1 gal. = 4 qt. = 8 pints = 128 fl. oz. = 3785.41 mL
1 pint = 16 fl. oz.
1 pint = 473 mL
1 fl. oz. = 29.57 mL
1 tsp = 5 mL (approx.)
1 tbsp = 15 mL(approx.)
1 fluid ounce (fl oz) is not the same as 1 ounce (oz) in weight.
1 oz = 1.04 fluid oz. by weight.
Fluid ounce (fl oz): Measures volume (how much space a liquid occupies).
Ounce (oz): Measures weight (the mass of a substance)
For water, 1 US fluid ounce is close to—but not exactly—1 ounce in weight. Specifically, 1 US fluid ounce of water weighs about 1.043 ounces (oz) by weight, due to the density of water and the way the units are defined
Product Strengths
Strength refers to the specific amount of active ingredient in each unit of a pharmaceutical product.
It describes thepotency of the medication and is directly related to dosing.
Strength is typically expressed as:
Weight units (mg, g, mcg)
Units of activity (e.g., International Units for insulin)
📌
Product strength refers to the amount of active pharmaceutical ingredient (API) in a given formulation.
It is usually expressed as a specific quantity of the API per unit of the product.
Example: 500 mgtab, 100 mgvial solution
Product Concentration
Concentration refers to the amount of active pharmaceutical ingredient (API) dispersed in a given amount of the total formulation.
It's essentially a measure of how "concentrated" the active ingredient is within the product.
📌
Concentration refers to the amount of solute (usually the API) in a specified amount of solvent or solution.
Concentration can be expressed in several ways:
Percentage (%) → parts per hundred (e.g., 2% lidocaine → 2 gm/100mL lidocaine)
Parts per million (ppm) or parts per billion (ppb)
Molarity (moles per liter)
Weight per volume (w/v) → grams per milliliter (g/mL)
Weight per weight (w/w) → grams per gram
Why are there different ways of expressing concentrations?
Different ways of expressing concentrations exist because various applications and fields require unique methods for conveying information about the amounts of substances present in mixtures or solutions. The choice of concentration units is often based on the nature of the substances involved, the required precision, the context of the measurement, and the ease of use. Here are some reasons for having different concentration units:
Varying concentration ranges: Different units of concentration are suitable for expressing varying ranges of concentrations. For example, molarity (M) is commonly used for solutions with relatively high concentrations, while parts per million (ppm) and parts per billion (ppb) are used for solutions with very low concentrations. Each unit is appropriate for a specific range of values and provides a clear and accurate representation of the concentration. We don’t want to make errors writing or reading many leading zeroes or it can lead to errors.
Nature of the substances: The type of substances present in a mixture or solution can determine the most appropriate concentration unit. For instance, mass/volume percentage (% w/v) is commonly used for solid solutes in liquid solutions, while mass/mass percentage (% w/w) is used for mixtures of solid substances. Similarly, volume/volume percentage (% v/v) is suitable for mixtures of liquid substances.
Specific applications: Some concentration units are more relevant to certain industries or applications. For example, in the pharmaceutical industry, the use of ppm and ppb is essential for expressing the concentrations of impurities or contaminants in drug products. In environmental sciences, these units are also commonly used to quantify trace amounts of pollutants.
Ease of use and understanding: Depending on the context, some concentration units are easier to use and understand than others. For example, mass/volume percentage is a straightforward and intuitive unit for expressing concentrations in many everyday applications, while molarity is more suitable for scientific and academic contexts.
International standards: Certain concentration units are established by international standards or regulatory agencies, ensuring uniformity and comparability of measurements across different regions and industries.
Relationship between product strength and concentration
Concentration and strength are related concepts in pharmaceuticals that describe how much active ingredient is present in a formulation, but they have distinct meanings and applications.
Concentration in Pharmaceuticals
Concentration refers to the amount of active pharmaceutical ingredient (API) dispersed in a given amount of the total formulation.
It's essentially a measure of how "concentrated" the active ingredient is within the product.
Concentration can be expressed in several ways:
Percentage (%) → parts per hundred (e.g., 2% lidocaine)
Parts per million (ppm) or parts per billion (ppb)
Parts per million (ppm)
Details…
Parts per million (ppm)
It’s a way of expressing very small concentrations of substances.
It’s a ratio used to express the concentration of a substance in a mixture.
It indicates the number of parts of the substance of interest per one million parts of the total mixture.
In other words, it is a unit of measurement that describes the concentration of one substance in relation to another.
Mathematically, 1 ppm can be represented as:
1 ppm = 1 part of solute / 1,000,000 parts of solution
—> (1 ppm = 1 mg of substance per liter of solution)
This relationship only works for aqueous solutions (water-based)
Aqueous solution explained…
An aqueous solution is a mixture where one or more substances are dissolved in water. The term "aqueous" comes from the Latin word for water, "aqua," and it specifically refers to water being the solvent in the solution.
Basic Components
Solvent: Water (H₂O)
Solute: The substance(s) dissolved in the water
Examples in Everyday Life
Salt water (sodium chloride dissolved in water)
Sugar water (sucrose dissolved in water)
Coffee and tea (various compounds dissolved in water)
Many household cleaners
Most bodily fluids like blood and urine
Importance
Aqueous solutions are fundamental in:
Biology: Most biochemical reactions occur in aqueous environments
Chemistry: Many chemical reactions happen in water
Environment: Natural water bodies contain dissolved minerals and gases
This works because:
Water has a density of approximately 1 g/mL or 1 kg/L
Therefore, 1 liter of water weighs about 1 kilogram (1,000,000 mg) Note: 1 kg = 1,000 g = 1,000,000 mg)
So 1 mg in 1 liter = 1 part in 1,000,000 parts = 1 ppm
Example calculations:
If you dissolve 5 mg of salt in 1 liter of water:
Concentration = 5 mg/L = 5 ppm
If a water sample has 0.5 ppm of chlorine:
This means there are 0.5 mg of chlorine in each liter of water
If you have 2 liters of solution containing 10 mg of a substance:
Concentration = 10 mg ÷ 2 L = 5 mg/L = 5 ppm
Common uses:
PPM is commonly used to measure:
Trace contaminants in water (e.g., lead levels)
Air pollutants (e.g., carbon monoxide)
Minerals in soil
Additives in food
Chemical concentrations in scientific research
⚠️ Important Note: This 1 ppm = 1 mg/L relationship is only true for dilute aqueous solutions.
For:
Very concentrated solutions
Solutions with solvents other than water
Gases or solids
The relationship changes because the density is no longer 1 kg/L.
The fundamental difference
In water-based solutions:
1 ppm = 1 mg/L (because water's density is 1 g/mL)
In non-aqueous solutions:
The conversion factor depends on the solvent's density
1 ppm ≠ 1 mg/L (unless the solvent happens to have a density of 1 g/mL)
Examples with different solvents
Ethanol (density = 0.789 g/mL):
If concentration = 10 mg/L
ppm = 10 mg/L ÷ 0.789 g/mL = 12.7 ppm
Hexane (density = 0.659 g/mL):
If concentration = 5 mg/L
ppm = 5 mg/L ÷ 0.659 g/mL = 7.6 ppm
Parts per billion (ppb) = 1 part in 1,000,000,000
Similar to ppm, parts per billion is another ratio used to express the concentration of a substance in a mixture.
It represents the number of parts of the substance of interest per one billion parts of the total mixture.
Mathematically, 1 ppb can be represented as:
1 ppb = 1 part of solute / 1,000,000,000 parts of solution
Applications of ppm and ppb in pharmaceutical calculations
Monitoring impurities in drug products
In pharmaceutical manufacturing, it is important to monitor and control the levels of impurities in drug products.
Impurities can arise from various sources, such as raw materials, manufacturing processes, or degradation.
These impurities can potentially impact the safety and efficacy of the drug product.
Hence, it is crucial to quantify impurities at very low concentrations, which is where ppm and ppb measurements come into play.
Assessing contaminants in the environment
Environmental contaminants, such as heavy metals, pesticides, and other pollutants, can be present in water, air, and soil.
These contaminants can make their way into the raw materials used in drug manufacturing, posing potential risks to patients.
Measuring these contaminants at very low concentrations using ppm and ppb allows for proper monitoring and control in pharmaceutical production.
Calculating dilutions and concentrations
In pharmacy practice, pharmacists often need to prepare drug solutions of varying concentrations.
For example, a pharmacist may need to prepare a solution containing a specific concentration of a drug or dilute a stock solution to achieve the desired concentration.
Calculating the appropriate amount of solute to add to a solution to achieve the desired ppm or ppb concentration is an essential skill for pharmacists.
Example problem
A pharmacist needs to prepare 1 L of a solution containing 5 ppm of a drug. How many milligrams (mg) of the drug should be added to prepare the solution?
Molarity (number of moles of solute per liter of solution)
Molarity (M)
Details…
Molarity is the number of moles of solute per liter of solution (mol/L). It is a widely used unit of concentration in chemistry and pharmacology.
One molar (1 M) solution contains one mole of solute per liter of solution.
A 0.5 M glucose solution contains 0.5 moles of glucose in every 1 L of solution.
Preparing a 0.9% Sodium Chloride Solution (Normal Saline)
Consider a situation where a pharmacist needs to prepare a 0.9% sodium chloride (NaCl) solution, also known as normal saline.
Normality (expresses the gram-equivalent weight of a solute per liter of solution. It relates to the reactive capacity of a solution.)
Normality (N)
Details…
Normality is the number of equivalents of solute per liter of solution.
It is used in the context of acid-base, oxidation-reduction, and other types of reactions.
One normal (1 N) solution contains one equivalent of solute per liter of solution.
Example: A 1 N hydrochloric acid solution contains 1 equivalent of HCl in every 1 L of solution.
Molality (number of moles of solute per kilogram of solvent)
Molality (m)
Details…
Molality is the number of moles of solute per kilogram of solvent.
This unit is temperature-independent and is used when the concentration is affected by changes in temperature and pressure.
Example: A 1.0 molal (1.0 m) sodium chloride solution contains 1.0 mole of sodium chloride in every 1 kg of water.
Percentage strength⭐
Weight per volume (w/v) → grams per milliliter (g/mL)
Weight per weight (w/w) → grams per gram
Details…
One common way of expressing product strength is through percentage strength. Percentage strength is a measure of the amount of active ingredient present in a given quantity of a pharmaceutical product.
There are three types of percentage strength:
Weight-in-weight (w/w) percentage preparations
Weight-in-weight percentage is used when the final product is a solid (powder, ointment, etc.), and the component you are measuring the percentage of is a also a solid.
Units in the numerator and denominator must be the same (gram/gram)
For example, a 2% (w/w) hydrocortisone cream contains 2 grams of hydrocortisone in every 100 grams of the cream.
Volume-in-volume(v/v) percentage preparations
Volume-in-volume percentage is used when the final product is a liquid(solution) and the component you are measuring the percentage of is also a liquid
Units in the numerator and denominator must be the same (mL/mL)
Example: A 70% v/v isopropyl alcohol solution contains 70 mL of isopropyl alcohol in every 100 mL of solution.
Weight-in-volume (w/v) percentage preparations
Weight-in-volume percentage is used when the final product is a liquid as indicated by the (v) in the denominator (eg., suspensions) and the component you are measuring the percentage of is a solid as indicated by the (w) in the numerator.
The numerator is always in grams and the denominator is always in milliliters.
For example, a 5% (w/v) dextrose solution contains 5 grams of dextrose in every 100 milliliters of the solution.
Ratios (e.g., 1:1000)
Ratio strength ⭐
Details…
Another way of expressing product strength is ratio strength.
Ratio strength is a way to express the concentration of a pharmaceutical product as a ratio of the active ingredient to the total preparation.
It is the proportion of the active ingredient to the total volume or weight of the product.
It's typically written in the format 1:X, where 1 represents one part of the active ingredient and X represents the total number of parts in the preparation.
📌
Express ratio strength as 1 to something (i.e., 1: total volume or wt.).
Example: 2 g of solute in 800 mL of preparation
The ratio strength is NOT 2:800, but rather is 1:400.
Why use ratio strength?
Expressing a pharmaceutical product as ratio strength is useful for several reasons:
Clarity in Low Concentrations:
Ratio strength is particularly effective for describing very dilute solutions, where the solute concentration is minimal.
For example, expressing epinephrine as 1:1000 clearly indicates that there is 1 gram of solute in 1000 milliliters of solution.
This format avoids confusion and provides an intuitive understanding of the dilution level.
Safety:
For certain critical medications (like epinephrine or local anesthetics), ratio strength provides a standardized way to communicate concentration that reduces medication errors.
Standardization:
Ratio strength provides consistency across different countries and healthcare systems.
Ratio strength uses a standardized format (e.g., 1:x), which makes it easier to interpret and calculate dosages compared to other methods like percentage strength or parts-per-million.
Ease of Conversion:
Ratio strength can be easily converted to other concentration expressions, such as:
percentage strength
milligram percent
using proportional relationships
This flexibility is valuable in pharmacy practice for accurate dosing and preparation of medications.
Precision in Formulations:
It is particularly useful in compounding and preparing solutions where the exact ratio of active ingredients to total product volume or weight needs to be specified, ensuring precise therapeutic effects.
Overall, ratio strength provides a clear, consistent, and practical way to express concentrations, especially for dilute pharmaceutical preparations.
Examples of ratio strength
Epinephrine 1:1000 (1 gram in 1000 mL, or 1 mg/mL)
Local anesthetics like lidocaine 1:100,000 with epinephrine
Converting percentage strength to ratio strength
Example 1️⃣: Express 0.02% w/v as a ratio strength
Example 2️⃣: What is the percentage strength (w/w) of a 1:500 zinc oxide ointment?
Example 3️⃣: An 80 mL solution contains 40 mg of drug. Express the concentration as a ratio strength.
Strength in Pharmaceuticals
Strength refers to the specific amount of active ingredient in each unit of a pharmaceutical product. It describes the potency of the medication and is directly related to dosing.
Strength is typically expressed as:
Weight units (mg, g, mcg)
Units of activity (e.g., International Units for insulin)
The Relationship Between Them
The key relationship between concentration and strength is:
Strength provides the absolute amount of active ingredient in a dosage unit (tablet, capsule, injection, etc.)
Concentration describes the relative amount of active ingredient compared to the total formulation
Interconversion: Concentration can often be derived from strength and vice versa. For example:
A 500mg tablet that weighs 1g total has a concentration of 50% w/w
A solution with concentration 10mg/mL has a strength of 10mg per milliliter
Concentration = Qty of Solute / Qty of Preparation
Qty of Preparation = (Qty of Solute + Qty of Diluent)
Examples of liquid diluents or base solution: water, NaCl, dextrose
Examples of solid diluent or base: petrolatum
Example of relationship between concentration and strengths:
A patient is getting chemotherapy with a medication called Docetaxel. The total dose the patient will need is 100 mg for each treatment.
The manufacturer makes Docetaxel in two different strengths:
80 mg vial and 160 mg vial
Docetaxel vials come in two different concentrations:
1️⃣ How many milliliters of Docetaxel is required to compounding 100 mg of Docetaxel in 250 mL of normal saline (NS)? Note that the pharmacy has in stock 10 mg/mL vial concentrations of Docetaxel.
2️⃣ What is the concentration of Docetaxel in the prepared IV bag?
Concentration = Qty of Solute / Qty of Preparation,
and Qty of Preparation includes Qty of Solute + Diluent (or base)
3️⃣ What is the percent strength of the prepared Docetaxel IV piggy bag (IVPB)?
4️⃣ Convert % strength to concentration (in mg/mL) if given 0.038% w/v
Dilutions
1️⃣ Stock solutions
Stock solutions are concentrated solutions from which weaker strength solutions can be easily made.
Practice problems
How many milliliters of a 10% w/v stock solution should be used in preparing 1 gallon of a 0.05% w/v solution? 1 gal. = 3785.41 mL ✅☑️ stock solution
[ans: 18.9 mL]
Solution 1
Solution 2 using equation
C1V1 = C2V2
where C1 and V1 are the concentration and volume of the stock solution, and C2 and V2 are the concentration and volume of the diluted solution.
First, we need to convert gallons to milliliters. There are 3.78541 liters in 1 gallon and 1,000 milliliters in 1 liter:
A 60-mL bottle of an oral solution contains a drug in a concentration of 15 mg/mL. A medication order requests that the drug concentration be reduced to 5 mg/mL by using three parts water to one part polyethylene glycol 400. How many milliliters of each of these two agents should be used? ✅ ☑️ concentrationdilution
[ans: 90 mL water, 30 mL PEG 400]
Solution
Explanation
To solve this problem, you will need to apply the concepts of concentration, dilution, and ratio.
Concentration: The initial concentration of the drug is given as 15 mg/mL in a 60-mL bottle.
Dilution: The goal is to reduce the drug concentration to 5 mg/mL.
Ratio: The diluent mixture is comprised of three parts water to one part polyethylene glycol 400.
Here's the step-by-step solution:
Calculate the total amount of drug in the initial solution:
60 mL * 15 mg/mL = 900 mg
Calculate the final volume needed to achieve the desired concentration of 5 mg/mL:
900 mg / 5 mg/mL = 180 mL
Determine the volume of the diluent mixture to be added:
180 mL (final volume) - 60 mL (initial volume) = 120 mL
Calculate the volume of each component in the diluent mixture using the given ratio:
Water: (3 parts / 4 parts) * 120 mL = 90 mL
Polyethylene glycol 400: (1 part / 4 parts) * 120 mL = 30 mL
So, you will need to add 90 mL of water and 30 mL of polyethylene glycol 400 to dilute the drug concentration to 5 mg/mL.
NEORAL oral solution contains 100 mg/mL of cyclosporine. If a pharmacist prepares 30 mL of an oral solution containing 10% w/v cyclosporine, how many milliliters of diluent should be used? ✅ ☑️ concentrationdilution
[ans: 0 mL]
Solution
Explanation
We are given the following information:
The concentration of NEORAL oral solution is 100 mg/mL of cyclosporine.
The desired final concentration is 10% w/v cyclosporine.
The desired final volume is 30 mL.
First, we need to convert the 10% w/v concentration into mg/mL. Since 10% w/v means 10 g of cyclosporine in 100 mL of solution, we can calculate the concentration as follows:
(10 g / 100 mL) * (1000 mg / 1 g) = 100 mg/mL
Now, we have the initial concentration (C1) and the desired final concentration (C2):
C1 = 100 mg/mL
C2 = 100 mg/mL
We also have the desired final volume (V2):
V2 = 30 mL
Using the dilution formula C1V1 = C2V2, we can find the volume of NEORAL solution (V1) needed:
V1 = (C2 * V2) / C1
Plugging in the values:
V1 = (100 mg/mL * 30 mL) / 100 mg/mL
V1 = 30 mL
Now, we know that the volume of the NEORAL solution required is 30 mL. Since the desired final concentration is the same as the initial concentration, no diluent is needed. The pharmacist can simply use 30 mL of the NEORAL oral solution to prepare the desired 30 mL oral solution containing 10% w/v cyclosporine.
A pharmacist receives an order for 60 mL of an oral solution containing memantine hydrochloride (NAMENDA) 1.5 mg/mL. She has on hand a 360-mL bottle of oral solution containing memantine hydrochloride, 10 mg/5 mL, and a diluent of sorbitol solution. How many milliliters each of the available oral solution and sorbitol solution may be used to fill the order? ✅ ☑️ dilutionalligation
[ans: 45 mL memantine oral solution; 15 mL sorbitol solution]
solution 1
solution 2
We are given the following information:
The desired final concentration of memantine hydrochloride is 1.5 mg/mL.
The desired final volume of the oral solution is 60 mL.
The initial concentration of the memantine hydrochloride oral solution is 10 mg/5 mL (or 2 mg/mL).
We need to find the volume of the available oral solution and the sorbitol solution needed to fill the order.
Using the dilution formula C1V1 = C2V2, where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume, we can find the volume of the available oral solution (V1) needed:
V1 = (C2 * V2) / C1
Plugging in the values:
V1 = (1.5 mg/mL * 60 mL) / 2 mg/mL
V1 = 45 mL
So, 45 mL of the available memantine hydrochloride oral solution is needed. To find the volume of the sorbitol solution needed, subtract the volume of the available oral solution from the desired final volume:
Volume of sorbitol solution = V2 - V1
Volume of sorbitol solution = 60 mL - 45 mL
Volume of sorbitol solution = 15 mL
So, the pharmacist should use 45 mL of the available memantine hydrochloride oral solution (10 mg/5 mL) and 15 mL of the sorbitol solution to prepare the 60 mL oral solution containing memantine hydrochloride 1.5 mg/mL.
How many milliliters of a 1% w/v stock solution of a certified red dye should be used in preparing 4000 mL of a mouthwash that is to contain 1:20,000 w/v of the certified red dye as a coloring agent? stock solution
[ans: 20 mL]
How much drug should be used in preparing 50 mL of a stock solution such that 5 mL diluted to 500 mL will yield a 1:1000 w/v solution? stock solution
[ans: 5 g]
How many grams of sodium chloride should be used in preparing 500 mL of a stock solution such that 50 mL diluted to 1000 mL will yield a 0.3% w/v solution for irrigation? stock solution
[ans: 30 g]
How many milliliters of a 17% w/v concentrate of benzalkonium chloride should be used in preparing 100 mL of a stock solution such that 5 mL diluted to 60 mL will yield a 0.13% w/v solution of benzalkonium chloride? stock solution
[ans: 9.18mL]
2️⃣ Dilutions of stock preparations
A dilution is performed when you take a certain percentage solution and add a 0% base to decrease the percentage concentration.
Analogy
A dilution is like watering down a strong drink to make it less intense. Imagine you have a glass of very strong orange juice, and you want to make it less concentrated. To do this, you add water (which has 0% orange juice) to the glass. This decreases the concentration of the orange juice, making it less intense. In the case of a solution, you're adding a "base" with 0% of the active ingredient to the original solution, which lowers the overall concentration.
Practice problems
How many milliliters of a 1:5000 w/v solution of the preservative lauralkonium chloride can be made from 125 mL of a 0.2% w/v solution of the preservative? ✅ ☑️ dilution
[ans: 1250 mL]
Solution 1
Solution 2 using C1V1 = C2V2 formula
To solve this problem, we need to use the formula:
C1V1 = C2V2
where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume.
In this case, we know:
C1 = 0.2% w/v (which means there are 0.2 g of solute per 100 mL of solution)
V1 = 125 mL
C2 = 1:5000 w/v (which means there is 1 g of solute per 5000 mL of solution)
We want to find V2, the final volume.
First, we need to convert the final concentration to a percentage:
1 g per 5000 mL = (1 g / 5000 mL) * (1000 mL / 1 L) = 0.2 g/L
0.2 g/L = 0.02% w/v
So, C2 = 0.02% w/v
Now, we can substitute the values into the formula:
C1V1 = C2V2
0.2% w/v * 125 mL = 0.02% w/v * V2
Simplifying, we get:
V2 = (0.2% w/v * 125 mL) / 0.02% w/v
V2 = 1250 mL
Therefore, 125 mL of a 0.2% w/v solution of lauralkonium chloride can make 1250 mL of a 1:5000 w/v solution of the same preservative.
How many milliliters of water should be added to 80 mL of a 20% w/v aqueous solution to prepare a 3% w/v solution? ✅ ☑️ dilution
[ans: 453.3 mL of water]
Solution 1
Solution 2 using formula
To solve this problem, we can use the concept of mass conservation. In this case, the mass of the solute (the substance being dissolved) remains constant, while the solvent (water) is being added.
Let's denote the mass of the solute as 'm' and the mass of the final solution as 'M'. We are given that the initial solution is 20% w/v, which means there are 20 grams of solute in 100 mL of solution. We are also given that the initial volume of the solution is 80 mL. We can calculate the mass of the solute (m) in the initial solution as follows:
m = (20 g/100 mL) * 80 mL = 16 g
Now, let 'x' be the volume of water (in mL) to be added to the initial solution to get a 3% w/v solution. Then, the total volume of the final solution will be (80 + x) mL. We can now set up the equation for the final solution concentration:
m / M = 3% w/v
16 g / (80 + x) mL = 3 g/100 mL
To solve for 'x', we can cross-multiply and then isolate 'x':
(16 g * 100 mL) / 3 g = 80 + x
1600 / 3 = 80 + x
Now, subtract 80 from both sides:
1600/3 - 80 = x
(1600 - 240) / 3 = x
1360 / 3 ≈ 453.33
Therefore, approximately 453.33 mL of water should be added to the 80 mL of 20% w/v aqueous solution to prepare a 3% w/v solution.
If 10 mL of an injection containing 50 mg of a medication is diluted to 1 L calculate the percent strength of the resulting solution. ✅ percent strength
[ans: 0.005% w/v]
Solution 1
Dopamine HCl injection is available in 5-mL vials each containing 40 mg of dopamine HCI per milliliter. The injection must be diluted before administration by intravenous infusion. If a pharmacist dilutes the injection by adding the contents of one vial to 250 mL of 5% dextrose injection, calculate the percent w/v of dopamine HCl in the infusion. ✅ percent strength
[ans: 0.078% w/v]
When the contents of one vial are added to 250 mL of 5% dextrose injection, the total volume of the infusion is:
5 mL + 250 mL = 255 mL
The amount of dopamine HCl in the infusion is still 200 mg, but now it is dispersed in 255 mL of solution.
Dilution and Concentration Problem
Concentration equations
C1V1 = C2V2 (dilution and concentration equation)
Q1C1 + Q2C2 = Q3C3 (aliquot equation)
Key concepts
Stock solution
Diluent
Dilution factor
Steps to alter product strength
Determining the desired concentration
Calculating the amount of stock solution needed
Calculating the amount of diluent (or base) needed
Mixing stock solution and diluent (or base)
Practical Examples and Exercises
If a pharmacist reconstitutes a vial to contain 1 g of cefazolin in 3 mL of injection, and then dilutes 1.6 mL of the injection with sodium chloride injection to prepare 200 mL of intravenous infusion, calculate the concentration of cefazolin in the infusion in percent and in mg/mL. ✅ concentrationpercent strength
[ans: 0.27% w/v, 2.7 mg/mL]
Solution
Fortification
Fortification is the process of adding more of the active pharmaceutical ingredient (API) to a preparation to increase its strength.
This can be done for various reasons, such as:
Adjusting the dose for a specific patient
Compensating for drug degradation during storage or transportation
Addressing shortages of specific drug concentrations
Providing a custom-made product not available in the market
There are two primary methods of fortification:
🅰️ Direct Fortification
Direct fortification is a process used to increase the strength or concentration of a medicine or solution by directly adding more of the main active ingredient. This active ingredient, called the active pharmaceutical ingredient (API), is responsible for the medicine's effect.
Analogy…
Direct fortification is like making a drink stronger by adding more of the main ingredient. Imagine you have a glass of lemonade that isn't sweet enough. To make it sweeter, you just add more sugar to the lemonade. In the case of medicines, the main ingredient is called the "API" or active pharmaceutical ingredient. Direct fortification means adding more of the API to the medicine to make it stronger or more effective.
Example (liquid): A pharmacist needs to add codeine phosphate to 180 mL of a 12 mg/5 mL elixir of acetaminophen with codeine to achieve a final concentration of 30 mg/5 mL of codeine phosphate. Calculate the additional amount of codeine phosphate powder that needs to be added. Assume no increase in the volume of the final liquid.
Example (solid): A pharmacist received a prescription for 120 mL of an amoxicillin suspension to contain 400 mg of drug in each 5 mL. The pharmacist has 120 mL of suspension containing 250 mg/5 mL and also has 500-mg tablets of the drug. How many tablets should be pulverized and added to the suspension to achieve the desired strength?Assume no increase in the volume of the suspension.
The pharmacist observed that after adding the pulverized tablets, the suspension measured 122 mL in volume. Calculate the concentration of the new suspension.
If a pharmacist fortified 10 g of a 0.1% w/w tacrolimus (PROTOPlC) ointment by adding 12.5 g of an ointment containing 0.03% w/w of the same drug, what would be the percentage strength of the mixture? ✅ ☑️ fortification
[ans: 0.061% w/w]
Solution
Explanation
We are given the following information:
The initial amount of 0.1% w/w tacrolimus ointment is 10 g.
The amount of 0.03% w/w tacrolimus ointment being added is 12.5 g.
We need to find the percentage strength of the resulting mixture.
Calculate the total amount of tacrolimus in each ointment:
In the 0.1% w/w ointment: (0.1 / 100) * 10 g = 0.01 g
In the 0.03% w/w ointment: (0.03 / 100) * 12.5 g = 0.00375 g
Calculate the total amount of tacrolimus in the mixture:
Total tacrolimus = tacrolimus in 0.1% w/w ointment + tacrolimus in 0.03% w/w ointment
Total tacrolimus = 0.01 g + 0.00375 g = 0.01375 g
Calculate the total weight of the mixture:
Total weight = weight of 0.1% w/w ointment + weight of 0.03% w/w ointment
Total weight = 10 g + 12.5 g = 22.5 g
Calculate the percentage strength of the mixture:
Percentage strength = (Total tacrolimus / Total weight) * 100
So, the percentage strength of the resulting mixture is approximately 0.0611% w/w.
How much Peruvian balsam should be added to 3 oz of a diaper rash ointment containing 4% w/w Peruvian balsam to increase the concentration to 10% w/w? 1 oz = 28.35 gm ✅ concentrationmass balancefortificationalligation Difficulty Level ⭐⭐⭐⭐⭐
[ans: 5.67g balsam]
Solution 1 using algebra
Solution 2 using alligation
🅱️ Indirect Fortification
Indirect fortification is a way to make a medicine with the right strength by mixing different versions of the same medicine that have different strengths.
Analogy…
Think of it like making a fruit punch with the perfect sweetness by mixing a very sweet punch and a less sweet punch together. The goal is to figure out how much of each punch to mix, so that when they're combined, you get the perfect taste. In the case of medicines, it's about finding the right balance of strengths to make a medicine that works just as the doctor intended.
Example: A pharmacist needs to prepare 150 mL of an amoxicillin suspension with a concentration of 350 mg/5 mL. The available suspensions are 500 mg/5 mL (Suspension A) and 250 mg/5 mL (Suspension B). Calculate the volume of each suspension needed to achieve the desired strength.
Alligations
🅰️ Alligation alternate
This technique is used for making dilutions when the diluent is zero percent or higher.
📌
You can only dilute to an intermediate percent (ie., you cannot add 10% to 20% and get a percent higher than 20% or lower than 10%).
The final product will be somewhere between 10% and 20%.
Sample problems
A pharmacist receives an order for 60 mL of an oral solution containing memantine hydrochloride (NAMENDA) 1.5 mg/mL. She has on hand a 360-mL bottle of oral solution containing memantine hydrochloride, 10 mg/5 mL, and a diluent of sorbitol solution. How many milliliters each of the available oral solution and sorbitol solution may be used to fill the order? ✅ ☑️ dilutionalligation
[ans: 45 mL memantine oral solution; 15 mL sorbitol solution]
solution 1
solution 2
We are given the following information:
The desired final concentration of memantine hydrochloride is 1.5 mg/mL.
The desired final volume of the oral solution is 60 mL.
The initial concentration of the memantine hydrochloride oral solution is 10 mg/5 mL (or 2 mg/mL).
We need to find the volume of the available oral solution and the sorbitol solution needed to fill the order.
Using the dilution formula C1V1 = C2V2, where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume, we can find the volume of the available oral solution (V1) needed:
V1 = (C2 * V2) / C1
Plugging in the values:
V1 = (1.5 mg/mL * 60 mL) / 2 mg/mL
V1 = 45 mL
So, 45 mL of the available memantine hydrochloride oral solution is needed. To find the volume of the sorbitol solution needed, subtract the volume of the available oral solution from the desired final volume:
Volume of sorbitol solution = V2 - V1
Volume of sorbitol solution = 60 mL - 45 mL
Volume of sorbitol solution = 15 mL
So, the pharmacist should use 45 mL of the available memantine hydrochloride oral solution (10 mg/5 mL) and 15 mL of the sorbitol solution to prepare the 60 mL oral solution containing memantine hydrochloride 1.5 mg/mL.
🅱️ Alligation medial
This method is used to obtain the average strength of a mixture of two or more substance whose concentration and percent strength are already known.
Practice problems
What is the percentage of zinc oxide (ZnO) in an ointment prepared by mixing 200 g of 10% ointment, 50 g of 20% ointment, and 100 g of 5% ointment? ✅ alligation medial
[ans: 10% w/w]
Solution
How many milliliters of a 1:5000 w/v solution of the preservative lauralkonium chloride can be made from 125 mL of a 0.2% w/v solution of the preservative? ✅ ☑️ dilution
[ans: 1250 mL]
Solution 1
Solution 2 using C1V1 = C2V2 formula
To solve this problem, we need to use the formula:
C1V1 = C2V2
where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume.
In this case, we know:
C1 = 0.2% w/v (which means there are 0.2 g of solute per 100 mL of solution)
V1 = 125 mL
C2 = 1:5000 w/v (which means there is 1 g of solute per 5000 mL of solution)
We want to find V2, the final volume.
First, we need to convert the final concentration to a percentage:
1 g per 5000 mL = (1 g / 5000 mL) * (1000 mL / 1 L) = 0.2 g/L
0.2 g/L = 0.02% w/v
So, C2 = 0.02% w/v
Now, we can substitute the values into the formula:
C1V1 = C2V2
0.2% w/v * 125 mL = 0.02% w/v * V2
Simplifying, we get:
V2 = (0.2% w/v * 125 mL) / 0.02% w/v
V2 = 1250 mL
Therefore, 125 mL of a 0.2% w/v solution of lauralkonium chloride can make 1250 mL of a 1:5000 w/v solution of the same preservative.
How many milliliters of water should be added to 80 mL of a 20% w/v aqueous solution to prepare a 3% w/v solution? ✅ ☑️ dilution
[ans: 453.3 mL of water]
Solution 1
Solution 2 using formula
To solve this problem, we can use the concept of mass conservation. In this case, the mass of the solute (the substance being dissolved) remains constant, while the solvent (water) is being added.
Let's denote the mass of the solute as 'm' and the mass of the final solution as 'M'. We are given that the initial solution is 20% w/v, which means there are 20 grams of solute in 100 mL of solution. We are also given that the initial volume of the solution is 80 mL. We can calculate the mass of the solute (m) in the initial solution as follows:
m = (20 g/100 mL) * 80 mL = 16 g
Now, let 'x' be the volume of water (in mL) to be added to the initial solution to get a 3% w/v solution. Then, the total volume of the final solution will be (80 + x) mL. We can now set up the equation for the final solution concentration:
m / M = 3% w/v
16 g / (80 + x) mL = 3 g/100 mL
To solve for 'x', we can cross-multiply and then isolate 'x':
(16 g * 100 mL) / 3 g = 80 + x
1600 / 3 = 80 + x
Now, subtract 80 from both sides:
1600/3 - 80 = x
(1600 - 240) / 3 = x
1360 / 3 ≈ 453.33
Therefore, approximately 453.33 mL of water should be added to the 80 mL of 20% w/v aqueous solution to prepare a 3% w/v solution.
If 10 mL of an injection containing 50 mg of a medication is diluted to 1 L calculate the percent strength of the resulting solution. ✅ percent strength
[ans: 0.005% w/v]
Solution 1
Dopamine HCl injection is available in 5-mL vials each containing 40 mg of dopamine HCI per milliliter. The injection must be diluted before administration by intravenous infusion. If a pharmacist dilutes the injection by adding the contents of one vial to 250 mL of 5% dextrose injection, calculate the percent w/v of dopamine HCl in the infusion. ✅ percent strength
[ans: 0.078% w/v]
When the contents of one vial are added to 250 mL of 5% dextrose injection, the total volume of the infusion is:
5 mL + 250 mL = 255 mL
The amount of dopamine HCl in the infusion is still 200 mg, but now it is dispersed in 255 mL of solution.
If a pharmacist reconstitutes a vial to contain 1 g of cefazolin in 3 mL of injection, and then dilutes 1.6 mL of the injection with sodium chloride injection to prepare 200 mL of intravenous infusion, calculate the concentration of cefazolin in the infusion in percent and in mg/mL. ✅ concentrationpercent strength
[ans: 0.27% w/v, 2.7 mg/mL]
Solution
If 30 g of a 1% w/w hydrocortisone ointment are mixed with 12 g of a nonmedicated ointment base, what would be the resulting concentration of hydrocortisone in the mixture? ✅ ☑️ dilutionalligation alternate
[ans: 0.714% w/w]
Solution
Explanation
To find the resulting concentration of hydrocortisone in the mixture, first, we need to determine the amount of hydrocortisone in the initial ointment.
1% w/w hydrocortisone ointment means there is 1 g of hydrocortisone in 100 g of ointment. We have 30 g of this ointment, so we need to find the amount of hydrocortisone in it:
(1 g hydrocortisone / 100 g ointment) * 30 g ointment = 0.3 g hydrocortisone
Now, we mix the 30 g of hydrocortisone ointment with 12 g of nonmedicated ointment base, resulting in a total weight of 42 g for the mixture (30 g + 12 g).
Next, we need to find the concentration of hydrocortisone in the mixture:
0.3 g hydrocortisone / 42 g mixture = x
x ≈ 0.007142857
To convert this to a percentage:
0.007142857 * 100% ≈ 0.714%
The resulting concentration of hydrocortisone in the mixture is approximately 0.714% w/w.
As a part of a clinical study, a pharmacist is asked to prepare modifications of standard 22 g 2% w/w mupirocin ointments by adding the needed quantities of either mupirocin powder or a nonmedicated ointment base. Required for the study are a 1.75% w/w mupirocin ointment and a 2.25% w/w mupirocin ointment. For each modified ointment, calculate the quantity of component to add to a standard ointment. ✅ ☑️ direct fortificationindirect fortification
[ans: 1.75%: 22 gram of 2%, plus 3.14 gram of base; 2.25%: 0.056 gram of mupirocin powder]
Solution 1
Solution 2
If a cough syrup contains in each teaspoonful 1 mg of chlorpheniramine maleate and if a pharmacist desired to double the strength, how many milligrams of that ingredient would need to be added to a 60-mL container of the syrup? Assume no increase in volume. direct fortification
[ans: 12 mg]
Flexible Collodion USP contains 2% w/w camphor and has a specific gravity of 0.78. The cap is broken on a one-pint bottle and most of the ether evaporates, leaving a volume of 135 mL. What is the concentration of camphor in the evaporated solution expressed as % w/v? 1 pint = 473 mL specific gravityvolume conversionfortificationpercent strength ✅
[ans: 5.47% w/v]
Solution
A pharmacist received a prescription for 100 mL of a cefuroxime axetil suspension to contain 300 mg of drug in each 5 mL. The pharmacist has 100 mL of a suspension containing 250 mg/5 mL and also has 250-mg scored tablets of the drug. How many tablets should be pulverized and added to the suspension to achieve the desired strength? Assume no increase in the volume of the suspension. fortification
[ans: 4 tablets]
How many milliliters of a 10% w/v stock solution should be used in preparing 1 gallon of a 0.05% w/v solution? 1 gal. = 3785.41 mL ✅☑️ stock solution
[ans: 18.9 mL]
Solution 1
Solution 2 using equation
C1V1 = C2V2
where C1 and V1 are the concentration and volume of the stock solution, and C2 and V2 are the concentration and volume of the diluted solution.
First, we need to convert gallons to milliliters. There are 3.78541 liters in 1 gallon and 1,000 milliliters in 1 liter:
How many milliliters of a 1% w/v stock solution of a certified red dye should be used in preparing 4000 mL of a mouthwash that is to contain 1:20,000 w/v of the certified red dye as a coloring agent? stock solution
[ans: 20 mL]
How much drug should be used in preparing 50 mL of a stock solution such that 5 mL diluted to 500 mL will yield a 1:1000 w/v solution? stock solution
[ans: 5 g]
How many grams of sodium chloride should be used in preparing 500 mL of a stock solution such that 50 mL diluted to 1000 mL will yield a 0.3% w/v solution for irrigation? stock solution
[ans: 30 g]
How many milliliters of a 17% w/v concentrate of benzalkonium chloride should be used in preparing 100 mL of a stock solution such that 5 mL diluted to 60 mL will yield a 0.13% w/v solution of benzalkonium chloride? stock solution
[ans: 9.18mL]
How many milliliters of 70% w/w concentrated glycolic acid (sp.gr. = 1.27) would be needed to prepare 2 fl.oz. of a 7.25% w/v solution? 1 fl.oz. = 29.5735 mL ✅ ☑️ stock solution
[ans: 4.82 mL]
Solution 1
Solution 2 using equation
To solve this problem, we'll first need to convert the 70% w/w concentrated glycolic acid to a w/v concentration. To do this, we'll use the specific gravity (sp.gr.) of the glycolic acid solution, which is given as 1.27. We'll also need to convert the volume of the final solution from fluid ounces to milliliters.
Convert the 70% w/w glycolic acid to a w/v concentration:
Since specific gravity (sp.gr.) is the ratio of the density of a substance to the density of water, we can multiply the specific gravity by the density of water (1 g/mL) to find the density of the glycolic acid solution:
Density = sp.gr. × density of water = 1.27 g/mL
Now we can calculate the mass of 1 mL of the glycolic acid solution:
Mass = density × volume = 1.27 g/mL × 1 mL = 1.27 g
Since we have a 70% w/w solution, 70% of the mass consists of glycolic acid:
Mass of glycolic acid = 1.27 g × 0.70 = 0.889 g
Now we can express the concentration as w/v:
70% w/w = 0.889 g/mL
Convert the volume of the final solution from fluid ounces to milliliters:
1 fluid ounce (fl.oz.) = 29.5735 mL
2 fl.oz. × 29.5735 mL/fl.oz. = 59.147 mL
Use the dilution formula C1V1 = C2V2:
C1 = concentration of the concentrated glycolic acid solution = 0.889 g/mL
V1 = volume of the concentrated glycolic acid solution (the value we need to find)
C2 = concentration of the final glycolic acid solution = 7.25% w/v = 0.0725 g/mL
V2 = volume of the final glycolic acid solution = 59.147 mL
0.889 g/mL × V1 = 0.0725 g/mL × 59.147 mL
To find V1, we can divide both sides by 0.889 g/mL:
What is the percentage of zinc oxide (ZnO) in an ointment prepared by mixing 200 g of 10% ointment, 50 g of 20% ointment, and 100 g of 5% ointment? ✅ alligation medial
[ans: 10% w/w]
Solution
What is the percentage strength of sucrose in a mixture of 500 mL of an aqueous solution containing 40% w/v sucrose, 400 mL of a second aqueous solution containing 21% w/v sucrose, and 100 mL of purified water to make a total of 1000 mL? [ans: 28.4% w/v]
A pharmacist-herbalist wishes to consolidate the following assayed batches of Gingko biloba leaves: 200 g containing 22% w/w glycosides, 150 g containing 26% w/w glycosides, and 80 g containing 27% w/w glycosides. Calculate the percent of glycosides in the combined mixture. [ans: 24.3% w/w]
In what proportion should 8% w/w and 2.5% w/w calamine ointments be mixed to make 5% w/w calamine? [ans: 2.5:3 or 5:6]
In what proportion should 20% benzocaine ointment be mixed with an ointment base to produce a 2.5% benzocaine ointment? [ans: 2.5:17.5]
A hospital pharmacist wants to use three lots of zinc oxide ointment containing, respectively, 50%, 20%, and 5% of zinc oxide. In what proportion should they be mixed to prepare a 10% zinc oxide ointment? [ans: 5 parts of 50%, 5 parts of 20%, 50 parts of 5%]
In what proportions may a manufacturing pharmacist mix 20%, 15%, 5%, and 3% zinc oxide ointments to produce a 10% ointment?
[ans. 1: 7 parts of 20%, 5 parts of 15%, 5 parts of 5%, 10 parts of 3%]
[ans. 2: 5 parts of 20%, 7 parts of 15%, 10 parts of 5%, 5 parts of 3%]
How many milliliters each of a 50% w/v dextrose solution and a 5% w/v dextrose solution is required to prepare 4500 mL of a 10% w/v solution? [ans: 500 mL of 50%, 4000 mL of 5%]
How many grams of 2.5% w/w hydrocortisone cream should be mixed with 360 g of 0.25% w/w cream to make a 1% w/w hydrocortisone cream? [ans: 180g of 2.5% cream]
How many grams of zinc oxide powder should be added to 3200 g of a 5% w/w zinc oxide ointment to prepare a 20% w/w zinc oxide ointment? [ans: 600 g of the powder]
A pharmacist received the following prescription:
The pharmacist has no clindamycin phosphate powder but does have clindamycin phosphate sterile solution, 150 mg/mL, in vials. From the label, the pharmacist learns that the solution is aqueous.
🅰️ How many milliliters of the clindamycin phosphate sterile solution should the pharmacist use in filling the prescription? ✅
[ans: 12 mL]
solution
🅱️How many milliliters of 95% v/v of alcohol are required? ✅
[ans: 65.7 mL]
solution
A pharmacist received the following prescription. The pharmacist has no hydrocortisone powder but does have a hydrocortisone cream, 1%. How many grams each of hydrocortisone cream and AQUAPHOR should be used in filling the prescription? ✅
[ans: 9 g cream, 6 g Aquaphor]
solution
A farm product contains 12.5% w/v concentrate of tiamulin hydrogen fumarate, used to treat swine dysentery when diluted as a medicated drinking water. How many gallons of medicated water may be prepared from a liter of concentrate if the final product is to contain 227 mg of tiamulin hydrogen per gallon? [ans: 550.7 gallons]
If a pharmacist added 12 g of azelaic acid to 50 g of an ointment containing 15% azelaic acid, what would be the final concentration of azelaic acid in the ointment? [ans: 31.45% w/w]
If 400 mL of a 20% w/v solution were diluted to 2 L, what would be the final percentage strength? [ans: 4% w/v]
Mupirocin ointment contains 2% w/w mupirocin. How many grams of a polyethylene glycol ointment base must be mixed with the contents of a 22-g tube of the mupirocin ointment to prepare one having a concentration of 5 mg/g? [ans: 66 g base]
How many grams of an 8% w/w progesterone gel must be mixed with 1.45 g of a 4% w/w progesterone gel to prepare a 5.5% w/w gel? [ans: 0.87g of 8% w/w gel]
Chlorhexidine gluconate is available in different products in concentrations of 4% w/v and 0.12% w/v. How many milliliters of the more dilute product may be prepared from each fluid ounce of the more concentrated product? [ans: 985.7mL]
A pharmacist fills a prescription for 30 g of a 0.1% w/w hydrocortisone cream by combining a 1% w/w hydrocortisone cream and a cream base. How many grams of each were used?
[ans: 3 g of 1% cream, 27g of base]
How many milliliters of water should be added to 1.5 L of a 20% w/v solution to prepare one containing 12%w/v of solute? [ans: 1000 mL]
If two tablespoonfuls of a 10% w/v povidone-iodine solution were diluted to 1 quart with purified water, what would be the ratio strength of the dilution? [ans: 1:315 w/v]
How many milliliters of a 1:50 w/v boric acid solution can be prepared from 500 mL of a 5% w/v boric acid solution? [ans: 1250 mL]
How many milliliters of water must be added to 250 mL of a 25% w/v stock solution of sodium chloride to prepare a 0.9% w/v sodium chloride solution? [ans: 6694 mL]
How many milliliters of undecylenic acid should be added to 30 mL of a 20% v/v undecylenic acid topical solution to change its concentration to 25% v/v? alligation
[ans: 2 mL]
A pharmacy intern is asked to prepare 3 L of a 30% w/v solution. The pharmacy stocks the active ingredient in 8-ounce bottles of 70% w/y strength. How many bottles will be needed as the source of the active ingredient? [ans: 6 bottles]
How many milliliters of a 10% w/v stock solution are needed to prepare 120 mL of a solution containing 10 mg of the chemical per milliliter? [ans: 12 mL]
How many milliliters of a 2.0 molar sodium chloride solution would be needed to prepare 250 mL of 0.15 molar sodium chloride solution? [ans: 18.75 mL]
NEORAL oral solution contains 100 mg/mL of cyclosporine. If a pharmacist prepares 30 mL of an oral solution containing 10% w/v cyclosporine, how many milliliters of diluent should be used? ✅ ☑️ concentrationdilution
[ans: 0 mL]
Solution
Explanation
We are given the following information:
The concentration of NEORAL oral solution is 100 mg/mL of cyclosporine.
The desired final concentration is 10% w/v cyclosporine.
The desired final volume is 30 mL.
First, we need to convert the 10% w/v concentration into mg/mL. Since 10% w/v means 10 g of cyclosporine in 100 mL of solution, we can calculate the concentration as follows:
(10 g / 100 mL) * (1000 mg / 1 g) = 100 mg/mL
Now, we have the initial concentration (C1) and the desired final concentration (C2):
C1 = 100 mg/mL
C2 = 100 mg/mL
We also have the desired final volume (V2):
V2 = 30 mL
Using the dilution formula C1V1 = C2V2, we can find the volume of NEORAL solution (V1) needed:
V1 = (C2 * V2) / C1
Plugging in the values:
V1 = (100 mg/mL * 30 mL) / 100 mg/mL
V1 = 30 mL
Now, we know that the volume of the NEORAL solution required is 30 mL. Since the desired final concentration is the same as the initial concentration, no diluent is needed. The pharmacist can simply use 30 mL of the NEORAL oral solution to prepare the desired 30 mL oral solution containing 10% w/v cyclosporine.
The formula for a buffer solution contains 1.24% w/v of boric acid. How many milliliters of a 5% w/v boric acid solution should be used to obtain the boric acid needed in preparing 1 L of the
buffer solution? [ans: 248mL]
In filling a hospital order, a pharmacist diluted 1 mL of an amphotericin B injection containing 50 mg/10 mL with a 5% w/v dextrose injection to prepare an intravenous infusion containing
amphotericin B, 0.1 mg/mL. How many milliliters of infusion did the pharmacist prepare? [ans: 50 mL]
What would be the concentration of a solution prepared by diluting 45 mL of a 4.2-molar solution to a volume of 250 mL? [ans: 0.76 mg/mL or 0.76 molar]
A pharmacist combines the contents of a 30-g tube of a 0.5% ointment and a 90-g tube of a 1.5% ointment of the same active ingredient. What is the concentration of the mixture?
[ans: 1.25% w/w]
How many milliliters of a 100 mg/mL concentrate of Rhus toxicodendron extract should be used in preparing the prescription? ✅ concentration
[ans: 0.01 mL]
Solution
If a pharmacist fortified 10 g of a 0.1% w/w tacrolimus (PROTOPlC) ointment by adding 12.5 g of an ointment containing 0.03% w/w of the same drug, what would be the percentage strength of the mixture? ✅ ☑️ fortification
[ans: 0.061% w/w]
Solution
Explanation
We are given the following information:
The initial amount of 0.1% w/w tacrolimus ointment is 10 g.
The amount of 0.03% w/w tacrolimus ointment being added is 12.5 g.
We need to find the percentage strength of the resulting mixture.
Calculate the total amount of tacrolimus in each ointment:
In the 0.1% w/w ointment: (0.1 / 100) * 10 g = 0.01 g
In the 0.03% w/w ointment: (0.03 / 100) * 12.5 g = 0.00375 g
Calculate the total amount of tacrolimus in the mixture:
Total tacrolimus = tacrolimus in 0.1% w/w ointment + tacrolimus in 0.03% w/w ointment
Total tacrolimus = 0.01 g + 0.00375 g = 0.01375 g
Calculate the total weight of the mixture:
Total weight = weight of 0.1% w/w ointment + weight of 0.03% w/w ointment
Total weight = 10 g + 12.5 g = 22.5 g
Calculate the percentage strength of the mixture:
Percentage strength = (Total tacrolimus / Total weight) * 100
So, the percentage strength of the resulting mixture is approximately 0.0611% w/w.
How much chlorhexidine gluconate should be used in preparing the prescription? 1 gal. = 3785.41 mL ✅
[ans: 14.42 g chlorhexidine gluconate]
solution
explanation
To prepare the prescription, we need to determine how much chlorhexidine gluconate is needed to make an 80 mL solution with a 1:4200 w/v dilution when 1 teaspoon is diluted to 1 gallon.
First, let's convert the volume measurements to consistent units.
1 gallon = 3.78541 L
1 teaspoon = 5 mL
Now, let's find the total volume of the final diluted solution when 1 tsp of the concentrated solution is added to 1 gallon of water:
5 mL (concentrated solution) + 3.78541 L (water) = 5 mL + 3785.41 mL = 3790.41 mL (final diluted solution)
Now, we know that the final dilution is 1:4200 w/v, so we can determine the amount of chlorhexidine gluconate in the final diluted solution:
1 g chlorhexidine gluconate / 4200 mL solution = x g chlorhexidine gluconate / 3790.41 mL solution
Solving for x:
x = (1 g / 4200 mL) * 3790.41 mL = 0.9020 g of chlorhexidine gluconate in the final diluted solution.
We know that 0.9020 g of chlorhexidine gluconate is in 1 teaspoon (5 mL) of the 80 mL concentrated solution. To find out how much chlorhexidine gluconate we need to add to the entire 80 mL concentrated solution, we can set up the ratio:
0.9020 g / 5 mL = y g / 80 mL
Now, we can solve for y:
y = (0.9020 g / 5 mL) * 80 mL = 14.432 g
So, you would need to add 14.432 grams of chlorhexidine gluconate to the 80 mL of purified water to prepare the prescription.
What would be the concentration of chlorhexidine gluconate in the solution prepared by the pharmacist, expressed as mg/mL? ✅
[ans: 180 mg/mL]
solution
How many milliliters of a 17% w/v stock solution of benzalkonium chloride should be used in preparing the prescription? ✅
[28.24 mL stock solution]
solution
A pharmacist-herbalist mixed 100-g lots of St. John's wort containing the following percentages of the active component hypericin: 0.3%, 0.7%, and 0.25%. Calculate the percent strength of
hypericin in the mixture. [ans: 0.42% hypericin]
How many milliliters of a lotion base must be added to 30 mL of oxiconazole nitrate (OXISTAT) lotion 1% w/v to reduce its concentration to 6 mg/mL? [ans: 20 mL lotion base]
How many milliliters of an 85% w/w solution of lactic acid with a specific gravity of 1.21 should be used in preparing the prescription?
[ans: 1.46 mL lactic acid]
A pharmacist receives a prescription for 60 g of a 0.75% w/w bexarotene gel. How many grams each of a 1% w/w bexarotene gel and gel base must be used? [ans: 45-g gel & 15-g base]
As a part of a clinical study, a pharmacist is asked to prepare a modification of a standard 22-g package of a 2% mupirocin ointment by adding the needed quantity of mupirocin powder to prepare a 3% w/w mupirocin ointment. How many milligrams of mupirocin powder are required? [ans: 226.8 mg]
A pharmacist receives an order for 60 mL of an oral solution containing memantine hydrochloride (NAMENDA) 1.5 mg/mL. She has on hand a 360-mL bottle of oral solution containing memantine hydrochloride, 10 mg/5 mL, and a diluent of sorbitol solution. How many milliliters each of the available oral solution and sorbitol solution may be used to fill the order? ✅ ☑️ dilutionalligation
[ans: 45 mL memantine oral solution; 15 mL sorbitol solution]
solution 1
solution 2
We are given the following information:
The desired final concentration of memantine hydrochloride is 1.5 mg/mL.
The desired final volume of the oral solution is 60 mL.
The initial concentration of the memantine hydrochloride oral solution is 10 mg/5 mL (or 2 mg/mL).
We need to find the volume of the available oral solution and the sorbitol solution needed to fill the order.
Using the dilution formula C1V1 = C2V2, where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume, we can find the volume of the available oral solution (V1) needed:
V1 = (C2 * V2) / C1
Plugging in the values:
V1 = (1.5 mg/mL * 60 mL) / 2 mg/mL
V1 = 45 mL
So, 45 mL of the available memantine hydrochloride oral solution is needed. To find the volume of the sorbitol solution needed, subtract the volume of the available oral solution from the desired final volume:
Volume of sorbitol solution = V2 - V1
Volume of sorbitol solution = 60 mL - 45 mL
Volume of sorbitol solution = 15 mL
So, the pharmacist should use 45 mL of the available memantine hydrochloride oral solution (10 mg/5 mL) and 15 mL of the sorbitol solution to prepare the 60 mL oral solution containing memantine hydrochloride 1.5 mg/mL.
If a pharmacist added each of the following to 22-g packages of 2% mupirocin ointment, what would be the percentage strengths of the resulting ointments: ✅ percentage strength
(a) 0.25 g mupirocin powder
[ans: 3.1% w/w]
(b) 0.25 g of nonmedicated ointment base?
[ans: 1.98% w/w]
How many milliliters of liquefied phenol (90% w/w phenol solution, sp.gr.= 1.07) would be needed to prepare 3 fl.oz. of a 4.5% w/v solution? [ans: 4.15 mL liquified phenol]
If 1 mL of a 0.02% w/v isoproterenol hydrochloride solution is diluted to 10 mL with sodium chloride injection before intravenous administration, calculate the percent concentration of the diluted solution. [ans: 0.002% w/v]
A 1:750 w/v solution of benzalkonium chloride diluted with purified water in a ratio of 3 parts of the benzalkonium solution and 77 parts of purified water is recommended for bladder and urethral irrigation. What is the ratio strength of benzalkonium chloride in the final dilution?dilution
[ans: 1:20,000 w/v]
How many milliliters of a suspension base must be mixed with 250 mL of a paroxetine (PAXIL) oral suspension, 10 mg/5 mL, to change its concentration to 0.1% w/v? [ans: 250 mL base]
A standing institutional order for a 25% w/w topical antibiotic ointment has been changed to one for a 10% w/w ointment. How many grams of white petrolatum must be mixed with each 120-g package of the 25% w/w preparation to make the new 10% w/w preparation? [ans: 180 gm white petrolatum]
How many grams of salicylic acid should be added to 75 g of a polyethylene glycol ointment to prepare an ointment containing 6% w/w of salicylic acid? [ans: 4.79 g salicylic acid]
How many grams of an ointment base must be added to 45 g of clobetasol (TEMOVATE) ointment, 0.05% w/w, to change its strength to 0.03% w/w? [ans: 30g ointment base]
How many grams of 2.5% ophthalmic hydrocortisone acetate ointment and how many grams of ophthalmic base (diluent) should be used in preparing the prescription? ✅
[ans: 1 g of 2.5% hydrocortisone acetate ointment; 9 g ophthalmic base]
solution
Thimerosal Tincture USP contains 0.1% w/v thimerosal and 50% v/v ethyl alcohol. If the cap is left off of a 15-mL bottle of the tincture, and the ethyl alcohol evaporates leaving a final volume of 9.5 mL, what is the concentration of thimerosal in the evaporated solution expressed as a ratio strength? [ans: 1:633.33 w/v]
How much zinc oxide should be added to the product to make an ointment containing 10% of zinc oxide? ✅
[ans: 1.67g zinc oxide]
If equal portions of tretinoin gel (RETIN-AMICRO), 0.1% w/w and 0.04% w/w, are combined, what would be the resultant percentage strength? [ans: 0.07% w/w]
A vaginal douche powder concentrate contains 2% w/w of active ingredient. What would be the percentage concentration of the resultant solution after a 5-g packet of powder is dissolved in enough water to make 1 quart of solution? [ans: 0.011% w/v]
How many milliliters of a 0.2% solution of a skin test antigen must be used to prepare 4 mL of solution containing 0.04 mg/mL of the antigen? [ans: 0.08 mL]
How many milligrams of sodium fluoride are needed to prepare 100 mL of a sodium fluoride stock solution such that a solution containing 2 ppm of sodium fluoride results when 0.5 mL is diluted to 250 mL with water? [ans: 100 mg sodium fluoride]
How many milliliters each of corn oil and a 10% solution of cyclosporine would be needed to prepare 30 mL of the prescription? ✅
[ans: 6 mL cycylosporine solution; 24 mL corn oil]
solution
If you then wished to dilute the prescription to a concentration of 1.5% cyclosporine, how many additional milliliters of corn oil would be required? ✅
[ans: 10 mL corn oil]
solution
A hospital pharmacist is to prepare three doses of gentamicin 0.6 mg/2 mL. In stock is gentamicin 20 mg/mL. How many milliliters each of the gentamicin on hand and appropriate diluent would be needed? [ans: 0.09 mL gentamicin solution, 5.91 mL diluent]
A hospital worker combined 2 fluid ounces of a povidone-iodine cleaner, 7.5% w/v, with 4 fluid ounces of a povidone-iodine topical solution, 10 % w/v. Calculate the resulting strength of the povidone-iodine mixture. (Assume volumes are additive.) [ans: 9.17%]
If 60 g of a combination gel of hydrocortisone acetate, 1% w/w, and pramoxine, 1% w/w, is mixed with 12.5 g of a gel containing hydrocortisone acetate, 2.5% w/w, and pramoxine, 1% w/w, calculate the percentage strength of each of the two drugs in the mixture. [ans: 1.26% w/w of hydrocortisone acetate; 1.00% w/w of pramoxine]
A drug is commercially available in capsules each containing 12.5 mg of drug and 37.5 mg of diluent. How many milligrams of additional diluent must be added to the contents of one capsule to make a dilution containing 0.5 mg of drug in each 100 mg of powder? [ans: 2450 mg]
In what proportion should 5% and 1% hydrocortisone ointments be mixed to prepare a 2.5% ointment? [ans: 3:5 (5%:1%)]
In what proportion should a 20% zinc oxide ointment be mixed with white petrolatum (diluent) to produce a 3% zinc oxide ointment? [ans: 3:17 (20% ointment:petrolatum)]
A parent diluted 1-mL ibuprofen oral drops (Infant's MOTRIN Concentrated Drops) with 15 mL of water prior to administering the medication. The concentrated drops contain ibuprofen, 50
mg/1.25 mL. Calculate the concentration of ibuprofen in the dilution in
🅰️ mg/mL
[ans: 2.5 mg/mL lbuprofen]
🅱️ as a percentage strength
[ans: 0.25% w/v ibuprofen]
How many milliliters of a 2.5% w/v chlorpromazine hydrochloride injection and how many milliliters of 0.9% w/v sodium chloride injection should be used to prepare 500 mL of a 0.3% w/v chlorpromazine hydrochloride injection? [ans: 60 mL chlorpromazine HCl, 400 mL NaCl]
How many milliliters of a 2% w/v solution of lidocaine hydrochloride should be used in preparing 500 mL of a solution containing 4 mg of lidocaine hydrochloride per milliliters of solution? [ans: 100 mL lidocaine HCl injection]
Dopamine hydrochloride injection is available in 5-mL vials containing 40 mg of dopamine hydrochloride per milliliter. The injection must be diluted before administration. If a physician wishes to use sodium chloride injection as the diluent and wants a dilution containing 0.04% w/v of dopamine hydrochloride, how many milliliters of sodium chloride injection should be added to 5 mL of the injection? [ans: 495 mL NacI]
A pharmacist is to prepare 10 mL of amikacin sulfate in a concentration of 0.4 mg/0.1 mL for ophthalmic use. Available is an injection containing amikacin sulfate, 250 mg/mL. How many milliliters of this injection and of sterile normal saline solution as the diluent should be used? [ans: 0.16 mL amikacin, 9.84 mL NaCl]
How many milliliters of sterile water for injection should be added to a 1-mL vial containing 5 ug/mL of a drug to prepare a solution containing 1.5 ug/mL of the drug? [ans: 2.33 mL sterile water]
How many milligrams of a 1:10 w/w powdered dilution of colchicine should be used by a manufacturing pharmacist in preparing 100 capsules for a clinical drug study if each capsule is to contain 0.5 mg of colchicine? [ans: 500 mg colchicine dilution]
A pharmacist receives a special request from an ophthalmologist to prepare a fortified tobramycin ophthalmic solution. The available solution contains tobramycin, 3 mg/mL. How many milliliters of a tobramycin injection containing 40 mg/mL must be aseptically added to a 5-mL container of the ophthalmic solution to prepare one 0.5% in concentration? [ans: 0.286 mL tobramycin injection]
How many milliliters of water must be added to 15 mL of a 23.4% solution of sodium chloride to dilute the concentration to 0.06 mEq/mL? (MW NaCl = 58.44) ✅ ☑️ concentrationdilutionmass balance
[ans: 986 mL water]
Solution
How much Peruvian balsam should be added to 3 oz of a diaper rash ointment containing 4% w/w Peruvian balsam to increase the concentration to 10% w/w? 1 oz = 28.35 gm ✅ concentrationmass balancefortificationalligation Difficulty Level ⭐⭐⭐⭐⭐
[ans: 5.67g balsam]
Solution 1 using algebra
Solution 2 using alligation
A 60-mL bottle of an oral solution contains a drug in a concentration of 15 mg/mL. A medication order requests that the drug concentration be reduced to 5 mg/mL by using three parts water to one part polyethylene glycol 400. How many milliliters of each of these two agents should be used? ✅ ☑️ concentrationdilution
[ans: 90 mL water, 30 mL PEG 400]
Solution
Explanation
To solve this problem, you will need to apply the concepts of concentration, dilution, and ratio.
Concentration: The initial concentration of the drug is given as 15 mg/mL in a 60-mL bottle.
Dilution: The goal is to reduce the drug concentration to 5 mg/mL.
Ratio: The diluent mixture is comprised of three parts water to one part polyethylene glycol 400.
Here's the step-by-step solution:
Calculate the total amount of drug in the initial solution:
60 mL * 15 mg/mL = 900 mg
Calculate the final volume needed to achieve the desired concentration of 5 mg/mL:
900 mg / 5 mg/mL = 180 mL
Determine the volume of the diluent mixture to be added:
180 mL (final volume) - 60 mL (initial volume) = 120 mL
Calculate the volume of each component in the diluent mixture using the given ratio:
Water: (3 parts / 4 parts) * 120 mL = 90 mL
Polyethylene glycol 400: (1 part / 4 parts) * 120 mL = 30 mL
So, you will need to add 90 mL of water and 30 mL of polyethylene glycol 400 to dilute the drug concentration to 5 mg/mL.
How many milliliters of a 17% solution of benzalkonium chloride should a pharmacist use in preparing 120 mL of a prescription such that when a patient adds 15 mL of the dispensed medication to a gallon of water, as a foot soak, the resulting benzalkonium chloride concentration will be 1:5000? ✅ ☑️ ratio strengthdilution
[ans: 35.63 mL solution of benzalkonium chloride]
Solution
Explanation
Let's break the problem down step by step:
Determine the final concentration of benzalkonium chloride in the foot soak.
Determine the total amount of benzalkonium chloride needed in the foot soak.
Determine the amount of benzalkonium chloride present in the 120 mL prescription.
Calculate the volume of the 17% benzalkonium chloride solution needed in the prescription.
Final concentration in the foot soak:
We are given a 1:5000 ratio, meaning 1 part benzalkonium chloride to 5000 parts of water.
Total amount of benzalkonium chloride in the foot soak:
We know that 1 gallon of water is approximately 3,785.41 mL. When the patient adds 15 mL of dispensed medication, the total volume becomes 3,785.41 + 15 = 3,800.41 mL.
Since the concentration is 1:5000, there are 3,800.41/5000 = 0.760082 mL of benzalkonium chloride in the foot soak.
Amount of benzalkonium chloride in the 120 mL prescription:
We have 15 mL of dispensed medication, so the proportion of benzalkonium chloride in the prescription is:
(0.760082 mL benzalkonium chloride) / (15 mL dispensed medication) = 0.050672 mL benzalkonium chloride/mL dispensed medication
Volume of the 17% benzalkonium chloride solution needed in the prescription:
Let x be the volume of the 17% benzalkonium chloride solution needed.
0.17x = 0.050672 * 120 mL
x ≈ 35.7 mL
Thus, the pharmacist should use approximately 35.7 mL of the 17% benzalkonium chloride solution in preparing the 120 mL prescription.
