PHARMACEUTICAL CALCULATIONS FALL 207 Contents General Vocab & Definitions... 2 Milliequivalent Calculations... 2 Millimole and Micromole Calculations... 5 Osmolarity... 6 Daily Water Requirement Calculations for Healthy Adult Patients (FYI)... 7 Practice Problems... 8 Objectives: Upon completion of this module, the student is expected to be able to. Calculate the milliequivalent weight from an atomic or formula weight. 2. Convert between milligrams and milliequivalents. 3. Calculate problems involving milliequivalents. 4. Calculate problems involving millimoles and milliosmoles. Benjamin Vroman Pharm.D., BCPS Content adopted from Ashley Stull, PharmD The following material is taken from Zatz (Chapter 9) and Ansel (Chapter 2). Please refer to class syllabus for specific notations regarding chapters covered in part.
General Vocab & Definitions Table. Concentration of ions in blood plasma.* For examination purposes: know which ions are Ions particles which carry an electric charge; products of molecule dissociation present, but do not memorize concentrations. in solution Cations meq/l Anions meq/l Nonelectrolytes substances not dissociated in solution (e.g. urea, dextrose) Na + 42 Cl 24 Electrolytes substances with varying degrees of dissociation in solution (e.g. K + 5 HCO3 05 Ca sodium chloride) 5 HPO4 2 2 Mg +2 2 SO4 2 Milliequivalent (meq) used almost exclusively in the US by clinicians, organic acids 6 physicians, pharmacists, and manufacturers to express the concentration of proteinate 6 electrolytes in solution total 54 total 54 represents amount (mg) of a solute equal to /000 of its gram equivalent weight, taking into account valence of ions *under normal conditions expresses the chemical activity or combining power of a substance relative to the activity of mg of hydrogen Milliequivalent Calculations For a given chemical compound: meq cation = meq anion = meq compound **However, it is important to note that while a given chemical compound may contain an equal amount of cations and anions in terms of milliequivalents, the weight of those respective components is not necessarily equal. Table 2. Equivalent weight data for selected ions. For examination purposes: memorize only highlighted values, but make sure that (given sufficient information) you are able to calculate all values by utilizing the equation to the right. Make sure to memorize the equation! Ion Formula Valence Atomic or Formula Weight Equivalent weight Aluminum Al +3 3 27 9 Ammonium NH4 + 8 8 Calcium Ca +2 2 40 20 Ferric Fe +3 3 56 8.7 Ferrous Fe +2 2 56 28 Lithium Li + 7 7 Magnesium Mg +2 2 24 2 Potassium K + 39 39 Sodium Na + 23 23 Acetate C2H3O2 +3 59 59 Bicarbonate HCO3 6 6 Carbonate CO3 2 2 60 30 Chloride Cl 35.5 35.5 Citrate C6H5O7 3 3 89 63 Gluconate C6HO7 95 95 Lactate C3H5O3 89 89 Phosphate H2PO4 97 97 HPO4 2 2 96 48 Sulfate SO4 2 2 96 48 * Z = atomic, formula, or molecular weight Equivalent weight = Z valence 2
Table 3. Conversion Equations & Examples Conversion Equation* Example How many milliequivalents of magnesium sulfate are represented in g of anhydrous magnesium sulfate (MgSO4)? meq = meq = mg valence Z MgSO4 000 mg 2 = 6.7 meq 20 mg to meq meq = mg valence Z Contained within the above calculation are the following steps: Equivalent weight (MgSO4) = Z MgSO4 valence = 20 2 = 60 g Equivalent weight (MgSO4) meq MgSO4 = = 60 g = 0.060 g = 60 mg 000 000 60 mg 000 mg = meq x meq x = 6.7 meq How many milligrams of Mg +2 represent 2.5 meq? mg= meq Z Mg valence mg= 2.5 meq 24 = 30 mg 2 meq to mg mg = meq Z valence Contained within the above calculation are the following steps: Equivalent weight (Mg) = Z Mg valence = 24 2 = 2 g Equivalent weight (MgSO4) meq MgSO4 = = 2 g = 0.02 g = 2 mg 000 000 2 mg meq = x mg 2.5 meq x = 30 mg What is the concentration, in milligrams per milliliter, of a solution containing 2 meq of potassium chloride (KCl) per milliliter? mg/ml= meq/ml Z KCl valence mg/ml= 2 meq/ml 74.5 = 49 mg/ml meq/ml to mg/ml mg/ml = meq/ml Z valence Contained within the above calculation are the following steps: Equivalent weight (KCl) = Equivalent weight (KCl) meq KCl = 000 2 meq/ml KCl = 2 meq ml Z KCl valence = 74.5 = 74.5 g = 74.5 g = 0.0745 g = 74.5 mg 000 74.5 mg = 49 mg/ml meq * Z = atomic, formula, or molecular weight 3
***REMEMBER: To find valence for molecules, find the absolute value of the total valence of the positive or negative radical. (See example below.) Example Problem What is the concentration, in grams per milliliter, of a solution containing 4 meq of calcium chloride (CaCl2 2H2O) per milliliter? To determine valence, we must consider the ions that this molecule will dissociate into. CaCl2 will dissociate into one Ca +2 ion and two Cl ions. The valence will be the absolute value of the total valence of the positive or negative radical: (+2) = 2 or 2 ( ) = 2 CaCl2 2H2O mg/ml= meq/ml Z valence The water of hydration molecules do not interfere with the calculations, but make sure to choose the correct molecular weight if given a table of values. (Differing water of hydration values will change MW.) In this case, Z = 47 Therefore, the valence for CaCl2 we will use in our calculation is 2. 4 meq/ml 47 2 = 294 mg/ml = 0.294 g/ml Example Problem 2 What is the percent (w/v) concentration of a solution containing 00 meq of ammonium chloride per liter? The molecular weight of NH4Cl is 53.5. mg/ml = meq/ml Z valence = (00 meq/000 ml) 53.5 = 5.35 mg ml = 5.35 g/l 5.35 g 000 ml = x g 00 ml x = 0.535 g Therefore, the percent (w/v) concentration of the solution is 0.535%. Example Problem 3 A person is to receive 2 meq of sodium chloride per kilogram of body weight. If the person weighs 32 lb, how many milliliters of a 0.9% NaCl solution should be administered? meq Z NaCl valence 32 lb = 60 kg 2 meq/kg 60 kg = 20 meq = 20 meq 58.5 = 7020 mg = 7.02 g NaCl 0.9 g 00 ml = 7.02 g x ml x = 780 ml 4
Example Problem 4 How many milliequivalents of Na+ would be contained in a 30-mL dose of the following solution? Disodium hydrogen phosphate 8 g Sodium biphosphate 48 g Purified water ad 00 ml In solving this problem, each salt must be considered separately to obtain the total amount of sodium ion present. For disodium hydrogen phosphate (Na2HPO4 7H20, Z = 268, valence = 2): meq = mg valence Z = 34.3 meq 00 ml 8000 mg 2 268 = x meq 30 ml x = 40.3 meq = 34.3 meq For sodium biphosphate (NaH2PO4 H20, Z = 38, valence = ): meq = mg valence Z = 347.8 meq 00 ml 48000 mg 38 = x meq 30 ml x = 04.3 meq = 347.8 meq For our final step, we can now combine our two sources to find the total amount of milliequivalents in 30 ml of the compound: 40.3 meq + 04.3 meq = 44.6 meq Millimole and Micromole Calculations Molecular weight is the weight, in grams, of one mole of a substance ( mole = 6.022479 0 23 particles) Millimole (mmol) = one-thousandth of a mole Micromole (µmol) = one-millionth of a mole mmol = Z 000 where Z = molecular weight Example Problem How many millimoles of monobasic sodium phosphate (Z = 38) are present in 00 g of the substance? 38 g mol = 00 g x mol x = 0.725 mol = 725 mmol **Make sure you can solve for other variables in the proportion as well. 5
Osmolarity Milliosmols of solute per liter of solution (mosmol/l) Depends on the total number of particles in solution, so dissociation plays a role in calculations Dextrose nonelectrolyte, mmol = formula weight in milligrams = mosmol NaCl electrolyte, dissociates into 2 particles (Na + & Cl ), mmol = 2 mosmol (assuming complete dissociation) CaCl2 electrolyte, dissociates into 3 particles (Ca + & 2Cl ), mmol = 3 mosmol (assuming complete dissociation) Na3C6H5O7 electrolyte, dissociates in to 4 particles (3Na + & C6H5O7 ), mmol = 4 mosmol Milliosmolar value of separate ions of an electrolyte may be obtained by dividing the concentration of the ion, in milligrams per liter, by its atomic weight Milliosmolar value of the whole electrolyte in solution is equal to the sum of the milliosmolar values of the separate ions Osmol = Z species where Z = molecular weight mosmol L = weight of substance (g L ) Z (g) number of species 000 (where number of species = number of particles substance dissociates into) In practice, as concentration increases actual osmolar values decrease because dissociation is not complete (calculations using the above equation are ideal and not actual) For example: for 0.9% NaCl solutions mosmol L = mosmol L = 9 g/l 58.5 g weight (g L ) number of species 000 Z (g) 2 000 = 307.69 mosmol L 308 mosmol/l Therefore the ideal osmolarity of the solution is 308 mosmol/l, but actual osmolarity is approximately 286 mosmol/l. Manufacturers may label products with calculated ideal osmolarities or with experimental/actual osmolarities important to identify this distinction in practice! Osmolarity vs. osmolality Osmolarity = mosmol of solute per liter of solution FYI: Osmolality = mosmol of solute per kg of solvent plasma (mosmol/kg) = 2([Na] + [K]) + [BUN] 2.8 + [Glucose] 8 measured by osmometer normal serum range = 275 to 300 mosmol/kg Where abnormal values can occur in the event of shock, Na & K are plasma concentrations in meq/l BUN & glucose concentrations are in mg/dl (mg/00 ml) trauma, burns, water intoxication (overload), electrolyte imbalance, hyperglycemia, or renal failure Dilute aqueous solutions may have approximately equal values, but as concentration increases the values diverge significantly Example Problem A solution contains 5% of anhydrous dextrose (Z = 80 g) in SWFI. How many mosmol/l are represented by this concentration? 5% solution= 5 g 00 ml = 50 g = 50 g/l 000 ml Dextrose is a nonelectrolyte, so number of species = (no dissociation) mosmol L = mosmol L = 50 g/l 80 g weight (g L ) number of species 000 Z (g) 000 = 277.78 mosmol/l 278 mosmol/l 6
Example Problem 2 A solution contains 56 mg of K + ions (Z = 39) per 00 ml. How many milliosmols are represented in a liter of the solution? 56 mg 00 ml =.56 g =.56 g/l 000 ml Already dissociated, so number of species = mosmol L = mosmol L = weight (g L ) number of species 000 Z (g).56 g/l 39 g 000 = 40 mosmol/l Example Problem 3 A solution contains 0 mg% of Ca ++ ions (Z = 40 g). How many milliosmols are represented in liter of the solution? 0 mg% = 0 mg 00 ml = 0. g = 0. g/l 000 ml Already dissociated, so number of species = mosmol L = mosmol L = weight (g L ) number of species 000 Z (g) 0. g/l 40 g 000 = 2.5 mosmol L Daily Water Requirement Calculations for Healthy Adult Patients (FYI) ml/m 2 /day = 500 ml/m 2 BSA or ml/kg/day = 20 to 35 ml/kg or ml/kg/day = 500 ml + [20 ml (weight 20 kg)] 7
Practice Problems. Convert a blood plasma level range of 5 to 20 µg/ml of tobramycin (Z = 467.52) to µmol/l. 2. A preparation contains in each milliliter, 236 mg of dibasic potassium phosphate (Z = 74.8) and 224 mg of monobasic potassium phosphate (Z = 36.09). Calculate the total concentration of phosphorus, in mmol/ml, in the preparation. 3. A 0-mL ampul of potassium chloride contains 2.98 g of KCl. What is the concentration of the solution in terms of milliequivalents per milliliter? 4. A person is to receive 36 mg of ammonium chloride per kilogram of body weight. If the person weighs 54 lb, how many milliliters of a sterile solution of ammonium chloride (NH4Cl, Z = 53.5) containing 0.4 meq/ml should be administered? 5. A sterile solution of potassium chloride (KCl) contains 2 meq/ml. If a 20-mL ampul of the solution is diluted to liter with SWFI, what is the percentage strength of the resulting solution? 8
6. A certain electrolyte solution contains, as one of the ingredients, the equivalent of 4.6 meq of calcium per liter. How many grams of calcium chloride (CaCl2 H2O, Z = 47) should be used in preparing 20 liters of the solution? 7. Sterile solutions of ammonium chloride containing 2.4 mg/ml are available commercially in 500- and 000-mL IV infusion containers. Calculate the amount, in terms of meq, of ammonium chloride (NH4Cl, Z = 53.5) in the 500-mL container. 8. A solution contains, in each 5 ml, 0.5 g of potassium acetate (C2H3KO2, Z = 98), 0.5 g of potassium bicarbonate (KHCO3, Z = 00), and 0.5 g of potassium citrate (C6H5K3O7 H2O, Z = 324). How many milliequivalents of potassium (K + ) are represented in each 5 ml of the solution? 9. How many grams of sodium chloride (NaCl) should be used in preparing 20 liters of a solution containing 54 meq/l? 0. Sterile solutions of potassium chloride (KCl) containing 5 meq/ml are available in 20-mL containers. Calculate the amount, in grams, of potassium chloride in the container. 9
. How many milliliters of a solution containing 2 meq of potassium chloride (KCl) per milliliter should be used to obtain 2.98 g of potassium chloride? 2. A patient is given 25 mg of phenytoin sodium (C5HN2NaO2, Z = 274) three times a day. How many milliequivalents of sodium are represented in the daily dose? 3. A 40-mL vial of sodium chloride solution was diluted to liter with sterile distilled water. The concentration (w/v) of sodium chloride (NaCl) in the finished product was 0.585%. What was the concentration, in milliequivalents per milliliter, of the original solution? 4. How many grams of sodium bicarbonate (NaHCO3, Z = 84) should be used in preparing a liter of a solution to contain 44.6 meq per 50 ml? 5. A solution contains 20 mg% (20 mg/00 ml) of Ca +2 ions. Express this concentration in terms of milliequivalents per liter. 0
6. A sterile sodium lactate solution is available commercially as a /6-molar solution of sodium lactate (C3H5NaO3, Z = 2). How many meq of sodium lactate would be provided by a liter of the solution? 7. A certain electrolyte solution contains 0.9% NaCl in 0% dextrose solution. Express the concentration of NaCl in terms of meq/l. 8. Consider the following prescription: Potassium chloride 0% Cherry syrup ad 480 ml Sig. i Tbsp PO BID How many milliequivalents of potassium chloride are represented in each prescribed dose? 9. How many milliequivalents of potassium are in 5 million units of penicillin V potassium (C6H7KN2O6S, Z = 388)? One milligram of penicillin V potassium represents 380 units. 20. The normal potassium level in blood plasma is 7 mg% (7 mg/00 ml). Express this concentration in terms of milliequivalents per liter.
2. How many grams of potassium citrate (C6H5K3O7 H2O, Z = 324) should be used in preparing 500 ml of a potassium ion elixir so as to supply 5 meq of K + in each 5-mL dose? 22. A potassium supplement tablet contains 2.5 g of potassium bicarbonate (KHCO3, Z = 00). How many milliequivalents of potassium (K + ) are supplied by the tablet? 23. Ringer s injection contains 0.86% of sodium chloride, 0.03% of potassium chloride, and 0.033% of calcium chloride. How many milliequivalents of each chloride are contained in liter of the injection? 24. Calculate the sodium (Na + ) content, in terms of milliequivalents, of g of ampicillin sodium (C6H8N3NaO4S, Z = 37). 25. A 20-mL vial of concentrated ammonium chloride solution containing 5 meq/ml is diluted to liter with sterile distilled water. a. Calculate the total milliequivalent value of the ammonium ion in the dilution. b. Calculate the percentage strength of the dilution. 2
26. Ringer s solution contains 0.33 g of calcium chloride per liter. Express the concentration in terms of milliequivalents of calcium chloride (CaCl2 2H2O, Z = 47) per liter. 27. How many milliequivalents of potassium would be supplied daily by the usual dose (0.3 ml TID) of saturated potassium iodide solution? Saturated potassium iodide solution contains 00 g of potassium iodide per 00 ml. 28. An intravenous solution calls for the addition of 25 meq of sodium bicarbonate. How many milliliters of 8.4% w/v sodium bicarbonate injection should be added to the formula? 29. Calcium gluconate (C2H22CaO4, Z = 430) injection 0% is available in a 0-mL ampul. How many milliequivalents of Ca +2 does the ampul contain? 30. A flavored potassium chloride packet contains.5 g of potassium chloride. How many milliequivalents of potassium chloride are represented in each packet? 3
3. How many milliequivalents of Li + are provided by a daily dose of four 300-mg tablets of lithium carbonate (Li2CO3, Z = 74)? 32. How many milliequivalents of ammonium (NH4 + ) ion are contained in liter a 4.2% w/v solution of ammonium chloride? 33. A patient is to receive 0 meq of potassium gluconate (C6HKO7, Z = 234) four times a day for 3 days. If the dose is to be tsp in a cherry syrup vehicle, a. How many grams of potassium gluconate should be used? b. What volume, in milliliters, should be dispensed to provide the prescribed dosage regimen? 34. A physician wishes to administer,200,000 units of penicillin G potassium every 4 hours. If unit of penicillin G potassium (C6H7KN2O4S, Z = 372) equals 0.6 µg, how many milliequivalents of K + will the patient receive in a 24-hour period? 4
35. Five milliliters of lithium citrate syrup contain the equivalent of 8 meq of Li +. Calculate the equivalent, in milligrams, of lithium carbonate (Li2CO3, Z = 74) in each 5-mL dose of the syrup. 36. How many milligrams of magnesium sulfate (MgSO4, Z = 20) should be added to an IV solution to provide 5 meq of Mg +2 per liter? 37. K-tab, a slow-release potassium chloride tablet, contains 750 mg of potassium chloride in a wax/polymer matrix. How many milliequivalents of potassium chloride are supplied by a dosage of tab PO TID? 38. An electrolyte solution contains 222 mg of sodium acetate (C2H3NaO2, Z = 82) and 5 mg of magnesium chloride (MgCl2, Z = 95) in each 00 ml. Express these concentrations in milliequivalents of Na + and Mg +2 per liter. 39. Ammonium chloride (NH4Cl, Z = 53.5) is to be used as a urinary acidifier with a dose of 50 meq. How many 500-mg tablets should be administered? 5
40. A patient has a sodium deficit of 68 meq. How many milliliters of isotonic NaCl solution should be administered to replace the deficit? 4. A normal 70 kg (54 lb) adult has 80 to 00 g of sodium in their body, primarily contained in the extracellular fluid. Body retention of an additional g of sodium results in excess body water accumulation of approximately 30 ml. If a person contains 00 meq of extra sodium, how many milliliters of additional water could be expected to be retained? 42. A patient receives 3 liters of an electrolyte fluid containing 234 mg of sodium chloride (Z = 58.5), 25 mg of potassium acetate (C2H3KO2, Z = 98), and 2 mg of magnesium acetate (C4H6MgO4, Z = 42) per 00 ml. How many milliequivalents each of Na +, K +, and Mg +2 does the patient receive? 43. How many milliliters of a 2% w/v solution of ammonium chloride (NH4Cl, Z = 53.5) should be administered intravenously to a patient to provide 75 meq? 6
44. The usual adult dose of calcium for elevating serum calcium is 7 to 4 meq. How many milliliters of calcium gluceptate injection, each milliliter of which provides 8 mg of elemental calcium, would provide the recommended dosage range? 45. The oral pediatric maintenance solution Pedialyte liquid has the following electrolyte content per liter: 45 meq of sodium, 20 meq of potassium, 35 meq of chloride, 30 meq of citrate. Calculate the equivalents quantities of each in terms of milligrams. 46. Calculate the milliequivalents of chloride per liter of the following parenteral fluid: Sodium chloride 56 mg Potassium chloride 89.4 mg Calcium chloride, anhydrous 27.8 mg Magnesium chloride, anhydrous 4.2 mg Sodium lactate, anhydrous 560 mg SWFI ad 00 ml 7
47. The pediatric infusion rate for potassium is 5 meq/hour. If 9 ml of a 39.2% solution of potassium acetate (KC2H3O2) is diluted to L of infusion solution, calculate the proper infusion rate in ml/hr. 48. Colyte, a colon lavage preparation contains the following mixture of dry powder to prepare 4 liters of solution: Sodium chloride 5.84 g Potassium chloride 2.98 g Sodium bicarbonate 6.72 g Sodium sulfate, anhydrous 22.72 g Polyethylene glycol 3350 240 g Calculate the milliequivalents each of sodium and chloride present per liter of prepared solution. 49. At 3:00 pm, a pharmacist received an order to add 30 meq/l of potassium chloride to the already running IV fluid for a patient. After checking the med order, the pharmacist found that the patient is receiving D5W in NS infusion at a rate of 85 ml/hour, and that the patient s liter of fluid was started at :30 pm. a. Assuming that it took 30 minutes to provide the needed potassium chloride to the floor nurse, how many milliequivalents of potassium chloride should have been added to the patient s running IV fluid to achieve the ordered concentration? 8
b. How many milliliters of an injection containing 2 meq of potassium chloride per ml should have been used to supply the amount of potassium chloride needed? c. What was the osmolality of the infusion with the potassium chloride added? Assume the complete dissociation of the NaCl and KCl. 50. A solution contains 322 mg of Na + ions per liter. How many milliosmoles are represented in the solution? 5. How many milliosmoles of sodium are represented in liter of 3% hypertonic NaCl solution? Assume complete dissociation. 52. A solution of sodium chloride contains 77 meq/l. Calculate its osmolar strength in terms of milliosmoles per liter. Assume complete dissociation. 9
53. Calculate the osmolar concentration, in terms of milliosmoles, represented by liter of a 0% w/v solution of anhydrous dextrose (Z = 80) in water. 54. Calculate the osmolarity, in milliosmoles per milliliter, of a parenteral solution containing 2 meq/ml of potassium acetate (KC2H3O2, Z = 98). 55. Given a 500-mL parenteral fluid containing 5% w/v sodium bicarbonate, a. Calculate milliequivalents per milliliter b. Calculate total milliequivalents c. Calculate osmolarity 2 0
56. What is the osmolarity of an 8.4% w/v solution of sodium bicarbonate? 57. A hospital medication order calls for the administration of 00 g of mannitol to a patient as an osmotic diuretic over a 24- hour period. Calculate a. how many milliliters of a 5% w/v mannitol injection should be administered per hour b. how many milliosmoles of mannitol (Z = 82) would be represented in the prescribed dosage. 58. In 47 ml of a 0% w/v calcium chloride (CaCl2 H2O, Z = 47) solution a. there are how many millimoles of calcium chloride? b. there are how many milliequivalents of calcium chloride? c. there are how many milliosmoles of calcium chloride? 2
59. Calculate the daily water requirement for a healthy adult weighing 65 lb. 60. Estimate the plasma osmolality, in milliosmoles per kilogram, from the following data: Sodium 36 meq/l Potassium 5 meq/l BUN 26 mg/00 ml Glucose 90 mg/dl 2 2