Problem 40 - Chemistry: Principles and Reactions

Question

Cholesterol in blood is measured in milligrams of cholesterol per deciliter of blood. If the unit of measurement were changed to grams of cholesterol per milliliter of blood, what would a cholesterol reading of \(185 \mathrm{mg} / \mathrm{dL}\) translate to?

Step-by-Step Solution

Answer

Question: Convert a cholesterol reading of 185 mg/dL to g/mL. Answer: The cholesterol reading of 185 mg/dL is equal to 0.00185 g/mL.

Step 1: Convert mass from milligrams to grams

To convert the mass of cholesterol from milligrams to grams, divide the given value (185 mg) by 1000, as there are 1000 milligrams in a gram: \(185 \mathrm{mg} \times \dfrac{1\mathrm{g}}{1000\mathrm{mg}}=0.185 \mathrm{g}\)

Step 2: Convert volume from deciliters to milliliters

To convert the volume from deciliters (dL) to milliliters (mL), multiply the given value (1 dL) by 100, as there are 100 milliliters in a deciliter: \(1 \mathrm{dL} \times \dfrac{100\mathrm{mL}}{1\mathrm{dL}}=100 \mathrm{mL}\)

Step 3: Divide the converted mass by the converted volume

Now, we need to divide the converted mass (0.185 grams) by the converted volume (100 mL) to find the cholesterol reading in the new unit of measurement (grams per milliliter): \(\dfrac{0.185 \mathrm{g}}{100\mathrm{mL}}=0.00185 \mathrm{g/mL}\) So, the cholesterol reading of \(185 \mathrm{mg/dL}\) would translate to \(0.00185 \mathrm{g/mL}\) when expressed in grams per milliliter.

Key Concepts

Cholesterol Measurement

Cholesterol measurement in blood is an important indicator of health. It is usually expressed in milligrams per deciliter (mg/dL). This unit shows how many milligrams of cholesterol are present in every one deciliter of blood. A common cholesterol reading might be around 185 mg/dL.

However, sometimes it needs to be converted to different units for analysis or comparison purposes. Understanding how to adjust units while preserving the true value is critical, especially for medical purposes. The conversion requires a clear understanding of the relations between different units used in measuring mass and volume.

Metric System

The metric system is a standardized system of measurement universally employed in science, medicine, and many countries around the world. It includes units like grams (g), milligrams (mg), liters (L), and milliliters (mL). These consistent relationships help facilitate easy conversions. For example:

• 1 gram = 1000 milligrams
• 1 liter = 1000 milliliters
• 1 deciliter = 100 milliliters

With this knowledge, we can easily navigate changes in unit expressions, such as converting from milligrams per deciliter to grams per milliliter.

Dimensional Analysis

Dimensional analysis is a powerful tool for unit conversion. It involves using conversion factors, which are ratios expressing the same quantity in different units. By applying these conversion factors, we transition between units without altering the measured value.

Take for instance the conversion of cholesterol from mg/dL to g/mL. First, convert milligrams to grams using:\[185 \text{ mg} \times \frac{1 \text{ g}}{1000 \text{ mg}} = 0.185 \text{ g}\]Then, convert deciliters to milliliters using:\[1 \text{ dL} \times \frac{100 \text{ mL}}{1 \text{ dL}} = 100 \text{ mL}\]Finally, compute grams per milliliter by dividing the mass by the volume.

Chemistry Calculations

Chemistry calculations often require converting units, similar to this example of cholesterol measurement. This practice is crucial for achieving precision and clarity, which is essential in chemical experiments and medical assessments.

Once the units are consistent, calculations become straightforward. In the current scenario:\[\frac{0.185 \text{ g}}{100 \text{ mL}} = 0.00185 \text{ g/mL}\]
This result provides the cholesterol measurement in grams per milliliter, demonstrating how chemistry calculations rely on basic unit conversions and dimensional analysis to render clear and accurate results. These skills are vital for students and professionals alike in fields like chemistry and medicine.