2.2 Percentage Strengths, Ratio Strengths & PPM Conversions
Key Takeaways
- % w/v represents grams of solute in 100 mL of solution; % v/v represents mL of solute in 100 mL; % w/w represents grams of solute in 100 g.
- Ratio strength expresses concentration as 1 in X, converted to percentage using Percentage = 100 / X.
- Adrenaline 1 in 1,000 w/v equals 0.1% w/v (1 mg/mL); Adrenaline 1 in 10,000 w/v equals 0.01% w/v (0.1 mg/mL).
- Parts per million (ppm) represents 1 part in 1,000,000 (1 mg/L w/v or 1 mg/kg w/w), equivalent to 0.0001% w/v.
- Converting between percentage, ratio, mg/mL, and ppm requires clear step-by-step conversion factors.
2.2 Percentage Strengths, Ratio Strengths & PPM Conversions
Introduction to Expression of Concentration
In pharmaceutical formulation, compounding, and clinical dispensing, active pharmaceutical ingredients (APIs) are expressed in various strength formats. Candidates preparing for the PSI Equivalence Examination must master rapid and error-free conversions between percentage strengths (% w/v, % v/v, % w/w), ratio strengths (1 in X), parts per million (ppm), and weight-in-volume expressions (mg/mL, g/L).
1. Percentage Strengths Defined
Percentage strength expresses the mass or volume of active substance present relative to 100 total units of the final preparation:
Three Core Types of Percentage Strengths:
- Percent Weight-in-Volume (% w/v):
- Definition: Grams of solid solute in 100 mL of final liquid preparation.
- Standard application: Liquid solutions, IV infusions, eye drops, and oral liquids.
- Formula: $%\text{ w/v} = \frac{\text{Mass of Solute (g)}}{\text{Volume of Solution (mL)}} \times 100$
- Percent Volume-in-Volume (% v/v):
- Definition: Millilitres of liquid solute in 100 mL of final liquid preparation.
- Standard application: Liquid-in-liquid mixtures (e.g., ethanol dilutions, aromatic waters).
- Formula: $%\text{ v/v} = \frac{\text{Volume of Solute (mL)}}{\text{Volume of Solution (mL)}} \times 100$
- Percent Weight-in-Weight (% w/w):
- Definition: Grams of solute in 100 grams of final solid or semi-solid preparation.
- Standard application: Ointments, creams, gels, and bulk powders.
- Formula: $%\text{ w/w} = \frac{\text{Mass of Solute (g)}}{\text{Total Mass of Preparation (g)}} \times 100$
2. Ratio Strengths
Ratio strength represents concentration as "1 part of active substance in $X$ total parts of final preparation", written as 1 in $X$ or 1:$X$.
Standard Definitions of Ratio Strengths:
- 1 in $X$ % w/v: 1 gram of solid solute in $X$ mL of solution.
- 1 in $X$ % v/v: 1 mL of liquid solute in $X$ mL of solution.
- 1 in $X$ % w/w: 1 gram of solid solute in $X$ grams of preparation.
Mathematical Conversion Equations:
Clinical Reference Examples:
- Adrenaline 1 in 1,000 w/v: $\frac{100}{1000} = 0.1%\text{ w/v} = 1\text{ mg/mL}$ (used for intramuscular anaphylaxis treatment).
- Adrenaline 1 in 10,000 w/v: $\frac{100}{10000} = 0.01%\text{ w/v} = 0.1\text{ mg/mL}$ (used for IV cardiac arrest resuscitation).
- Chlorhexidine 1 in 2,000 w/v: $\frac{100}{2000} = 0.05%\text{ w/v} = 0.5\text{ mg/mL}$.
3. Parts Per Million (PPM) Conversions
Parts per million (ppm) is used to express extremely dilute concentrations, such as trace element additives in parenteral nutrition, fluoride levels in water supplies, or heavy metal contaminant limits in raw materials.
Definition and Equivalencies:
Conversion Quick Reference Table:
| Concentration Format | Equivalent % w/v | Ratio Strength | mg/mL Equivalent |
|---|---|---|---|
| 10,000 ppm | $1.0%\text{ w/v}$ | 1 in 100 | $10\text{ mg/mL}$ |
| 1,000 ppm | $0.1%\text{ w/v}$ | 1 in 1,000 | $1\text{ mg/mL}$ |
| 100 ppm | $0.01%\text{ w/v}$ | 1 in 10,000 | $0.1\text{ mg/mL}$ |
| 1 ppm | $0.0001%\text{ w/v}$ | 1 in 1,000,000 | $0.001\text{ mg/mL}$ ($1\ \mu\text{g/mL}$) |
4. Step-by-Step Worked Numerical Examples
Worked Example 2.2.1: Percentage to Ratio Strength & mg/mL Conversion
Clinical Scenario: A prescriber's order calls for Chlorhexidine digluconate 0.02% w/v mouthwash. Express this concentration as:
- A ratio strength (1 in $X$).
- Concentration in mg/mL.
Solution:
- Part 1: Convert 0.02% w/v to Ratio Strength (1 in $X$)
- Part 2: Convert 0.02% w/v to mg/mL
Worked Example 2.2.2: Adrenaline Resuscitation Ampoule Quantity
Clinical Scenario: An emergency resuscitation kit contains a 10 mL pre-filled syringe of Adrenaline 1 in 10,000 w/v. Calculate the total mass of adrenaline (in mg) present in the full 10 mL syringe.
Solution:
- Step 1: Understand 1 in 10,000 w/v Definition
- Step 2: Convert to mg/mL
- Step 3: Calculate Mass in 10 mL Syringe
Worked Example 2.2.3: Fluoride PPM to % w/v and Total Content Calculation
Clinical Scenario: A public health fluoride supplement solution contains 2.5 ppm of fluoride ion (w/v).
- Express this concentration as a percentage strength (% w/v).
- Calculate the mass of fluoride ion (in mg) contained in a 500 mL bottle of this solution.
Solution:
- Part 1: Convert 2.5 ppm to % w/v
- Part 2: Calculate mg of Fluoride in 500 mL
5. Summary Table
| Expression | Definition | Example | Equivalent in mg/mL |
|---|---|---|---|
| % w/v | Grams per 100 mL | 0.9% w/v NaCl | 9 mg/mL |
| Ratio Strength | 1 g per X mL | 1 in 1,000 Adrenaline | 1 mg/mL |
| PPM (w/v) | 1 mg per L (1,000 mL) | 5 ppm Fluoride | 0.005 mg/mL (5 \mu g/mL) |
| % w/w | Grams per 100 g | 1% w/w Hydrocortisone | N/A (Solid/Semi-solid) |
Express a solution of concentration 1 in 4,000 % w/v as a percentage strength (% w/v).
How many milligrams of adrenaline (epinephrine) are present in a 10 mL pre-filled syringe of adrenaline 1 in 10,000 w/v solution?
A fluoridated water sample contains 5 ppm of fluoride ion (w/v). Express this concentration as a percentage strength (% w/v).
A pharmacist is asked to supply 250 g of 2.5% w/w hydrocortisone ointment. What mass of active hydrocortisone powder is required to prepare this formulation?