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**Quantity and Concentration Expression**

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**Expressions of Quantity of Drugs**

One molecule of a substance is too small a quantity to be pharmaceutically useful. It is convenient to measure in a larger unit. Usually the unit used for this purpose is the mole (abbreviated mol), which is Avogadro’s number (6.023 X 1023) of molecules. The molecular weight (MW) of a compound is the weight in grams of one mole of the compound. Millimoles (mmol) often are used in pharmacy rather than moles because the required quantities and concentrations of drugs are relatively small.

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**Expressions of Quantity of Drugs**

The equivalent weight of an element or compound is that weight which combines chemically with one equivalent of another element or compound Equivalent weight = Atomic or Molecular Weight Number of Equivalents per Atomic or Molecular Weight ( valence) Milliequivalents (mEq) are used often in pharmacy because, when dosing electrolytes, we are usually dealing with small quantities.

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**Expressions of Quantity of Drugs**

Example Calculation 1 You have a formula that calls for 0.5 moles of Sodium Hydroxide (NaOH). Sodium Hydroxide is available as a solid. How many grams of NaOH should you weigh? (MW of NaOH = 40) 1 mole of NaOH g 0.5 mole of NaOH x g x = 0.5 x 40 = 20 g 1

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**Expressions of Quantity of Drugs**

Example Calculation 2 You have a liquid formulation that has 600 mg of Potassium Chloride (KCl) in each teaspoonful of syrup. How many millimoles of KCl this would be? (MW of KCl = 74.5)

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**Expressions of Quantity of Drugs**

Example Calculation 3 A potassium supplement tablet contains 10 mEq of KCl. How many milligrams of KCl are in each tablet? (MW of KCl = 74.5) 1 mEq of KCl mg 10 mEq of KCl x mg x = 10 x = 745 mg 1

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**Expressions of Quantity of Drugs**

Example Calculation 4 A dose of Calcium Chloride is given as 136 mg of calcium ions. How many milligrams of CaCl2 are needed? CaCl2 is available as the monohydrate (CaCl2.H2O), which has a MW = 147; calcium ion has an atomic weight of 40.

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**Expressions of Quantity of Drugs**

Example Calculation 5 The power for oral solution for a bowel cleansing product contains 568 mg of anhydrous Sodium Sulfate (Na2SO4). How many milliequivalents of Na in this product? (MW of Na2SO4 = 142)

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**Expressions of Quantity of Drugs**

Osmols and milliosmols An osmol is the number of moles of solute present multiplied by the number of particles per molecule when the solute is dissolved in water. Nonelectrolytes such as dextrose do not dissociate therfore, one mole dextrose yields one osmol. Sodium chloride dissociates into two ions in aqueous solution therefore, one mole sodium chloride gives two osmols. Sodium sulfate dissociate into three ions in aqueous solutions therefore, one mole sodium sulfate gives three osmols Milliosmols are often used in pharmacy and medicine.

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**Expressions of Quantity of Drugs**

Example Calculation 6 Isotonic Sodium Chloride Solution has 9 g of NaCl in each liter of solution. How many osmols are there in each liter of solution? (MW of NaCl = 58.5) 1 mole NaCl g 1 mole NaCl osmol 2 osmol g x osmol g x = 2 x 9 = osmol 58.5

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**Expressions of Quantity of Drugs**

Example Calculation 7 You want to add solute to a liter of water so that there are 300 mOsmol in this solution. Your source of solute is Magnesium Sulfate Heptahydrate (MgSO4.7H2O), which has MW = How many milligrams of this solute should you add?

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**Expressions of Concentration**

Concentration gives quantity of drugs or active ingredients per amount (volume or weight) of product or preparation. Pharmaceutically useful expressions of concentration are: Percentage weight in volume (w/v) Percentage volume in volume (v/v) Percentage weight in weight (w/w) Ratio strength Molarity (M) Normality (N) Molality (m) Mole fraction (x)

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**Expressions of Concentration**

Percentage weight in volume (w/v) indicates the number of grams of a constituent per 100 ml of solution Percentage volume in volume (v/v) indicates the number of milliliters of a constituent in 100 ml of liquid formulation. Percentage weight in weight (w/w) indicates the number of grams of a constituent per 100 g of formulation (solid or liquid) Ratio strength, as the name implies is the expression of concentration by means of a ratio.

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**Expressions of Concentration**

Molarity (M) is the number of moles of solute per liter of solution. Molality (m) is the number of moles of solute per 1000 grams of solvent. Normality (N) is the number of equivalents per liter of solution. Osmolality is the number of osmols per kilogram of water. Osmolarity is the number of osmols per liter of solution. Mole fraction (x) is the ratio of the moles of one constituent of a solution to the total moles of all constituents. To express in percentage, multiply x by 100.

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**Expressions of Concentration**

Example Calculation 8 Diluted Hydrochloric Acid NF contains 10 g of HCl in 100 ml of solution. Calculate its molarity. (MW of HCl = 36.5)

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**Expressions of Concentration**

Example Calculation 9 You want to make 500 ml of a 1 M solution of Sulfuric Acid. How many grams of H2SO4 do you need? (MW of H2SO4 = 98.1)

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**Expressions of Concentration**

Example Calculation 10 Syrup NF contains 850 g of Sucrose in 1000 ml of solution. The solution has a density of 1.3. The MW of Sucrose = 342. Calculate the molarity and molality of the solution. 1 mole g x mole g x = 2.49 mole there are 2.49 mole per liter, the concentration is 2.49M For molality: Weight of solution = 1000 ml x 1.3 g/ml = 1300 g Weight of solvent = 1300 g – 850 g = 450 g 2.49 mole g x mole g x = 5.5 mole there are 5.5 mole per 1000 g solvent, the concentration is 5.5 m.

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**Expressions of Concentration**

Example Calculation 11 A patient medical record from a former hospitalization shows a cholesterol level of 320 mg/dl. What is the equivalent of this level in mmol/l? (MW of cholesterol = 387)

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**Expressions of Concentration**

Example Calculation 12 You want to make 500 ml of a 1 N solution of Sulfuric Acid. How many grams of H2SO4 do you need? (MW of H2SO4 = 98.1) 1 Eq Wt. = 98.1 / 2 = 49 g 0.5 Eq Wt. = x x = 24.5 g

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**Expressions of Concentration**

Example Calculation 13 You have a pint of Potassium Chloride Syrup that is labeled 10%. What is the concentration in mEq per one tablespoonful? (MW of KCl = 74.5) 10 g ml x g ml x = 1.5 g 1 mEq mg x mEq mg x = 20.1 mEq

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**Expressions of Concentration**

Example Calculation 14 Sodium Chloride Injection is 0.9% NaCl. Calculate its concentration in mOsmol/l. (MW of NaCl = 58.5)

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Test your self An aqueous solution of FeSo4 is prepared by adding 41.5 g FeSo4 to enough water to make 1000 ml of solution. The density of the solution is and the MW of FeSo4 is calculate: the molarity, the molality, the mole fraction of FeSo4 and water, the mole percent of the two constituents, and the percent by weight of FeSo4.

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