Pharmacy Calculations

2. Prepare 50 ml of 5% acetylcysteine solution using NS and 20% acetylcysteine

(amount of solute needed)/(amount of solution desired )= (concentration of desired solution)/ (concentration of on - hand solution)

3. Prepare 2 L of 20% NaHCO3 solution using H2O and NaHCO3 crystals.

(amount of solute needed)/(amount of solution desired )= (concentration of desired solution)/ (concentration of on - hand solution)

4. Prepare 1 L of NS using H2O and NaCl crystals.

(amount of solute needed)/(amount of solution desired )= (concentration of desired solution)/ (concentration of on - hand solution)

5. Prepare 1 L of 2% acetic acid using water and vinegar (5%).

(amount of solute needed)/(amount of solution desired )= (concentration of desired solution)/ (concentration of on - hand solution)

Mixing Solutions • When mixing two solutions to obtain a desired drug percentage, the following formula is used:

(amount of solute needed)/(amount of solution desired )= (concentration of desired solution)/ (concentration of on - hand solution)

Mixing Solutions • Example - prepare 5 ml of a 5% solution of acetylcysteine, using 20% acetylcysteine and normal saline

(x/5) = (5/20) therefore X = (25/20) x = 1.25 To prepare 5 ml of 5% acetylcysteine, mix 1.25 ml of the 20% acetylcysteine with 3.75 ml normal saline.

How many milligrams of active drug are in 100 ml of a 1% solution?

0.01 = (x gm/100ml) x = 1 gm (1000 mg)

H ow many milliliters of a 5% solution would be needed to deliver500 mg of active drug?

0.05 = (0.5 gm / x ml) x = 10 ml

W/V: When a solute is measured by weight and the solution by volume, concentration is not dimensionless. If 1.25 g of NaCl is dissolved in sufficient water to make 55 mL of solution, the concentration is

1.25 g/55 mL = 0.0227 g/mL (w/v). The % w/v is expressed as #g/100 mL (e.g., 2.27% or 2.27 g/100 mL).

W/W: If the quantity of solute and of the preparation are expressed in the same units of weight, the concentration is dimensionless. If 10 g of charcoal are mixed with 65 g of another powder to make a total of 75 g, the charcoal concentration is

10 g/75 g = 0.133 by weight (or 13.3% w/w).

V/V: If the solute and the preparation are expressed in the same units, then concentration is dimensionless. For example, 10 mL of alcohol dissolved in a sufficient quantity of water to make 40 mL of solution is dimensionless:

10 mL/40 mL= 0.250 (or 25% v/v).

ALIQUOT METHOD (ALLIGATION) Alligation is a method that is particularly useful when mixing two or more preparations of known strengths to prepare a mixture of an intermediate desired strength. The final mixture will be an average of the individual strengths, which are calculated as proportional parts.

Alligation Alternate and Alligation Medial are methods that can be used to solve any type of dilution or concentration problem, including concentrations expressed in mg/mL, ratios, mixtures of liquids of known specific gravities, etc. The strengths of all preparations being mixed and the final mixture are expressed in a common denomination (of weight, volume, percentage, etc.) when setting up the alligation equation. When diluting a preparation, the strength of the diluent is considered to be 0%. When increasing the strength of a given mixture by adding more drug/active ingredient, the strength of the active ingredient to be added is considered to be 100%. A final proportion allows a correlation between the parts and any specific denomination needed.

RATIO A ratio is a comparison of two numbers. In pharmacy calculations, a ratio can be used to express strength of drug concentration.

Example: A 1:25 solution of wintergreen oil means that 1 mL of wintergreen oil is contained in each 25 mL of solution.

STOCK SOLUTIONS A stock solution, commonly referred to as bulk bottle, is a large volume of a reagent (in chemistry) or in this case, medication. These stock solutions can be prepared by a manufacturer or compounded in the pharmacy. Pharmacists typically take stock solutions and use them to prepare weaker solutions of medications or chemicals for laboratory or clinical use.

How many mL of a 0.5% gentian violet stock solution is needed to prepare 1 pint of a 1:2000 solution?

Calculating Pediatric Doses • Fried's rule (infants under 1 year)

Infant dose = (infant age (months) / (150 months)) x Adult Dose

INTRAVENOUS INFUSIONS, PARENTERAL ADMIXTURES, AND FLOW RATES

Intravenous infusions are large volumes of sterile, aqueous preparations administered intravenously (through a vein) over an extended period of time.

INTERPRETATION OF MEDICATION ORDERS Example 1: A prescription for prednisone 5 mg should be taken as follows: 2 tablets three times daily the first day; 1 tablet three times daily on the second day; 1 tablet twice daily for 7 days; and 1 tablet daily thereafter. How many tablets should be dispensed for a 30-day supply?

Solution: Dispense 44 tablets in total

TPN CALCULATIONS

Total parenteral nutrition (TPN) provides all of the patient's daily nutritional requirements and generally contains dextrose (carbohydrate), amino acids (protein source), vitamins, trace minerals, electrolytes, and fat emulsions. TPN solutions may also include insulin and occasionally therapeutic drugs. The amount of protein, dextrose, and fat are calculated based on the patient's daily kcal (calories) needed and available stock solutions. Other ingredients do not contain calories.

Calculating Pediatric Doses • Clark's rule

child dose = (child weight (lbs)/150 lb) x adult dose

Calculating Pediatric Doses • Using body surface area - considered to be most accurate

child dose = ( child BSA (m squared))/ 1.73 m squared) x adult dose

Calculating Pediatric Doses • Young's rule (1 to 12 years)

child dose = ((child age (years))/(child age + 12 years)) x adult dose

Calculating Drug Doses & Percentages To calculate drug dosages, remember one basic statement: One gram or ml of drug in 99 ml of diluent will yield a 1% solution. Therefore, 1 ml of a 1% solution contains .01 gm (10 mg) of the drug.

• The formula that proves this statement is: % (in decimals) = amount of solute (gm)/total amount of solution (ml)

1. A .3 ml dose of 5% Metaprel contains how many mg metaproterenol?

% (in decimals) = (amount of solute (gm))/(total amount of solution (ml)

3. How many ml of 1:200 Proventil would be needed to deliver 5 mg albuterol?

% (in decimals) = ( amount of solute (gm)/total amount of solution (ml))

4. What is the percentage strength of a solution of Ventolin that contains 5 mg albuterol per ml?

% (in decimals) = ( amount of solute (gm)/total amount of solution (ml))

5. What is the ratio strength of an epinephrine solution that contains 1 mg epinephrine per ml?

% (in decimals) = ( amount of solute (gm)/total amount of solution (ml))

2. A .5 ml dose of 1:200 Isuprel contains how many mg isproterenol? First, convert 1:200 to a percentage (in decimal form)

% (in decimals) = (amount of solute (gm)/total amount of solution (ml))

express 1:100 as a percent

% = (1/100) X 100====>>1%

PPM AND PPB (PARTS PER MILLION AND PARTS PER BILLION) When ppm or ppb is used as a designation for concentration, some systems are w/w, some are v/v and some are w/v. Concentration is always a ratio or fraction in w/w and v/v situations. Weight by volume (w/v) concentrations are always defined in terms of grams and milliliters. The same default rules are followed as for percentage systems. Express 2 ppm of ferrous gluconate in water in percentage strength and ratio strength.

(1/500,000) * 100 = %

1. Prepare 250 ml of 1% NaCl using H2O and 10% NaCl solution.

(amount of solute needed)/(amount of solution desired )= (concentration of desired solution)/ (concentration of on - hand solution)