Pharmacy Calculations: Concentrations - PTCB PTCE, NAPLEX, NCLEX Test Prep CPhT Pharmacy Technician
Summary
This video explains pharmacy concentration calculations for liquid and topical products, defining concentration as the amount of active ingredient per total weight or volume. It details three ways concentrations are expressed: drug strength (e.g., mg/mL), percentage (e.g., % w/v, w/w, v/v), and ratio (e.g., 1:1000). The presenter walks through numerous examples for each type, demonstrating how to solve problems using equivalent fractions, cross-multiplication, and division, emphasizing the importance of matching units for accurate calculations. It also covers common IV abbreviations like D5W and NS.
Key Insights
Ratio strengths are used for very dilute solutions but are less common due to errors.
Ratio strengths are used for expressing concentrations of weak solutions where percentage strength would be very low (e.g., 1:10,000 equals 0.01%). However, they are not very common anymore because they have been linked to medication errors. The FDA required removal of ratio strengths from single-ingredient product labels, though they may still appear on multi-ingredient products.
Convert a drug strength (mg/mL) to a ratio strength.
To convert a strength of 1 mg/mL to a ratio: First, convert mg to grams (1 mg = 0.001 g). The strength is 0.001 g/mL. To express as a ratio (1:X), set up fractions: (0.001 g / 1 mL) = (1 g / x mL). Cross-multiply (1 * 1 = 1). Divide by 0.001 (1 / 0.001 = 1000). The ratio is 1:1000.
Solve all concentration problems by setting up equivalent fractions, cross-multiplying, and dividing.
The general steps for solving concentration questions involve setting up equivalent fractions with matching units for numerators and denominators, then cross-multiplying and dividing to solve for the unknown. Convert to the required units at the end if necessary.
Sections
What are Concentrations?
Concentrations define the strength of liquid and topical pharmaceutical products.
Concentrations are the strengths of liquid and topical products. Specifically, a concentration is the amount of active ingredient per the total weight or volume of the product. The general formula for determining concentration is: concentration = amount of active ingredient / total weight or volume of the product.
Concentrations can be expressed as drug strength, percentage, or ratio.
There are a few different ways that a product's concentration can be expressed: as a drug strength (e.g., amoxicillin suspension 250 milligrams per 5 milliliters), as a percentage (e.g., 5 percent dextrose IV solution), or as a ratio (e.g., epinephrine one to one thousand injection). Drug strength and percentage are more common; ratio is less common.
Concentration as Drug Strength
Drug strength is the amount of active drug per a given amount of product.
Concentration as a drug strength is the amount of active drug per a given amount of drug product, specifically for liquid and topical products. There are many different units of measure, generally something per something (e.g., milligrams per milliliter, micrograms per milliliter, units per gram, grams per milliliter).
Drug strength can be expressed as drug per dosage unit or per quantity.
Drug strength concentrations can be formulated as amount of drug per dosage unit (e.g., albuterol nebulizer solution 2.5 milligrams per 3 milliliter vial), amount of drug per quantity of liquid (e.g., amoxicillin suspension 250 milligrams per 5 milliliters), or amount of drug per quantity of a topical product (e.g., nystatin cream 100,000 units per gram).
Solve drug strength problems using equivalent fractions, cross-multiplication, and division.
To solve drug strength concentration questions, set up equivalent fractions where numerators have the same units and denominators have the same units. Then, cross-multiply and divide to solve for the unknown variable. For example, to find milligrams of prednisolone in 100 mL of a 15 mg/5 mL solution: (15 mg / 5 mL) = (x mg / 100 mL). Cross-multiply (15 * 100 = 1500) and divide by 5 (1500 / 5 = 300 mg).
Calculate amoxicillin dose: 4000 mg in 50 mL of 400 mg/5 mL suspension.
Example calculation for amoxicillin: Given 400 mg per 5 mL suspension, how many mg in 50 mL? Set up equivalent fractions: (400 mg / 5 mL) = (x mg / 50 mL). Cross-multiply (400 * 50 = 20,000) and divide by 5 (20,000 / 5 = 4,000 mg).
Calculate acetaminophen per teaspoon: 160 mg in 5 mL of Tylenol suspension.
Example calculation for acetaminophen: If 800 mg are in 25 mL, how many mg per teaspoon (5 mL)? Set up equivalent fractions: (800 mg / 25 mL) = (x mg / 5 mL). Cross-multiply (800 * 5 = 4,000) and divide by 25 (4,000 / 25 = 160 mg).
Concentration as a Percentage
Percentage means 'per 100'; units can be weight/weight, weight/volume, or volume/volume.
Percent means per 100, or divided by 100. There are three types of percentage concentrations: weight per weight (grams of drug per 100 grams of product), weight per volume (grams of drug per 100 milliliters of product - most common), and volume per volume (milliliters of drug per 100 milliliters of product).
Understand common IV fluid abbreviations and their percentage concentrations.
Common IV products include: D5W (dextrose 5%, meaning 5 grams dextrose per 100 mL sterile water), NS (normal saline, 0.9% NaCl, meaning 0.9 grams NaCl per 100 mL sterile water), and half NS (0.45% NaCl, meaning 0.45 grams NaCl per 100 mL sterile water).
Calculate grams of dextrose in D5W using equivalent fractions.
To find the grams of dextrose in 250 mL of D5W (5% dextrose), set up equivalent fractions: (5 g / 100 mL) = (x g / 250 mL). Cross-multiply (5 * 250 = 1250) and divide by 100 (1250 / 100 = 12.5 g).
Calculate grams of NaCl in Normal Saline (NS) based on volume.
To find grams of NaCl in 1 liter (1000 mL) of NS (0.9% NaCl, or 0.9 g/100 mL), set up equivalent fractions: (0.9 g / 100 mL) = (x g / 1000 mL). Cross-multiply (0.9 * 1000 = 900) and divide by 100 (900 / 100 = 9 g).
Convert percentage concentration to specific drug amount in a given product weight.
To find milligrams of hydrocortisone in 1 gram of 2.5% hydrocortisone cream: 2.5% means 2.5 g per 100 g. Set up fractions: (2.5 g / 100 g) = (x g / 1 g). Cross-multiply (2.5 * 1 = 2.5) and divide by 100 (2.5 / 100 = 0.025 g). Convert to milligrams (0.025 g * 1000 mg/g = 25 mg).
Concentration as a Ratio
Ratio strength expresses concentration as 1 gram per a specific volume (e.g., 1:1000).
Ratio strength describes a drug concentration as a ratio, typically 1 to something (e.g., 1:1000, 1:2000). The formula for ratio strength is grams to milliliters, so a 1:1000 ratio means 1 gram in 1000 milliliters of solution.
Ratio strengths are used for very dilute solutions but are less common due to errors.
Ratio strengths are used for expressing concentrations of weak solutions where percentage strength would be very low (e.g., 1:10,000 equals 0.01%). However, they are not very common anymore because they have been linked to medication errors. The FDA required removal of ratio strengths from single-ingredient product labels, though they may still appear on multi-ingredient products.
Calculate medication amount from ratio strength using equivalent fractions.
To find milligrams of epinephrine in 10 mL of a 1:200 solution: First, convert ratio to g/mL: 1:200 means 1 g per 200 mL. Set up fractions: (1 g / 200 mL) = (x g / 10 mL). Cross-multiply (1 * 10 = 10) and divide by 200 (10 / 200 = 0.05 g). Convert to milligrams (0.05 g * 1000 mg/g = 50 mg).
Convert a drug strength (mg/mL) to a ratio strength.
To convert a strength of 1 mg/mL to a ratio: First, convert mg to grams (1 mg = 0.001 g). The strength is 0.001 g/mL. To express as a ratio (1:X), set up fractions: (0.001 g / 1 mL) = (1 g / x mL). Cross-multiply (1 * 1 = 1). Divide by 0.001 (1 / 0.001 = 1000). The ratio is 1:1000.
Summary and Key Points
Concentration defines active ingredient amount per total product weight or volume.
Concentrations are the strengths of liquids and topical products, defined as the amount of drug per the total weight or volume of the product. The three main ways to express concentrations are drug strength, percentage, and ratio.
Drug strength concentrations use various units like mg/mL or units/gram.
Drug strength concentrations come in many units of measure, such as milligrams per milliliter, grams per milliliter, micrograms per milliliter, or units per gram.
Percentage concentrations require grams or milliliters per 100 units.
Percentage concentrations mean 'per 100'. The units are typically grams or milliliters of drug per 100 grams or 100 milliliters of the total product.
Ratio concentrations are generally expressed as 1 gram per a specific volume.
Ratio concentrations usually mean one to something. The units for ratio concentrations are grams to milliliters (e.g., 1 gram per 1000 milliliters).
Solve all concentration problems by setting up equivalent fractions, cross-multiplying, and dividing.
The general steps for solving concentration questions involve setting up equivalent fractions with matching units for numerators and denominators, then cross-multiplying and dividing to solve for the unknown. Convert to the required units at the end if necessary.
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