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Pharmacy Calculations Concentrations
Introduction Concentrations
Concentrations : As a pharmacy student, mastering the concept of concentration is essential. Concentrations are the foundation of pharmacy calculations, and the ability to convert from one concentration to another is a critical skill. This guide provides an in-depth understanding of concentrations and their applications in pharmaceutical calculations.
Pharmaceutical formulations often consist of multiple ingredients, known as excipients, contained within a vehicle. These excipients may be solids or liquids, necessitating an understanding of various concentration expressions. The concentration of a medicine informs healthcare professionals about the amount of active drug present, making it a crucial aspect of pharmaceutical practice. Additionally, proficiency in converting between different types of concentrations is vital for ensuring accurate medication preparation and administration.
Types of Concentration Expressions
Concentration refers to the ratio of an ingredient’s amount to the total product amount. Various expressions of concentration include:
- Weight/Volume (w/v): When a solid ingredient is dissolved in a liquid vehicle.
- Volume/Weight (v/w): When a liquid ingredient is incorporated into a solid vehicle.
- Volume/Volume (v/v): When both the drug and vehicle are liquids.
- Weight/Weight (w/w): When both the drug and vehicle are solids.
When dealing with ratio strengths, percentage strengths, and parts per million (ppm), the same units must be used to ensure consistency and accuracy.
Example 1: Expressing Ratios
| Ingredient | Product | Expression |
| 5mL | 12mL | 5:12 v/v |
| 3mg | 5mg | 3:5 w/w |
| 3mg | 5g (5,000mg) | 3:5,000 w/w |
Amount Strengths
Example 2
A solution contains 1,200mg of sodium chloride dissolved in 120mL of water. Express the concentration as amount strength.
Amount strength is commonly expressed as mg/100mL, mg/mL, g/100mL, or g/L. Using proportional relationships:
| Sodium Chloride | Water (mL) |
| 1,200mg | 120mL |
| z mg | 100mL |
Solving for z, we find that 12mg of NaCl is present per mL of solution, which equates to 12mg/mL or 0.012g/mL.
Ratio Strengths
Ratio strengths are expressed in the form 1 in r, where 1 represents the numerator and r represents the denominator. The units used depend on whether the substance is a solid or a liquid.
Example 3
A solution contains 50mL of ethanol in 2L (2,000mL) of water. Express this as a ratio strength.
| Ethanol (mL) | Product (mL) |
| 50 | 2,000 |
| 1 | r |
By calculation, r = 40, meaning the ratio strength is 1 in 40 v/v.
Example 4
A product contains 250mg of sulfur in 5g of yellow soft paraffin. Express this as a ratio strength.
250mg = 0.25g, so:
| Sulfur (g) | Product (g) |
| 0.25 | 5 |
| 1 | r |
Solving for r, we get 1 in 20 w/w.
Parts Per Million (ppm)
Parts per million is used to express extremely low concentrations.
| Standard Convention | Expression |
| 1ppm w/v | 1g in 1,000,000mL |
| 1ppm w/w | 1mg in 1,000,000mg |
| 1ppm v/v | 1mL in 1,000,000mL |
Example 5
Fluoride in water supply exceeds 0.7ppm w/v. Express this as mg/L.
0.7ppm w/v = 0.7g in 1,000,000mL = 700mg in 1,000L = 0.7mg/L.
Percentage Concentration
Percentage concentrations are calculated by expressing the amount of ingredient relative to 100 parts of the product.
Example 7
A cream contains 12g of drug X in 100g of base. The percentage concentration is 12% w/w.
Example 8
A 1 in 500 w/v potassium permanganate solution is expressed as:
| Ingredient (g) | Product (mL) |
| 1 | 500 |
| x | 100 |
Solving for x, we get 0.2% w/v.
Converting Expressions of Concentration
A general method for conversion is illustrated in the table below:
| Expression | Formula |
| Percentage (p) | (a/b) * 100 |
| Ratio Strength (r) | b/a |
| Parts per Million (ppm) | (a/b) * 1,000,000 |
Example 11
A solution contains 20mL of ethanol in 500mL of product. Express the concentration as a ratio strength and percentage.
| Ingredient (mL) | Product (mL) |
| 20 | 500 |
| p | 100 |
| r | 1 |
Solving for p, we get 4% v/v, and for r, 1 in 25 v/v.
Calculating Ingredient Amount for a Percentage Solution
Proportional relationships are used to determine the required amount of ingredient.
| Amount | Percentage |
| a | p |
| b | 100 |
Example 16
How many mg of aluminum acetate are needed to prepare 500mL of a 0.03% w/v solution?
0.03% w/v = 0.03g per 100mL = 30mg per 100mL.
| Aluminum Acetate (mg) | Product (mL) |
| x | 500 |
| 30 | 100 |
Solving for x, we get 150mg.
Conclusion
Understanding concentrations and their conversions is fundamental for pharmacy practice. By mastering these calculations, pharmacy students can ensure accuracy in medication formulation and administration. With practice and a methodical approach, pharmacy calculations can be performed efficiently and correctly.