L1-Acids-Bases 2 PDF - pH and pKa Problems

Topic 1: Solving pH and pKa Problems Junmei Wang Ph.D. Associate Professor Department of Pharmaceutical Sciences School of Pharmacy Tel: 412-383-3268 Email: Jun...

Topic 1: Solving pH and pKa Problems Junmei Wang Ph.D. Associate Professor Department of Pharmaceutical Sciences School of Pharmacy Tel: 412-383-3268 Email: [email protected] Course website: https://mulan.pharmacy.pitt.edu/group/courses/5118/ Lab website: https://clickff.org/wanglab/ Why Do We Learn Principles of Medicinal Chemistry? ibuprofen naproxen Structurally similar, but ibuprofen is a shorter acting agent, while naproxen is longer acting agent. Plasma protein binding: 98% for ibuprofen, 99% for naproxen pKa: 4.5 for ibuprofen, 4.15 for naproxen 2 Reference book for Medicinal Chemistry Section Basic Concepts in Medicinal Chemistry By Marc W. Harrold and Robin M. Zavod 3  Learning Objectives 1. Explain the similarities, differences, and interrelationships between the pKa of a functional group and the pH of an environment. 2. Explain how the Henderson-Hasselbalch equation was constructed and how it can be used to calculate pH values, pKa values, and the ratio of ionized to unionized functional groups. 3. Solve both qualitative and quantitative pH/pKa problems. 4  Basic Concepts pH 𝑝𝐻 = −log[𝐻+ ] pOH 𝑝𝑂𝐻 = −log[𝑂𝐻− ] 𝑝𝐻 + 𝑝𝑂𝐻 = 14 Hydrogen Ion Concentration (M) 0.0001 0.1 1.0 10 pH pOH 5  Basic Concepts pKa 𝐻𝐴 + 𝐻2 𝑂 ⇌ 𝐻3 𝑂+ + 𝐴− (Actual equilibrium equation) 𝐻𝐴 ⇌ 𝐻 + + 𝐴− (Simplified form) 𝐻 + [𝐴− ] 𝐾𝑎 = (dissociation constant) [𝐻𝐴] 𝐻+ 𝐴− 𝑝𝐾𝑎 = −𝑙𝑜𝑔 𝐻𝐴 Suppose an acidic drug’s concentration is 1.0 M, i.e., the sum of unionized and ionized forms is 1.0. Calculate 𝑝𝐾𝑎 for the acid. Ionized form (%) 0.01 0.1 1.0 10 𝑝𝐾𝑎 0.0001 × 0.0001 −𝑙𝑜𝑔 =8 0.9999 6  Basic Concepts pKa for basic functional groups 𝐵: 𝐻+ ⇌ 𝐵: +𝐻 + 𝐻 + [𝐵:] 𝐾𝑎 = (dissociation constant) [𝐵:𝐻 + ] 𝐻+ 𝐵: 𝑝𝐾𝑎 = −𝑙𝑜𝑔 𝐵: 𝐻 + Consistency between acids and bases Acid 𝑯𝑨 ⇌ 𝐻+ + 𝐴− Conjugated Base Conjugated Acid 𝐵: 𝐻 + ⇌ 𝑩: + 𝐻+ Base Protonated Deprotonated Forms Forms 7  Key Summary Points for pH and pKa A pH value is a property of the environment, or solution, in which drug molecules and functional groups reside. The pH of a solution can change based on what is added or removed from the solution. Low pH values indicate acidic environments, while high pH values indicate basic environments. A pH at or about 7.0 indicates a neutral environment. Key pH values: Saliva (6.4), Stomach (2.0), Duodenum (5.4), Plasma (7.4), Urine (5.7) A pKa value is a property of a specific acidic or basic functional group. Although exceptions can occur, pKa values should generally be treated as constants (i.e., the secondary amine of epinephrine has a pKa of 10, regardless whether it is in the stomach fluid, the blood, or the urine). Low pKa values indicate either strongly acidic functional groups or weakly basic functional groups. In comparing functional groups, the one with the lower pKa value is the stronger acid or the weaker base. High pKa values indicate either weakly acidic functional groups or strongly basic functional groups. In comparing functional groups, the one with the higher pKa value is the weaker acid or the stronger base. 8  Henderson-Hasselbalch Equation 𝐻 + 𝐴− 𝐴− 𝐴− 𝑝𝐾𝑎 = −𝑙𝑜𝑔 = −𝑙𝑜𝑔 𝐻 + − 𝑙𝑜𝑔 = 𝑝𝐻 − 𝑙𝑜𝑔 𝐻𝐴 𝐻𝐴 𝐻𝐴 𝐴− 𝐻𝐴 ⇌ 𝐻 + + 𝐴− 𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 𝐻𝐴 𝐵: 𝐻 + ⇌ 𝐵: +𝐻+ 𝐻 + [𝐴− ] 𝐾𝑎 = 𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 𝐵𝑎𝑠𝑒 𝐹𝑜𝑟𝑚 𝐻+ [𝐵: ] [𝐻𝐴] 𝐴𝑐𝑖𝑑 𝐹𝑜𝑟𝑚 𝐾𝑎 = [𝐵: 𝐻+ ] 𝑝𝐻 = −log[𝐻+ ] 𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 𝑈𝑛𝑝𝑟𝑜𝑡𝑜𝑛𝑎𝑡𝑒𝑑 𝐹𝑜𝑟𝑚 [𝐵: ] 𝑃𝑟𝑜𝑡𝑜𝑛𝑎𝑡𝑒𝑑 𝐹𝑜𝑟𝑚 𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 [𝐵: 𝐻+ ] 𝐼𝑜𝑛𝑖𝑧𝑒𝑑 𝐹𝑜𝑟𝑚 𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 for acid only 𝑈𝑛𝑖𝑜𝑛𝑖𝑧𝑒𝑑 𝐹𝑜𝑟𝑚 𝑈𝑛𝑖𝑜𝑛𝑖𝑧𝑒𝑑 𝐹𝑜𝑟𝑚 𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 for base only 𝐼𝑜𝑛𝑖𝑧𝑒𝑑 𝐹𝑜𝑟𝑚 9  Equilibria for Acids and Bases Monoprotic Acid Diprotic Acid Base 10  Application of Henderson-Hasselbalch Equation Question: The drug molecule shown below has a functional group with a pKa of 4.5. Will this functional group be primarily ionized or primarily unionized in the urine at a pH of 5.9? 𝐴− 𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 𝐻𝐴 Flurbiprofen Answer: [𝐴− ] 5.9 = 4.5 + 𝑙𝑜𝑔 [𝐻𝐴] − [𝐴 ] 1.4 = 10 = 25 [𝐻𝐴] 11 Three Scenarios on the Relationship of pH and pKa 𝐴− [𝐵: ] 𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 𝐻𝐴 [𝐵: 𝐻+ ] Scenario 1 Scenario 2 Scenario 3 𝒑𝑯 = 𝒑𝑲𝒂 𝒑𝑯 > 𝒑𝑲𝒂 𝒑𝑯 < 𝒑𝑲𝒂 Acids 𝐴− = [𝐻𝐴] 𝐴− > [𝐻𝐴] 𝐴− < [𝐻𝐴] 𝐴− [𝐻𝐴] 𝐴− [𝐻𝐴] Bases 𝐵 = 𝐵: 𝐻 + 𝐵 > 𝐵: 𝐻+ 𝐵 < 𝐵: 𝐻 + 𝐵 [𝐵: 𝐻 + ] 𝐵 [𝐵: 𝐻 + ] Relative difference between the pH and the pKa values is more important than the actual pH and pKa values. 12  Solving Qualitative pH and pKa Problem 𝑝𝐾𝑎 = 2.4 Amoxicillin 𝑝𝐾𝑎 = 9.6 Predominant forms of the two functional groups 𝒑𝑯 < 𝟐. 𝟒 𝒑𝑯 = 𝟐. 𝟒 𝟗. 𝟔 > 𝒑𝑯 > 𝟐. 𝟒 𝒑𝑯 = 𝟗. 𝟔 𝒑𝑯 > 𝟗. 𝟔 Acid 𝐶𝑂𝑂𝐻 [𝐶𝑂𝑂𝐻] = [𝐶𝑂𝑂− ] 𝐶𝑂𝑂− 𝐶𝑂𝑂− 𝐶𝑂𝑂− Base 𝑁𝐻3+ 𝑁𝐻3+ 𝑁𝐻3+ 𝑁𝐻2 = [𝑁𝐻3+ ] 𝑁𝐻2 13  Key Summary Points on Solving Qualitative Problems The initial step in solving these types of problems is to identify the acidic and basic functional group(s) and correctly assign the given pKa value(s). Problems that only require the determination of whether a functional group is primarily ionized or unionized can be solved by simply comparing pH and pKa values. The Henderson-Hasselbalch equation is not required to solve these types of problems; however, the answers derived are consistent with this equation. When the pH equals the pKa, the functional group is 50% ionized and 50% unionized. When the pH is greater than the pKa, acidic functional groups are primarily ionized, and basic functional groups are primarily unionized. (both acidic and basic functional groups are deprotonated) When the pH is less than the pKa, acidic functional groups are primarily unionized, and basic functional groups are primarily ionized. (both acidic and basic functional groups are protonated) If a drug molecule contains more than one acidic or basic functional group, each functional group and its associated pKa must be evaluated separately. Quaternary ammonium functional groups, such as that found within bethanechol, are always 100% ionized regardless of the environmental pH. Nonelectrolytes, such as dexamethasone, are 100% unionized regardless of the physiological pH. 14  Solving Quantitative pH and pKa Problem Question: The drug molecule shown below has a functional group with a pKa of 8.9. What’s the percent of its ionized from at a physiological pH of 7.4? Answer: [𝐵] 7.4 = 8.9 + 𝑙𝑜𝑔 [𝐵: 𝐻 + ] [𝐵] + = 10−1.5 = 0.0316 [𝐵: 𝐻 ] [𝐵:𝐻 + ] [𝐵:𝐻 + ] Ionized form: = [𝐵:𝐻 + ]+[𝐵] [𝐵:𝐻 + ]+0.0316[𝐵:𝐻 + ] 1 𝑝𝐾𝑎 = 8.9 Ionized form: 1+0.0316 × 100 = 96.9% 15  Calculating the pH of An Environment Question: The following drug has a functional group with a pKa of 4.5, calculate pH for the following drug to be 80% ionized. Answer: [𝐴− ] 𝑝𝐻 = 4.5 + 𝑙𝑜𝑔 [𝐻𝐴] 80 𝑝𝐻 = 4.5 + 𝑙𝑜𝑔 20 = 4.5 + 0.60 = 5.1 𝑝𝐾𝑎 = 4.5 Indomethacin 16  Calculating pKa of A Function Group Question: The highlighted functional group is 10% ionized in a urine pH of 5.5. What’s pKa of this functional group? Acid form Base form Answer: [𝐴− ] 5.5 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 [𝐻𝐴] 10 5.5 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 90 10 𝑝𝐾𝑎 = 5.5 − 𝑙𝑜𝑔 = 5.5 − −0.95 = 6.45 90 17  𝐴− The Rule of Nines 𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 𝐻𝐴 𝒑𝑯 − 𝒑𝑲𝒂 𝑹𝒂𝒕𝒊𝒐 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝒊𝒐𝒏𝒊𝒛𝒆𝒅 𝒂𝒏𝒅 𝒖𝒏𝒊𝒐𝒏𝒊𝒛𝒆𝒅 𝒇𝒐𝒓𝒎𝒔 Percentage of the dominated form 0 50:50 50 1 90:10 90 2 99:1 99 3 99.9:0.1 99.9 4 99.99:0.01 99.99 5 99.999:0.001 99.999 Question: The pKa of the highlighted functional group is 6.8, what percentage will be ionized in solution with a pH of 7.8? 𝑝𝐾𝑎 = 6.8 18  Key Summary Points on Solving Quantitative Problems The Henderson-Hasselbalch equation provides the relationship between the pH of the environment, the pKa of a given functional group, and the ratio of [Base Form]/[Acid Form] for the functional group in the given environment. If given any two of these three facts, the other one can be calculated. Two initial steps are recommended prior to using the equation. Using these initial steps will allow a means of verifying that the calculated value is consistent with the given data. Identify the acid/base character of the specific functional group in question. Use the given data to qualitatively predict if the functional group should be primarily ionized or primarily unionized, or if the calculated pH should be greater than or less than the given pKa, or if the calculated pKa should be greater than or less than the given pH. The [Base Form]/[Acid Form] value is a ratio. When solving percent ionization problems using the Henderson-Hasselbalch equation, this ratio must be converted to a percentage as explained in the given examples. The calculated percentages can be compared and expressed as a ratio; however, this ratio is not the same as that initially calculated by the Henderson-Hasselbalch equation. The Rule of Nines can be used in lieu of the Henderson-Hasselbalch equation if the difference between the pH and pKa is an integer. This method involves some approximations and thus should not be used if very specific and precise values need to be calculated. 19 The Importance of pH and pKa in Drug Therapy – Aqueous Solubility 𝑝𝐾𝑎 = 3.8 𝑝𝐾𝑎 = 4.8 Methotrexate ▪ High-dose methotrexate is used to treat resistant or aggressive tumors ▪ Methotrexate could be precipitate in the renal tubules ▪ The pKa values of two carboxylic acids are 3.8 and 4.8 ▪ The normal pH of the urine ranges from 5 to 6 ▪ In order to assure that these two acidic functional groups are highly ionized and thus highly water soluble, it is necessary to alkalinize the urine. 20 The Importance of pH and pKa in Drug Therapy – Duration of Action Phenobarbital ▪ Phenobarbital is an acid, and its renal elimination is pH-dependent ▪ If the urine pH is decreased, the unionized form will increase, leading to its passive renal reabsorption, thus decrease its renal elimination. 21 The Importance of pH and pKa in Drug Therapy – The Influence on Drug Binding Interactions Binding Site An ionic bond can form over long distance and is often the initial binding attraction between a drug and its biological target. 22 Key Summary Points Involving the Importance of pH and pKa Drug Therapy The urinary and gastric pH values can be altered; However, the pH of blood and other tissues are relatively constant and cannot be significantly changed Drug molecules can be altered to increase or decrease the pKa of their functional groups Alternations of the pH of the environment or the pKa of acidic and/or basic functional groups can affect: a) The water solubility of a drug molecule b) The dissolution of drug molecule c) The bioavailability of a drug molecule d) The prevalence of specific adverse drug reactions e) Complication arising from specific disease states f) The duration of action of a drug molecule g) The ability of a drug molecule to bind to its biological target(s) h) The therapeutic activity of a specific drug molecules i) The prevalence of specific types of drug interactions 23  In Class Practice -1 The drug molecule shown below has a functional group with a pKa of 9.2. Will this functional group be primarily ionized or unionized at physiological pH? 𝐵 𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 𝐵: 𝐻 + 24  In Class Practice -2 The drug molecule has a pKa of 4.5. What percent of this drug molecule will be ionized at a urinary pH of 5? 25  In Class Practice -3 For a drug molecule shown below, the highlighted functional group is 10% ionized in a urine pH of 5.5, calculate the pKa for this functional group. 26  In Class Practice -4 For acetaminophen shown below, the pKa value is 9.7. Determine the environmental pH that is necessary for acetaminophen to be 5% ionized. 27  In Class Practice -5 dexamethasone Ciprofloxacin Ciprofloxacin is an antibacterial agent that is formulated as a solution with dexamethasone (CiproDex) for typic use in the treatment of swimmer’s ear. Ciprofloxacin has two pKa values, 6.0 and 8.8 A. Identify the functional groups that have the two pKa values B. In this formulation, Ciprofloxacin is presented as a hydrochloride salt. Modify the structure to show the salt form of the drug. Which form is more water soluble? C. The pH of the CiproDex formulation is ~5. Determine which, if any of the functional groups will be predominantly ionized in the environment. What’s percent of the ionized form? 28 Application of Henderson-Hasselbalch Equation with Excel Change Blue numbers to calcuate pH/pKa or percentage of deprotonated form 1. Calculate pH value given percentage of deprotonated form and pKa Percentage of deprotonated form 100 × [A-]/([HA]+[A-]) 60 % pKa value of a functional group pKa 7 Molar ratio of deprotonated/protonated [A-]/[HA] 1.5 pH of environment 7.18 2. Calculate pKa value given percentage of deprotonated form and pH Percentage of deprotonated form 100 × [A-]/([HA]+[A-]) 20 % pH of environment pH 8 Molar ratio of deprotonated/protonated [A-]/[HA] 0.25 pKa value of a functional group 8.60 3. Calculate percentage of deprotonated form given pKa and pH values pKa value of a functional group pKa 6 𝐴− pH of environment pH 5 𝑙𝑜𝑔 𝐻𝐴 = 𝑝𝐻 − 𝑝𝐾𝑎 Molar ratio of deprotonated/protonated [A-]/[HA] 0.1 Percentage of deprotonated form 100 × [A-]/([HA]+[A-]) 9.090909091 % 4. Calculate percentage of the deprotonated form given the difference of pH and pKa values - "Rule of 9" Difference of pH and pKa pH-pKa 2 𝐴− Molar ratio of deprotonated/protonated [A-]/[HA] 100 𝑙𝑜𝑔 = 𝑝𝐻 − 𝑝𝐾𝑎 𝐻𝐴 Percentage of ionized form 100 × [A-]/([HA]+[A-]) 99.00990099 % 29  Calculate pKa According to Its Definition Calculate pKa value given the percentage of deprotonated form of an acid: Assuming [H+]=[A-] Percentage of ionized form Ionized form 10 Dissociation constant Ka 0.011111111 pKa value pKa 1.954242509 30  Homework Each of the following four drugs has at least one functional group that is either acidic or basic in character. The pKa values are listed in the table in the next slide. Acetaminophen Naproxen Baclofen Dyclonine Red: protonated form; Blue: deprotonated form 31  Homework - Continued 1. Which environments listed in the table below are acidic, basic or neutral? 2. Evaluate each physiological environment to determine if the functional group is predominantly (>50%) ionized, unionized, or will be 50% ionized/50% unionized. 3. For the acidic and basic functional groups found in naproxen and dyclonine, use the Henderson- Hasselbalch equation to determine the following: Is the functional group predominantly ionized or unionized in plasma? What is the percentage of ionized and unionized drug in the plasma? Drug (pKa Value) Saliva Stomach Duodenum Plasma Urine (pH = 6.4) (pH = 2) (pH = 5.4) (pH = 7.4) (pH = 5.7) Acetaminophen (9.7) Unionized Naproxen (4.2) Ionized Baclofen (5.4) Ionized Baclofen (9.5) Ionized Dyclonine (8.2) Ionized 32  L1: Homework - Continued 1. For the acidic and basic functional groups found in naproxen and dyclonine, use the Henderson-Hasselbalch equation to determine the following: Is the functional group predominantly ionized or unionized in plasma (pH = 7.4)? What is the percentage of ionized and unionized drug in the plasma? Naproxen (pKa = 4.2) Dyclonine (pKa = 8.2) 33