Question

Lipitor, a pharmaceutical drug that has been shown to lower “bad” cholesterol levels while raising “good” cholesterol levels in patients taking the drug, had over $3 billion in sales in 2015. Assuming one 2.5-g pill contains 4.0% of the active ingredient by mass, what mass in kg of active ingredient is present in one bottle of 100 pills?

Short answer

The mass of the active ingredient present in one bottle of 100 pills is \(0.01 kg\).

Step-by-step solution

Finding the mass of the active ingredient in one pill

Given that each 2.5-g pill contains 4.0% of the active ingredient, we can find the mass of the active ingredient in one pill by multiplying the pill's total mass by the percentage of the active ingredient. Mass of active ingredient in one pill = (Total mass of pill) x (Percentage of active ingredient) = \(2.5 g \times 0.04\)

Calculate the mass of the active ingredient in one pill

Now, perform the multiplication: Mass of active ingredient in one pill = \(2.5 g \times 0.04\) = \(0.1 g\)

Calculate the mass of the active ingredient in 100 pills

To find the mass of the active ingredient in 100 pills, multiply the mass of the active ingredient in one pill by the total number of pills in a bottle. Mass of active ingredient in 100 pills = (Mass of active ingredient in one pill) x (Number of pills) = \(0.1 g \times 100\)

Calculate the mass of the active ingredient in kg

Now, perform the multiplication and convert the mass of the active ingredient to kg: Mass of active ingredient in 100 pills = \(0.1 g \times 100\) = \(10 g\) To convert the mass to kg, divide by 1000: Mass of active ingredient = \(\frac{10}{1000} kg\) = \(0.01 kg\) The mass of the active ingredient present in one bottle of 100 pills is 0.01 kg.

Key concepts

Pharmaceutical Calculations

Pharmaceutical calculations are essential in the formulation and dispensing of medication to ensure patients receive the correct dosage for effective treatment. In our exercise, the focus is on calculating the mass of the active ingredient in medication pills.
To do this, we must first understand the percentage of the active ingredient by mass within a single pill. Percentage by mass helps us know how much of a pill's total mass contributes to the active ingredient.
Here’s how you can tackle such calculations:

• Identify the total mass of the pill. For instance, in our example, each pill weighs 2.5 grams.
• Determine the percentage of the active ingredient. In this case, it's 4%.
• Calculate the mass of the active ingredient by multiplying the total mass by the percentage in decimal form (e.g., 4% becomes 0.04).

Using these simple steps, pharmaceutical professionals can ensure accurate dosing, which is critical for patient safety and achieving the desired therapeutic outcomes.

Mass Conversion

Mass conversion is a crucial concept when working with pharmaceutical calculations, particularly when dosing accuracy is required. In this exercise, we need to convert the mass of the active ingredient calculated from grams to kilograms. Converting units can help in comparing or communicating the dose requirements across different measurement systems.
In mass conversion, particularly from grams to kilograms, it's important to remember that:

• 1 gram (g) equals 0.001 kilograms (kg).
• To convert a mass in grams to kilograms, you divide the mass in grams by 1000.

Applying this conversion, once we calculated that 100 pills contain 10 grams of active ingredient, we converted it into kilograms by dividing by 1000, giving us 0.01 kilograms.
This conversion is a simple but critical step in ensuring that you are utilizing the appropriate units for calculations and discussions in pharmaceutical contexts.

Active Ingredient Concentration

Active ingredient concentration is necessary to determine how much of a medication's dosage is comprised of the ingredients that produce the therapeutic effect. In pharmacology, knowing the exact concentration of an active ingredient allows professionals to understand both efficacy and potential toxicity of a drug.
In our example, calculating the concentration of the active ingredient within Lipitor pills follows a straightforward process:

• First, note the percentage of the active ingredient provided (4% in this exercise).
• Next, apply this percentage to the total mass of a single pill to find the actual mass of the therapeutic component.

This direct approach helps avoid over or under dosing, ensuring that patients receive the correct amount of therapeutic substance. Correct understanding and application of these calculations are cornerstones in pharmaceutical practices, influencing both development and administration of medications.