The publication of the first edition of Physical Pharmacy generated broad excitement throughout the national and international academic and industrial research communities in pharmacy and the pharmaceutical sciences. In addition, purchasers of the text can access the searchable full text online by going to the Martin's Physical Pharmacy and Pharmaceutical Sciences, Sixth Edition, website at thePoint.lww.com/Sinko6e.
INTRODUCTION
1 Understanding of the basic tools needed to analyze and interpret data sets from the clinic, laboratory or literature. 10 Explain the slopes of the lines and how they relate to absorption and elimination from the body.
Each assignment must be read and explained, and assigned problems must be solved outside the classroom. The teacher's comments will then serve to clarify doubtful points and help the student to improve his or her judgment and reasoning ability.
MEASUREMENTS, DATA, PROPAGATION OF UNCERTAINTY
The number of significant digits in numbers like 11,000 is uncertain because a decimal point is missing. Both zeros in the value are significant and the number contains a total of four significant digits.
In using logarithms for multiplication and division, retain the same number of significant figures in the mantissa as there are in the original numbers. This does not mean that you made a mistake in the experiment or the collection of the data.
ERROR AND DESCRIBING VARIABILITY
The techniques used to analyze the accuracy of results, which in turn provide a measure of the undetermined errors, will be considered first, and the detection and elimination of determined errors or inaccuracies will be discussed later. While the population is the entire category considered, the sample is the portion of the population used in the analysis.
DESCRIPTIVE STATISTICS
The standard deviation σ (the Greek lowercase letter sigma) is the square root of the mean of the squares of the deviations. A sample calculation involving the arithmetic mean, the standard deviation, and the estimate of the standard deviation follows.
VISUALIZING RESULTS: GRAPHIC METHODS, LINES
A plot of the logarithm of oil separation from an emulsion versus concentration on a rectangular grid. The absorption rate is greater than the elimination rate to the left of the vertical line in Figure 1–6.
CHAPTER SUMMARY
By inserting an actual value of x into equation (1–19), we obtain the value of y to be found at that particular value of x. The value agrees with the experimental value, and so this point lies on the statistically calculated slope plotted in Figure 1–8.
Recommended Readings
4 Appreciate the differences in the strength of intermolecular forces, which are responsible for the stability of structures in different aggregate states. 7 Describe the pharmaceutical significance of the various states of matter for drug delivery systems by referring to specific examples in the text boxes.
BINDING FORCES BETWEEN MOLECULES
1 Understand the nature of the intra- and intermolecular forces involved in the stabilization of molecular and physical structures. In this position, the potential energy of the two molecules is a minimum and the system is most stable (Fig. 2-1).
If two magnets of the same size are slid onto a table so that the opposite poles completely overlap, the resulting interaction is attractive and energetically the most favored configuration. a) The attractive, (b) partially repulsive, and (c) fully repulsive interactions of two magnets brought together. The nature of the molecules determines which of these factors is most influential on the attraction.
STATES OF MATTER
In hydrogen chloride, a molecule with about 20% ionic character, the effect of orientation is still important, but the dispersion force contributes a large part to the total interaction energy between the molecules. Hydrogen iodide is mainly covalent, with its intermolecular attraction supplied mainly by the London force or dispersion.
The ionic crystal sodium chloride is included in Table 2-2 for comparison to show that its stability, as reflected in its large total energy, is much greater than that of molecular aggregates, and yet the dispersion force exists in such ionic compounds even as it does. in molecules.
THE GASEOUS STATE
The approximate molecular weight of a gas can be determined using the ideal gas law. The fundamental kinetic equation (2–9) turns out to be comparable to the ideal gas equation, because the kinetic theory is based on ideal state assumptions.
THE LIQUID STATE
The pressure of the saturated vapor above the liquid is then known as the equilibrium vapor pressure. The temperature at which the vapor pressure of the liquid is equal to the external or atmospheric pressure is known as the boiling point.
SOLIDS AND THE CRYSTALLINE STATE
Ray Diffraction
The lowering of the melting point with increasing pressure is used in ice skating. The pressure of the skate lowers the melting point and thus causes the ice under the skate to melt.
THE LIQUID CRYSTALLINE STATE
This phenomenon is probably because alkanes with an odd number of carbon atoms are less efficiently packed into the crystal. In the smectic state, the molecules are mobile in two directions and can rotate about a single axis (Figure 2–15a).
PROPERTIES AND SIGNIFICANCE OF LIQUID CRYSTALS
It is these intermediate states that make up the liquid crystalline phase or mesophase, as the liquid crystalline phase is called. Friberg wrote a monograph on liquid crystals.35b For a more detailed discussion of the liquid crystal state, see the review by Brown,37 which serves as a handy introduction to the literature.
THE SUPERCRITICAL FLUID STATE
The loss of the flavor-adding compounds resulted in a poor taste and an unacceptable product. Additional studies showed that adding water to the supercritical CO2 significantly reduced the loss of flavor.
THERMAL ANALYSIS
R in turn depends on the temperature, the nature of the sample and the packaging of the material in the pans. As the sample is heated or cooled, the response will vary because the mobility of the molecular dipoles will change.
A positive change in weight would indicate that the solid is absorbing (collectively called sorption) the solvent, in this case water, from the atmosphere inside the container. Water vapor sorption/desorption can be used to study changes in the solvate state of a crystalline material.55,56 Variations of commercial instruments also allow the determination of sorption/desorption of other solvents.
PHASE EQUILIBRIA AND THE PHASE RULE
Since we need to know two variables to fully define a gaseous system, we say that the system has two degrees of freedom. Similarly, if the temperature of a gas is defined, the volume, pressure, or some other variable must be known to fully define the system.
CONDENSED SYSTEMS
By separating the two phases, we would find 75 g of phase A (containing 11% by weight phenol) and 25 g phase B (containing 63% by weight phenol). Curves on the triangle diagrams at temperature 1, t2 and t3. b) The three-dimensional arrangement of the diagrams in the order of increasing temperature.
1 Understand the theory of thermodynamics and its use to describe energy-related changes in reactions. Thermodynamics deals with the quantitative relationships of interconversion of the various forms of energy, including mechanical, chemical, electrical and radiant energy.
THE FIRST LAW OF THERMODYNAMICS
Equation (3–1) also expresses the fact that work and heat are equivalent ways of changing the internal energy of the system. The internal energy is related to the microscopic movement of the atoms, ions or molecules of which the system is composed.
The following example shows the type of problem that can be solved using the first law of thermodynamics. If the volume of the system remains constant during the change of state, dV=0, the first law can be expressed as
THERMOCHEMISTRY
Some of the specific limitations placed on the law seen up to this point in the chapter, along with the resulting modifications to the law, are brought together in Table 3-1. A comparison of the entries in Table 3–1 with the material that has gone before will serve as a comprehensive review of the first law.
Many of the common covalent and other bond-type energies can be found commonly in books on thermodynamics, such as those listed in the footnote in the opening of this chapter. Because some heat is absorbed in the ionization of the weak electrolyte, the heat evolved falls below the value for the neutralization of completely ionized species.
THE SECOND LAW OF THERMODYNAMICS
It can be seen that only part of the heat Qhot (1000 cal) is converted into work (200 cal) in the engine. However, this spontaneity criterion is not practical because it requires a calculation of the entropy change in both the system and the surroundings.
THE THIRD LAW OF THERMODYNAMICS
Thus, the increase in entropy with increasing number of configurations is nicely described by the Boltzmann concept given in equation (3-46).
FREE ENERGY FUNCTIONS AND APPLICATIONS
With a phase change, the free energy changes for 1 mole of the liquid vapor are given by equation (3–72). Since the chemical potential of a solid is constant (it does not depend on its concentration), the equilibrium constant depends only on the pressure (or volatility) of the gases.
MOLECULAR STRUCTURE, ENERGY, AND RESULTING PHYSICAL PROPERTIES
2 Understand the differences in energy of these forces and how they relate to different molecules. 4 Understand the differences between atomic and molecular spectroscopic techniques and the information they provide.
ADDITIVE AND CONSTITUTIVE PROPERTIES
The molar refractions of the atoms are additive, but the carbon and oxygen atoms are constitutive in refraction. The rest of this chapter describes some of the well-defined interactions that are important for determining the physical properties of molecules.
DIELECTRIC CONSTANT AND INDUCED POLARIZATION
The capacitance of the capacitor in Figure 4–3 depends on the type of medium separating the plates as well as the thickness. If the capacitance ratios are close, then there is greater resistance to charge separation.
The electronic structure will not favor a large charge separation in the molecule and must have a lower dielectric constant. This will cause an interaction of the molecule relative to the ions in solution and produce an induced dipole.
PERMANENT DIPOLE MOMENT OF POLAR MOLECULES
1.43 =46.5 cm3/mol The concept of induced dipole moments can be extended from the condenser model just discussed to the model of a nonpolar molecule in solution surrounded by ions. The distribution and ease of attraction or repulsion of electrons in the nonpolar molecule will influence the magnitude of this induced dipole, as well as the applied external electric field strength.
ELECTROMAGNETIC RADIATION
The electric field component is largely responsible for phenomena such as transmission, reflection, refraction, absorption, and emission of electromagnetic radiation, which give rise to many of the spectroscopic techniques discussed in this chapter. The magnetic component is responsible for the absorption of energy in electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR), techniques described at the end of the chapter.
ATOMIC AND MOLECULAR SPECTRA
The energy of a photon of electromagnetic radiation E is related to the frequency of the radiation by equation (4–12). The energy required for this process, which leads to the ionization of the atom according to.
ULTRAVIOLET AND VISIBLE SPECTROPHOTOMETRY
Small differences in the vibrational and rotational nature of the excited electronic state complicate the spectrum. A= −logT =log(I0/I)=εbC (4–16) where I0 is the intensity of the incident light beam and I is the intensity of the light after it exits the sample.
FLUORESCENCE AND PHOSPHORESCENCE
The singlet (S) and triplet (T) states relate to the electronic structure of the molecule after excitation. Schulman and Sturgeon18 provide a thorough review of the use of photoluminescence for the analysis of traditional medicines.
INFRARED SPECTROSCOPY
The frequencies of the infrared absorption bands closely match the vibrations from certain parts of the molecule. Infrared spectra can be complex, and the characteristic frequencies vary depending on the physical state of the molecule.
NEAR-INFRARED SPECTROSCOPY
The exact position and shape of the infrared band associated with the hydroxyl group depends on the concentration of the alcohol and the degree of hydrogen bonding. A thorough review of infrared spectroscopy techniques and applications is provided by Smith21 and Willard et al.22.
ELECTRON PARAMAGNETIC AND NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY
The multiple splitting pattern can provide valuable information about the nature of neighboring nuclei. As the natural abundance of the isotope decreases, the relative sensitivity of NMR becomes proportionally smaller.
REFRACTIVE INDEX AND MOLAR REFRACTION
Molar polarization, Pi [equation (4-16)], can be considered roughly equivalent to molar refraction, Rm, and can be written as. 3πNαp (4–27) From this equation, the polarizability, αp, of a non-polar molecule can be obtained by a refractive index measurement.
OPTICAL ROTATION
The subscript Don [α] indicates that the measurement of specific rotation is made at a wavelength, λ, of 589 nm for sodium light. The specific rotation of steroids, carbohydrates, amino acids and other compounds of biological importance is given in the CRC Handbook.35.
OPTICAL ROTATORY DISPERSION
Organic chemists use specific rotation as a tool to help confirm the identity of a synthesized compound whose molecular properties are already defined. Changing the wavelength of light changes the specific rotation of the optically active substance due to the electronic structure of the molecule.
CIRCULAR DICHROISM
Variation of the spin angle (solid line) in the vicinity of an absorption band of polarized light (dashed line). Circular dichroism has also been applied to the determination of penicillin activity, as described by Rasmussen and Higuchi.42 Activity was measured as a change in the CD spectra of penicillin upon addition of penicillinase, which enzymatically cleaves the β-lactam ring. to form the penicillate ion, as shown for benzylpenicillin in Figure 4-27.
ELECTRON AND NEUTRON SCATTERING AND EMISSION SPECTROSCOPY
These emissions can be measured over a linear region of the sample or in the entire sample. SEM provides a picture of the surface of the split tablet that can be used to look at formulation conditions.
A solution consisting of only two substances is known as an abinary solution, and the components or constituents are referred to as the solvent and the solute. However, when a solid is dissolved in a liquid, the liquid is usually taken as the solvent and the solid as the solute, regardless of the relative amounts of the ingredients.
PHYSICAL PROPERTIES OF SUBSTANCES
CONCENTRATION EXPRESSIONS
Mole fraction X,N The ratio between the moles of one component (eg solute) of the solution and the total number of moles of all components (solute and solvent). Volume percentage is expressed as the volume of solute in milliliters in 100 ml of solution.
EQUIVALENT WEIGHTS
What is the number of equivalents per mole of K3PO4, and what is the equivalent weight of this salt. When used for its phosphate content, the equivalent weight of KH2PO4 is one third of the molecular weight g, because the valence of phosphate is 3.
IDEAL AND REAL SOLUTIONS
If used for its potassium content, the equivalent weight is identical to its molecular weight, or 136 g. The molecular weight and therefore the equivalent of NaCl is 58.5 g/Eq or 58.5 mg/mEq.
The partial vapor pressure of the components is greater than expected by Raoult's law and the system should show a positive deviation. The higher the vapor pressure of a liquid - that is, the more volatile it is - the lower the boiling point.
COLLIGATIVE PROPERTIES
If the vapor pressure curves show a minimum (ie negative deviation from Raoult's law), the azeotrope has the highest boiling point of all possible mixtures; therefore, it is the least volatile and remains in the flask while pure A or pure B is distilled off. Mixtures of ethanol and water and methanol and benzene behave in the opposite way, with minima on the boiling point curves and maxima on the vapor pressure curves.
Due to this fact, the freezing point of a solution is always lower than that of the pure solvent. The vapor pressure p◦ of water in the pure solvent under the influence of the atmospheric pressure Po.
MOLECULAR WEIGHT DETERMINATION
It was found that 15 grams of the new drug dissolved in water to make 1000 ml of solution at 25°C produced an osmotic pressure of 0.6 atm. We replace the molality from the equation m=Tf/Kf with the equation of osmotic pressure,π =RTm to obtain at 0◦C,.
PROPERTIES OF SOLUTIONS OF ELECTROLYTES
Arrhenius1 was able to combine the results of these various investigations into a broad generalization known as the theory of electrolytic dissociation. This chapter begins with a discussion of some of the properties of ionic solutions that led to Arrhenius' theory of electrolytic dissociation.
Equation (6–17) can thus be written as Subscriptxis is no longer needed onRand is therefore dropped.) It would be difficult to measure landA, but it is a simple matter to determine the cell constant experimentally. What is the specific conductivity and what is the equivalent conductivity of the solution at this concentration.
THEORY OF ELECTROLYTIC DISSOCIATION
The equivalent conductance of acetic acid at 25◦C and at infinite dilution is 390.7 ohm cm2/eq. In other words, according to the result of Example 6-7, the fraction of acetic acid present as free ions in a 0.10 m solution is 0.011.
THEORY OF STRONG ELECTROLYTES
The Van't Hoff factor, i, can be related to the degree of dissociation, α, as follows. The degree of dissociation of a weak electrolyte can be satisfactorily calculated from the conductivity ratio oc/0 or obtained from the van't Hoffi factor.
It is customary to define the activity of the solvent on the mole fraction scale. Under this condition, the mole fraction can be set equal to the activity of the solvent, or.
COEFFICIENTS FOR EXPRESSING COLLIGATIVE PROPERTIES
Zografi et al.11 used the extended Debye–H¨uckel equation [(Eq. (6–61))] in the study of the interaction between orange dye II and quaternary ammonium salts.
For accuracy in the preparation and labeling of parenteral solutions, osmolality should be carefully measured with a vapor pressure or freezing point osmometer (rather than by calculation) and the results converted to osmolarity using Equation (6–65) or (6–66). In Example 6–20, it is found that although NaCl contributes mainly to blood osmolality and lowering its freezing point, a value of 1 was used for blood instead of gν=1.86 for NaCl solution.
Recommended Reading
This value is of course equivalent to a freezing point lowering of +0.5712◦C below the freezing point of water because the freezing point of water is taken as 0.000◦C at atmospheric pressure. The milliosmolality for blood obtained by various workers using osmometry, vapor pressure and freezing point depression apparatus varies from approximately 250 to 350 mOsm/kg.17 The normal osmolality of body fluids is stated in medical textbooks18 as 275 to 295 mOsm/kg. , but normal values are likely to fall in an even narrower range of 286 ± 4 mOsm/kg.19.
3 Understand the concepts of acid-base equilibria and the ionization of weak acids and weak bases. Other theories have been proposed for describing acid-base reactions, the most famous of which is Lewis's electronic theory.3.
According to Lewis theory, an acid is a molecule or ion that accepts an electron pair to form a covalent bond. The Lewis system is probably too broad for convenient use in common acid-base reactions, and those processes most conveniently expressed in terms of this electronic classification should simply be designated as a.
ACID–BASE EQUILIBRIA
Calculate the pH of a 1 g/100 ml solution of ephedrine sulfate. a) Ephedrine sulfate, (BH+)2SO4, completely dissociates into two BH+ cations and one SO42 anion. Calculate the pH of a solution containing succinic acid and tribasic sodium phosphate, each at a concentration of 0.01 M. The second acidity constant for the succinic acid system is 2.3 × 10-6.
ACIDITY CONSTANTS
The student must understand the concepts of acid-base equilibria and ionization of weak acids and weak bases. 2 Understand the relationship between pH, pKa and ionization for weak acids and weak bases.
THE BUFFER EQUATION
The pH of the buffer solution containing acetic acid and sodium acetate is determined using the buffer equation (8–8): Addition of neutral salts to buffers changes the pH of the solution by changing the ionic strength, as shown in equation (8-13).
BUFFER CAPACITY
Therefore, increasing the concentration of the buffer components results in greater buffer capacity or efficiency. What is the maximum buffer capacity of an acetate buffer with a total concentration of 0.020 mol/liter.
What is the buffer capacity of a hydrochloric acid solution with a hydrogen ion concentration of 10−2 mol/liter. The buffering capacity of a solution of the strong acid HCl is marked below a pH of 2, and the buffering capacity of a strong base NaOH becomes significant above a pH of 12.
BUFFERS IN PHARMACEUTICAL AND BIOLOGIC SYSTEMS
S¨orensen14 suggested a mixture of salts of sodium phosphate for buffer solutions of pH 6 to 8. Potassium chloride is added to (e), the borate buffer, to achieve an ionic strength comparable to that of (d), the phosphate. buffer, where the pH in the two buffer series overlaps.
Especially when the electrolyte concentration is high, it can be found that the pH calculated using the buffer equation is somewhat different from the experimental value. Thus, the buffering capacity should be optimized to produce rapid absorption and minimal gastric irritation of orally administered aspirin.
Hind and Goyan25 pointed out that the pH for maximum stability of an ophthalmic drug may be well below that of the optimal physiological effect. Under such conditions, the drug solution can be buffered at a low buffer capacity and at a pH that is a compromise between that of optimal stability and the pH for maximum therapeutic effect.
BUFFERED ISOTONIC SOLUTIONS
However, when the solution is drunk into the eye, the tears participate in the gradual neutralization of the solution; conversion of the drug takes place from the physiologically inactive form to the undissociated base. As the base is absorbed at the pH of the eye, more of the salt is converted into base to preserve the constancy of pKb; thus the alkaloidal agent is gradually absorbed.
One of the first references to the determination of the freezing point of blood and tears (as was necessary to make solutions isotonic with these liquids) is that of Lumiere and Chevrotier,32 in which the values are −0.56◦C and −0.80◦C given for the two liquids respectively. In the class I methods, sodium chloride or another substance is added to the solution of the drug to lower the freezing point of the solution to −0.52◦C and thus make it isotonic with body fluids.
Methods
If we wanted to use dextrose instead of sodium chloride to adjust the tonicity, we would estimate the amount by setting the following ratio. X= Y(additional amount of NaCl for isotonicity) E(grams of NaCl corresponding to 1 g of isotonic agent). 8–46), where X is the grams of isotonic substance required to adjust tonicity, Y is the additional amount of NaCl for isotonicity over and above the osmotic equivalence of NaCl provided by the drugs in solution, and E is the sodium chloride equivalent of the isotonic substance. .
Methods
To complete the isotonic solution, enough isotonic sodium chloride solution, another isotonic solution, or an isotonic buffered dilution solution is added to make 30 mL of the final product. The volume of isotonic solution in milliliters for 1 g of the drug can also be tabulated if desired by multiplying the values in column 4 by 3.3.).
GENERAL PRINCIPLES
The entropy of the system increases due to the mixing of the solute and the solvent (entropy of mixing), but it also decreases locally due to the new short-range order introduced by the presence of the solute, as shown by the molecules of light purple.”4 (Adapted from Bhattachar et al. 2006.4). The United States Pharmacopeia (USP) describes the solubility of drugs as the fraction of solvent required per fraction of solution.
SOLVENT–SOLUTE INTERACTIONS
As the length of a nonpolar chain of an aliphatic alcohol increases, the solubility of the compound in water decreases. Branching of the carbon chain reduces the nonpolar effect and leads to increased water solubility.
The difference in the acidic and basic character of the components in the Lewis donor-acceptor sense also contributes to specific interactions in solutions. In addition to the factors already listed, the solubility of substances also depends on structural characteristics, such as the ratio between polar and non-polar groups of the molecule.
SOLUBILITY OF LIQUIDS IN LIQUIDS
In a system such as phenol and water, the mutual solubilities of the two conjugate phases increase with temperature until the compositions at the critical solution temperature (or the upper solution temperature) become identical. What is the weight of the aqueous layer and of the phenolic layer in 500 g of the mixture, and how many grams of phenol are there in each of the two layers.
SOLUBILITY OF SOLIDS IN LIQUIDS
An analogous derivation can be performed to obtain the equation for the solubility of a weak base as a function of the pH of a solution. This phenomenon is known as cosolvency, and solvents that, in combination, increase the solubility of the solute are called cosolvents.
What is the minimum pH required for complete solubility of the drug in a stock solution containing 6 g of phenobarbital sodium in 100 ml of a 30% by volume alcoholic solution. The molecules of a-amino-n-butyric acid pack less efficiently into the crystal, partly because of the protruding side chains, and the crystal energy is reduced.
DETERMINING THERMODYNAMIC AND “KINETIC” SOLUBILITY
