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Chapter 1: Problem 89

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 \(\$ 11\) billion in sales in 2006 . Assuming one \(2.5-\mathrm{g}\) pill contains \(4.0 \%\) of the active ingredient by mass, what mass in \(\mathrm{kg}\) of active ingredient is present in one bottle of 100 pills?

Short Answer

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

Step by step solution

01

Calculate mass of active ingredient in one pill

Given the percentage of the active ingredient by mass, we can find the mass of the active ingredient in one pill. The pill's overall mass is \(2.5 \ g\) and the percentage of active ingredient (by mass) is \(4.0 \%\). So, we can calculate the mass of active ingredient as follows: Mass of active ingredient in one pill = (Percentage of active ingredient / 100) * Pill's mass
02

Compute the active ingredient mass in one pill

Now we can substitute the values into the formula. Mass of active ingredient in one pill = (4.0 / 100) * 2.5 g Mass of active ingredient in one pill = \(0.04 * 2.5 \ g\) Mass of active ingredient in one pill = 0.1 g Thus, each pill contains 0.1 g of the active ingredient.
03

Calculate mass of active ingredient in 100 pills

We now know the mass of the active ingredient in just one pill. So, to calculate the mass of the active ingredient in one bottle of 100 pills, simply multiply the mass of active ingredient in one pill by 100: Mass of active ingredient in 100 pills = (Mass of active ingredient in one pill) * 100 pills
04

Compute the mass of active ingredient in the whole bottle

Now we can substitute the value of the active ingredient's mass in one pill that we found earlier: Mass of active ingredient in 100 pills = 0.1 g * 100 pills Mass of active ingredient in 100 pills = 10 g Thus, there is 10 g of the active ingredient in the whole bottle of 100 pills.
05

Convert the mass to kg

To find the mass of active ingredient in kg, we need to convert 10 g into kg. To do this, we divide the mass in grams by 1000 (since 1 kg = 1000 g): Mass of active ingredient in kg = (Mass of active ingredient in g) / 1000 Now, we substitute the value of the mass in grams: Mass of active ingredient in kg = 10 g / 1000 Mass of active ingredient in kg = 0.01 kg So, the mass of active ingredient present in one bottle of 100 pills is 0.01 kg.

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Most popular questions from this chapter

Sterling silver is a solid solution of silver and copper. If a piece of a sterling silver necklace has a mass of \(105.0 \mathrm{~g}\) and \(\mathrm{a}\) volume of \(10.12 \mathrm{~mL}\), calculate the mass percent of copper in the piece of necklace. Assume that the volume of silver present plus the volume of copper present equals the total volume. Refer to Table \(1.5\). Mass percent of copper \(=\frac{\text { mass of copper }}{\text { total mass }} \times 100\)

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