sucrose), triclinic (boric acid), and hexagonal (iodoform). ### Types of Unit Cells | Unit Cell Type | a, b, c | α, β, γ | Example | |-------------------|--------------------|------------------------|--------------------| | Simple cubic | a=b=c | α = β = γ = 90° | - | | Tetragonal | a=b=c | α = β = γ= 90° | - | | Rhombic | abc | α = β = γ = 90° | - | | Monoclinic | azbzc | α = γ = 90°, β= 90° | - | | Triclinic | abc | αβγ 90° | - | | Hexagonal | a=b=c | α = β = 90°, γ = 120° | - | ### Types of Bonding in Crystalline Solids | Type of Solid | Form of | Forces between | Property | Examples | |-------------------|----------|------------------|----------------------------------------------------------------------------|--------------------------------------------------------------------------------| | Molecular solid | Molecules | London, dipole, | Soft, low MP, poor conductor | Argon, methane, sucrose, Dry ice | | | | dipole, hydrogen | | | | Covalent network | Atoms | Covalent | Very hard, highest MP/BP, poor conductor | C(graphite), C(diamond), quartz | | | | | | | | Ionic | Positive & | Electrostatic | Hard, High MP, poor conductor | NaCl | | | negative | attractions | | | | | ions | | | | | Metallic | Atoms | Metallic | Malleable, Low to very High MP, good conductor | Cu, alloy | | | | bonds | | | ### Polymorphism * Many pharmaceutical solids can exist in different physical forms. * Polymorphism is the ability of a drug substance to exist as two or more crystalline phases that have different arrangements and/or conformations of the molecules in the crystal lattice. * Amorphous solids consist of disordered arrangements of molecules and do not possess a distinguishable crystal lattice. * Solvates are crystalline solid adducts containing amounts of a solvent incorporated within the crystal structure. If the incorporated solvent is water, the solvates are also commonly known as hydrates. * Polymorphs and/or solvates of a pharmaceutical solid can have different physical properties such as melting point, apparent solubility, dissolution rate, optical and electrical properties, vapor pressure, and density. * Numbers of methods have been employed for characterizing polymorphs in pharmaceutical solids. Polarizing optical microscopy and thermomicroscopy have proven to be useful tools. Thermal analysis procedures, such as differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA), can be used to obtain additional information. ### Examples on polymorphism * Theobroma oil is capable of existing in four polymorphic forms: the unstable gamma form, melting at 18°C; the alpha form, melting at 22°C; the beta prime form, melting at 28°C; and the stable beta form, melting at 34.5°C. * The polymorphic state of chloramphenicol palmitate has a significant influence on the biologic availability of the drug. * Cortisone acetate exists in at least five different forms, four of which are unstable in the presence of water and change to a stable form.