Question

How many \(325-\mathrm{mg}\) tablets can be produced from \(2.50 \mathrm{~kg}\) of powdered aspirin?

Short answer

7692 tablets can be produced.

Step-by-step solution

Convert Kilograms to Milligrams

First, we need to convert the total amount of powdered aspirin from kilograms to milligrams. We know there are 1,000 grams in a kilogram, and there are 1,000 milligrams in a gram. Therefore, we multiply the given kilograms by 1,000 to convert to grams, and then multiply by 1,000 again to convert to milligrams. \[2.50 \text{ kg} \times 1000 \frac{\text{g}}{\text{kg}} = 2500 \text{ g} \]\[2500 \text{ g} \times 1000 \frac{\text{mg}}{\text{g}} = 2500000 \text{ mg} \]

Calculate Number of Tablets

Now, divide the total milligrams of aspirin by the milligrams per tablet to find out how many tablets can be produced. Each tablet is 325 mg.\[ \text{Number of tablets} = \frac{2500000 \text{ mg}}{325 \text{ mg/tablet}} \]

Perform the Division

Perform the division to calculate the number of tablets.\[ \frac{2500000}{325} \approx 7692.31 \]

Interpret the Result

Since you can only produce whole tablets, round down to the nearest whole number. Therefore, the maximum number of 325 mg tablets that can be produced is 7692.

Key concepts

Understanding Unit Conversion

Unit conversion is essential when solving problems in stoichiometry, as it allows us to transform measurements from one unit to another in order to work with consistent units. For instance, converting mass from kilograms to milligrams, as seen in this exercise, involves a two-step approach.

• First, you multiply the kilograms by 1000 to change them into grams. This is because there are 1000 grams in a kilogram.
• Then, you multiply the grams by 1000 again to transform them into milligrams, since each gram equals 1000 milligrams.

These conversions are imperative because they enable calculations to be straightforward and manageable, keeping all measurements in a single, unified unit. In the given problem, starting with 2.50 kg and converting to 2,500,000 mg ensures we can easily divide by 325 mg per tablet to find the total count of aspirin tablets.

Converting Mass to Moles

Converting mass to moles is another important concept, although not directly necessary for this specific exercise, it's a key stoichiometric process in general chemistry. It involves using the molar mass of a substance to convert between the mass of a substance and the amount in moles. Here’s how you can understand it better:

• First, determine the molar mass of the substance; for aspirin (8HC7O5), it's approximately 180 g/mol.
• Then, divide the mass of the substance in grams by this molar mass to get the number of moles.

For example, if converting mass to moles was part of this problem, you would find the number of moles in the given mass before moving onto quantity calculations like in the problem at hand. Though not used here, this process is fundamental when dealing with chemical reactions and needing to determine reactant or product quantities.

The Dosage Calculation Process

Dosage calculation is critical in fields such as pharmacy and medicine, ensuring the right amount of medication is administered. In our exercise, the main job is to calculate how many standard dosage tablets (in this case, 325 mg) can be produced from a specific quantity of powdered aspirin.

• First, ensure that the total available medication (2,500,000 mg) is in the same unit as the dosage per tablet (325 mg).
• Then, divide the total quantity by the dose per tablet to find out the total number of tablets: 3\[ \frac{2500000 \text{ mg}}{325 \text{ mg/tablet}} \approx 7692.31 \]
• Finally, since partial tablets cannot physically exist, round down to the nearest whole number for practical purposes.

This straightforward process ensures dosage accuracy, which is not only vital for effectiveness but also patient safety and resource management.