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Chapter 1: Problem 95

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

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

Step by step solution

01

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) = \(2.5 g \times 0.04\)
02

Calculate the mass of the active ingredient in one pill

Now, perform the multiplication: Mass of active ingredient in one pill = \(2.5 g \times 0.04\) = \(0.1 g\)
03

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) = \(0.1 g \times 100\)
04

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.

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