Lecture 10 - Fall 2024.pdf

Foundations of Pharmaceutical Sciences Lecture #10 I. Introduction to Ionic Equilibria II. pH calculations Dr. Lewis Stevens [email protected] 1  General guidelines for this module 1. Ask questions....

Foundations of Pharmaceutical Sciences Lecture #10 I. Introduction to Ionic Equilibria II. pH calculations Dr. Lewis Stevens [email protected] 1  General guidelines for this module 1. Ask questions. We have a fair amount of material to cover. Spend some time every day reviewing concepts. Each will build on the other, so if the material is confusing, contact me EARLY. Email me questions, and I’ll get back within a day, but usually sooner. If the question doesn’t translate well in email (molecular structures, lots of math, etc.), call my office phone: 319-335-8823. 2. Use the homework as a study guide. Numerical keys will be posted to ICON later. 3. An equation sheet (posted to ICON same time as the homework) will be provided at this end-of-module exam. Don’t spend time memorizing equations, our goal is to learn what they mean and when to apply them. Use the lecture slides from this module and the homework as your end-of-module exam study guides. 2  Learning objectives for this module 1. Describe the significance of ionic equilibria to understanding how pharmaceuticals work. 2. From a drug’s molecular structure, identify the functional group(s) that impart the drug’s acid/base properties and assign reasonable pKa values. 3. Estimate/calculate the pH of drug (free form and salt form) solutions and the fraction ionized. 4. Describe the preparation of a buffer for a specific pH and calculate its buffering capacity. Identify pharmaceutically relevant buffer systems. Distinguish the relative components of a drug solution formulation. 5. Estimate/calculate the predicted affect of pH change on the solubility of a drug. 3  Overview Introduction to acid-base equilibrium Describe and quantify equilibrium using KA, KB, KW, pKA, pKB and pH expressions Describe Brönsted-Lowry acid-base theory Distinguish strong and weak acids/bases Rank order weak acids/bases in terms of strength using KA, KB, pKA or pKB Identify classes of organic functional groups that contribute to the acid/base properties of drugs Assign predicted pKA values to specific functional groups pH equations and calculations for strong and weak acids 4  Introduction You’ve been introduced the BCS classification system with two primary discriminators Solubility Permeability Each of these are directly impactful to amount of drug that is available to the site of action The solubility of a drug is significantly impacted by the drug’s ionization state (charged or not) Ionized forms are MORE water-soluble but less lipid-soluble Non-ionized forms are MORE lipid-soluble, i.e. more permeable to lipid membranes Changes in the ionization state can directly affect: Drug solubility Absorption/bioavailability Drug stability 5  Introduction Many drugs are weak acids or bases which change their Compartment pH ionization state (charged vs. not Gastric acid 1-4 charged) as the pH in the body Lysosomes 4.5 changes. Human skin 5.5 Far majority of current drugs are weak Urine 6.0 acids/bases (∼ 95%) Pure H2O at 37 °C 6.81 Healthy human saliva 6.5-7.4 To understand drug action requires Cytosol 7.2 a recognition of a drugs’ acid/base Cerebrospinal fluid (CSF) 7.5 properties. Blood 7.34–7.45 Mitochondrial matrix 7.5 Small changes in pH can yield Pancreas secretions 8.1 significant changes in ionization state Affects drug absorption and its distribution through the body 6  Introduction Where does a drug pass upon ingestion? Note the wide range of pH exposures as the drug moves through the body. Stomach: pH = 1 – 3 Duodenum: pH = 6 Small intestine (jejunum, ilium): pH = 7 – 8 Blood: pH = 7.4 We suspect already that various pH environments are going to impact the ionization state of our drug. Higher water solubility with the ionized form. Higher lipid solubility (think higher absorption) with the unionized form. We’re going to address this through our concept of fraction ionized. 7  Introduction Generally, orally delivered drugs are absorbed into small intestine through passive diffusion. Cell-to-cell tight junctions limits paracellular (“para” = beside) drug absorption. Particularly for biologics (proteins, peptides, monoclonal antibodies, etc.) An ionized form of the drug is less lipid soluble, and thus absorption would be slowed/reduced. Changes to bioavailability The extent (or fraction) of ionization changes as a function of pH 8  Introduction An example PCOA (Pharmacy Curriculum Outcomes Assessment) question. One tool to assess your preparation in Key concept: Non-ionized form is more lipophilic. basic sciences for the NAPLEX 9  Introduction A first step is to define criteria by which we classify acids and bases Our definition of acids and bases follows that of Bronsted-Lowry theory Acids – a species that can donate a proton (H+) Note, the strength of an acid depends upon its ability to donate a proton. Strong acids easily donate a proton, weak acids have a slight tendency to donate a proton Base – a species that can accept a proton For relevance we restrict ourselves to acid/base behavior in an aqueous system with pH from 0 – 14 This will limit the number of ionizable functional groups we need to be concerned about. 10  Introduction The question becomes, how are these ionizable species going to react in water? To understand that question, we need to first look at water itself before introducing the acid or base. autoionization of water For pure water, there exists an equilibrium balance between H3O+, OH- and H2O and that balance is described by KW. 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝐻𝐻3 𝑂𝑂+ 𝑂𝑂𝐻𝐻 − 𝐾𝐾𝑊𝑊 = = = 𝐻𝐻3 𝑂𝑂+ 𝑂𝑂𝐻𝐻 − = 1 × 10−14 @ 25 oC 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝐻𝐻2 𝑂𝑂 2 For pure water, [H3O+] and [OH-] are the same. Two important concepts that stem from this. In pure water [H 3O + ] = [OH − ] =1×10−14 = 1×10−7 pH for pure water = 7.0 11  Introduction Water, being the solvent we’re concerned with can act as either an acid or a base (amphoteric), i.e. we could write two equilibrium expressions. One with water accepting H+ and one with water donating H+. K KA = [H O ][A ] 3 + −  → HA + H 2O ← A +  H 3O + A − [HA] KB [ ][ ] K A K B = H 3O + OH − = KW  → HA] [OH − ] A− + H 2O ← −  OH + HA KB = [ [A ] − From the expression on the far right for KW, then we may write: pKA + pKB = pKW = 14 and pH + pOH = pKw = 14 𝑝𝑝𝑋𝑋 = − log 𝑋𝑋 Thus, if you’re provided one (pKA or pKB) you can easily convert to the other. This will be useful when we calculate pH. 12  Introduction Now, when an acid is added to water, [H3O+] ↑ 𝐾𝐾𝑊𝑊 = 𝐻𝐻3 𝑂𝑂+ 𝑂𝑂𝐻𝐻 − = 1 × 10−14 => [OH-] ↓ to maintain equilibrium KW at 1x10-14 This is an intrinsic property of water and doesn’t change when => solution is acidic (pH < 7) you add an acid/base to water. What changes is the relative hydronium and hydroxide When, a base is added to water, [OH-] ↑, [H3O+] ↓ concentration! => solution is basic (pH > 7) We’ll discuss this more during next lecture of calculating pH, but keep this general concept in mind. Add an acid to water, pH goes down (below 7), [H3O+] ↑ and [OH-] ↓ Add a base to water, pH goes up (above 7), [H3O+] ↓ and [OH-] ↑ 13  Introduction Note this process of donating and accepting protons occurs between specific pairs of partners, and we refer these as below,  → H O + + A− HA + H 2O ← Acid (unionized, free form) → Conjugate base  3 (ionized, deprotonated) Base (unionized, free form) → Conjugate acid  → BH + + OH − B + H 2O ← (ionized, protonated)  Acid Base Conjugate acid Conjugate base 14  Introduction Conjugate species are related by the loss or gain a single proton (H+) Consider ibuprofen in solution, what are the conjugate species? Is water acting like an acid or a base? We’ll see this idea of conjugate species when we discuss, Fraction ionized Henderson-Hasselbalch equation Buffers Solubility Hence, be sure this concept is well established to you. 15  Introduction Conjugate species are related by the loss or gain a single proton (H+) Consider ibuprofen in solution, what are the conjugate species? Is water acting like an acid or a base? acid base conjugate base conjugate acid 16  Introduction KA To develop our quantitative description of  → H O + + A− HA + H 2O ← acid-base behavior, consider the following  3 general weak acid (HA) chemical reaction KA is the equilibrium constant referred to as KA = [H O ][A ] 3 + − pK A = − log(K A ) the acidity constant [HA] KA (or pKA) provides us ability to distinguish and rank-order acids from strong to weak. Strong acid. Is KA large Remember, strong acids essentially or small? completely dissociate into separate ions: HCl (hydrochloric acid) H2SO4 (sulfuric acid) Weak acid. HI (hydroiodic acid) Is KA large HClO4 (perchloric acid) or small? HNO3 (nitric acid) HBr (hydrobromic acid) 17 Introduction KA = [H O ][A ] 3 + − pK A = − log(K A ) [HA] This is what you would expect for a strong acid (like those listed on previous slide, HCl, HBr, etc.). In a strong acid you get complete dissociation, and KA would be very large (and pKA very small, actually negative). Very little of the free form (HA) dissociated into H+ and A-, and KA is thus much smaller. This is typical behavior for most of the weak acids we’re going to work with. 18  Introduction Remember these general guidelines, as the strength of the acid increases, [H3O+] increases KA increases pKA decreases Consider the following series of weak acids. How would you rank order their relative strengths (highest to lowest)? Pentobarbital Acetaminophen Ibuprofen pKA = 8.1 pKA = 9.46 pKA = 4.91 19  Introduction Consider the following series of weak acids. How would you rank order their strengths (highest to lowest)? Pentobarbital Acetaminophen Ibuprofen pKA = 8.1 pKA = 9.46 pKA = 4.91 Remember that if KA goes up, pKA goes down. Since a higher KA equals a stronger weak acid, that also means a lower pKA indicates a stronger weak acid. In the above questions, the strongest weak acid is ibuprofen, followed by pentobarbital, followed last by acetaminophen. 20  Introduction In the literature, however, you rarely see explicit reference to pKB but rather only pKA. When you retrieve a literature value, a listed pKA value alone does NOT imply the drug substance is an acid only. You need another piece of information (like molecular structure) to ascertain whether the drug is an acid or a base. pKA = 9.2 For a weak base, if a pKA is listed it referring to the pKA of the conjugate acid of the weak base. Consider codeine (a weak base), Base Acid Conjugate Conjugate Acid Base But, it’s easy to convert. Remember, pKA + pKB = 14 21  Introduction Need to be able to recognize common functional groups in drug molecules that impart acid/base properties to the drug. For weak acids, we’ll focus on six groups: 1. Sulfonic Acids (R-SO3H) 2. Carboxylic Acids (R-COOH) benzene sulfonic acid formic acid acetic acid Estimated pKA range 0 - 2 Estimated pKA range 3 - 5 22  Introduction Continuing on the series of organic weak acids: 3. Aryl Sulfonamides (Ar-SO2NHR) 4. Phenols (Ar-OH) benzene sulfonamide phenol p-nitrophenol Estimated pKA range 6 - 9 Estimated pKA range 8 - 11 23  Introduction And finally we have: 5. Imides (R-OCNHCO-R) 6. Thiols (R-SH) thiophenol phthalimide Estimated pKA range 8 - 10 Estimated pKA range 9 - 11 24  Introduction Taking the entire set together we have, Question. If you were to separately prepare a 0.1 M solution of compound A and a 0.1 M solution of compound B, which would have the Organic weak acid Estimated pKA range lower pH? Increasing strength of the acid. group A B 1. Sulfonic Acids 0-2 2. Carboxylic Acids 3-5 3. Aryl sulfonamides 6–9 pKA = 8.1 pKA = 9.46 4. Phenols 8 – 11 5. Imides 8 – 10 6. Thiols 9 – 11 Commit these functional groups and their pKA ranges to memory. 25  Introduction Note that alcohols (with the exception of phenols) are absent from this list of organic weak acids. Those molecules that do not have any appreciable acid/base character are referred to as non-electrolyte. The pKA range for an alkyl alcohol (R-OH) is approximately 14 – 18. Consider glucose below: Physically this means at any realistic solution pH (between 0 and 14) this compound will NOT be ionized. 26  Introduction Alternatively, we to further identify organic weak bases, and we’ll consider five groups: 1. Aliphatic and alicyclic amines 2. Aromatic amine (Ar-NH2) Treat this class as essentially the same in strength of basicity, but typically: Secondary > Tertiary > Primary aniline Estimated pKB range, 9 – 13 Estimated pKA range, 1 - 5 Estimated pKB range, 3 – 4 Estimated pKA range, 10 - 11 27  Introduction Continuing on the series of organic weak bases: 3. Aromatic and heterocyclic nitrogens 4. Amidines (R-CNH-NH2) pyridine isoquinoline Estimated pKB range, 4 – 5 Estimated pKB range, 10 – 13 Estimated pKA range, 9 - 10 Estimated pKA range, 1 - 4 28  Introduction And finally we have: Taking the entire set together we have, 5. Guanidines (RHN-CNH-NH2) Organic weak Estimated pKB Increasing strength of the base. base group range 1. Guanidines 1-2 2. Aliphatic 3-4 nitrogens 3. Amidines 4–5 4. Ar-NH2 9 – 13 5. Aromatic 10 – 13 Estimated pKB range, 1 - 2 nitrogens Estimated pKA range, 12 - 13 Commit these functional groups and their pKB ranges to memory. 29  Introduction Note that amides are absent from this list of organic weak bases. An example amide functional group is shown below, For example, we’ve seen acetaminophen. We know the proton (circled in red) is acidic, but could the N (blue Amides have a pKB in the range of 15 – 17, square) accept a proton? which (as we saw for alcohols) means that any realistic solution pH (0 – 14) amides are NOT going to be ionized. 30  Introduction Note that amides are absent from this list of organic weak bases. An example amide functional group is shown below, For example, we’ve seen acetaminophen. We know the proton (circled in red) is acidic, but could the N (blue Amides have a pKB in the range of 15 – 17, square) accept a proton? which (as we saw for alcohols) means that any realistic solution pH (0 – 14) amides are NOT ANS: No, this nitrogen is part going to be ionized. of an amide functional group, it is therefore not basic (won’t accept a proton). 31  Introduction Based from these assignments, we can broadly classify molecules as, Classification Description Nonelectrolyte No acid or base functionality. Monoprotic acid Capable of donating 1 proton (H+)/molecule Polyprotic acid Capable of donating >1 proton/molecule Monoprotic base Capable of attaching 1 proton (H+)/molecule Polyprotic base Capable of attaching >1 proton/molecule Ampholyte Has both acid and base functionality. 32  Introduction Example 1. Identify the acidic and/or basic functional groups within the following. Assign estimated pKA value(s) to each of your identifications and classify the molecule. amoxicillin 33  Introduction Example 1. Identify the acidic and/or basic functional groups within the following. Assign estimated pKA value(s) to each of your identifications. aliphatic amine basic, pKA 10 - 11 Not acid or base because amoxicillin it’s an amide. Not an acid because there’s proton to donate. phenol acidic, pKA 8 - 11 Not acid or base because it’s an amide. carboxylic acid acidic, pKA 3 - 5 34  Introduction Example 2. Identify the acidic and/or basic functional groups within the following. Assign estimated pKA value(s) to each of your identifications. captopril 35  Introduction Example 2. Identify the acidic and/or basic functional groups within the following. Assign estimated pKA value(s) to each of your identifications. thiol Not acid or base because acidic, pKA 9 - 11 it’s an amide. captopril carboxylic acid acidic, pKA 3 - 5 36  Introduction Example 3. Identify the acidic and/or basic functional groups within the following. Assign estimated pKA value(s) to each of your identifications. cefaclor 37  Introduction Example 3. Identify the acidic and/or basic functional groups within the following. Assign estimated pKA value(s) to each of your identifications. aliphatic amine basic, pKA 10 - 11 Not acid or base because it’s an amide. cefaclor Not acid or base carboxylic acid because it’s an amide. acidic, pKA 3 - 5 38  pH calculations The pH scale is logarithmic representation of the [H3O+] concentration. pH is defined as, [ pH = − log H 3O + ] This equation may be re-written as Remember, because of KW we [H O ] = 10 3 + − pH can also say that, pH + pOH = 14 where, We see from above, if the pH were to change from pH = 1 ([H3O+] = 10-1) to pH = 2 ([H3O+] = 10-2) the pOH = − log[OH − ] [OH ] = 10 − − pOH [H3O+] decreased by a factor of 10. 39  pH calculations Example. What is Strong acids and strong bases completely dissociate the pH of a 0.1% w/v when added to water. HCl solution? HCl (aq) → H3O+ + Cl- MW of HCl = 36.5 NaOH (aq) → Na+ + OH- g/mol a) 1.00 b) 1.57 c) 3.00 d) 6.47 Complete dissociation means that none of original compound exists in solution, So, for every mole of HCl put into solution, you get one mole of H3O+ and one mole of Cl- Same is true for the NaOH example. Therefore, calculating pH of strong acid, 𝑝𝑝𝑝𝑝 = − log 𝐻𝐻3 𝑂𝑂+ = − log 𝐶𝐶𝑎𝑎 And for calculating pH of a strong base, 𝑝𝑝𝑝𝑝 = 14 − 𝑝𝑝𝑝𝑝𝑝𝑝 = 14 − − log 𝑂𝑂𝐻𝐻 − = 14 + log 𝐶𝐶𝑏𝑏 40  pH calculations Example. What is the pH of a 0.1% w/v HCl Strong acids and strong bases completely solution? MW of HCl = 36.5 g/mol dissociate when added to water. HCl (aq) → H3O+ + Cl- ANS: When calculating pH our NaOH (aq) → Na+ + OH- concentrations are required to be in molarity (M), i.e. mol/L. First, we need to convert the concentration provided above: Complete dissociation means that none of Ca = 0.1% w / v HCl = 1g HCl  1 mol    = 0.027 M HCl original compound exists in solution, 1 L  36.5 g HCl  So, for every mole of HCl put into solution, you get Now, we recognize that HCl is a strong acid, one mole of H3O+ and one mole of Cl- so we’re going to use, Same is true for the NaOH example. Therefore, calculating pH of strong acid, [ ] pH = − log H 3O + = − log[Ca ] = − log(0.027) = 1.57 [ ] pH = − log H 3O + = − log[Ca ] Our answer makes sense because if we put And for calculating pH of a strong base, an acid in water the pH would be below 7. ( [ ]) pH = 14 − pOH = 14 − − log OH − = 14 + log[Cb ] 41  pH calculations Now moving on to weak acids/bases, remember we had: We’re going to plug these values into here.  → H O + + A− [ H 3O + ][ A− ] HA + H 2O ←  3 (weak acid) Ka = [ HA]  → BH + + OH − B + H 2O ← (weak base) Kb = [ BH + ][OH − ]  [ B] So, when we put a e.g. weak acid in Species [ ]o Δ[ ] [Equil] solution, we can’t simply say that all the moles of HA become H3O+ and A- , but HA Ca -x Ca-x rather only some of HA is going to A- 0 +x x convert over. H+ 0 +x x Consider the ICE (Initial, Change, Starting Ending Equilibrium) table shown to the right. 42  pH calculations From the previous slide, for a weak acid in solution we may write: [ H 3O + ][ A− ] x⋅x x2 KA = = = [ HA] Ca − x Ca − x And once we find out what “x” equals, then we can calculate our pH. We could solve for “x” using the quadratic formula, 2 Use either of these − K a ± K a + 4 K a Ca =x [H = ] + equations for calculating 2 But we’re going to make a simplification at pH of a weak acid this point, i.e. KA