Question

An extra-strength aspirin tablet contains \(0.500 \mathrm{~g}\) of the active ingredient, acetylsalicylic acid. Aspirin strength used to be measured in grains. If 1 grain \(=60 \mathrm{mg}\), how many grains of the active ingredient are in 1 tablet? (Report your answer to three significant figures.)

Short answer

8.33 grains are in one tablet.

Step-by-step solution

- Identify the given information

The problem states that an extra-strength aspirin tablet contains 0.500 grams (g) of acetylsalicylic acid, and 1 grain is equal to 60 milligrams (mg).

- Convert grams to milligrams

Since 1 gram (g) is equal to 1000 milligrams (mg), convert 0.500 grams to milligrams using the formula:\[0.500 \text{ g} \times 1000 \text{ mg/g} = 500 \text{ mg} \text{ of acetylsalicylic acid}.\text{So, there are }500\text{ mg in one tablet.}\]

- Convert milligrams to grains

Now, using the conversion factor from the problem (1 grain = 60 milligrams), convert 500 mg to grains:\[\text{Number of grains} = \frac{500 \text{ mg}}{60 \text{ mg/grain}} \approx 8.33 \text{ grains}.\text{So, there are approximately }8.33 \text{ grains in one tablet.}\]

- Report the final answer to three significant figures

Since the problem asks for the answer to be reported to three significant figures, the final answer to the number of grains in one tablet containing 0.500 g of acetylsalicylic acid is approximately 8.33 grains.

Key concepts

grams to milligrams conversion

Understanding how to convert between grams and milligrams is essential in chemistry calculations. Since 1 gram (g) is equal to 1000 milligrams (mg), this conversion is relatively simple. You simply multiply the number of grams by 1000 to get the equivalent amount in milligrams.

For example, in the problem provided, we are given 0.500 grams of acetylsalicylic acid. To convert this to milligrams, we use the formula:
\(0.500 \text{ g} \times 1000 \text{ mg/g} = 500 \text{ mg}\)

Therefore, 0.500 grams of acetylsalicylic acid is equal to 500 milligrams. This step is crucial before we proceed with further conversions.

milligrams to grains conversion

Converting milligrams (mg) to grains is a bit more specialized and is typically used in pharmacology. According to the exercise, 1 grain is equal to 60 milligrams. To convert milligrams to grains, you need to divide the number of milligrams by the conversion factor (60 mg/grain).

For example, after converting 0.500 grams to 500 milligrams, we then convert 500 milligrams to grains:
\( \frac{500 \text{ mg}}{60 \text{ mg/grain}} \approx 8.33 \text{ grains} \)

Therefore, there are approximately 8.33 grains of acetylsalicylic acid in one extra-strength aspirin tablet. Understanding this conversion can help in interpreting different measurement units used in various disciplines.

significant figures in chemistry calculations

Significant figures are crucial in chemistry because they indicate the precision of a measurement. When performing calculations, it's important to account for the significant figures of the given data.

In the provided exercise, we need to report our final answer to three significant figures. This ensures that our answer, approximately 8.33 grains, accurately reflects the precision of the given data (0.500 grams). Remember, the number of significant figures in your answer should be based on the least precise measurement in your calculation.

Following these rules helps maintain the integrity and consistency of scientific data and calculations.