Problem 71 - Chemistry

Question

Concentrations of substances dissolved in solution are often expressed as mass per unit volume. For example, normal human blood has a cholesterol concentration of about \(200 \mathrm{mg} / 100 \mathrm{~mL}\). Express this concentration in the following units: (a) \(\mathrm{mg} / \mathrm{L}\) (b) \(\mu \mathrm{g} / \mathrm{mL}\) (c) \(\mathrm{g} / \mathrm{L}\) (d) \(\mathrm{ng} / \mu \mathrm{L}\) (e) How much total blood cholesterol in grams does a person have if the normal blood volume in the body is \(5 \mathrm{~L}\) ?

Step-by-Step Solution

Answer

(a) 2000 mg/L, (b) 2000 µg/mL, (c) 2 g/L, (d) 2000 ng/µL, (e) 10 g.

Step 1: Unit Conversion for (a) mg/L

To convert cholesterol concentration from \(\mathrm{mg}/100 \, \mathrm{mL}\) to \(\mathrm{mg}/\mathrm{L}\), we note that \(100 \, \mathrm{mL} = 0.1 \, \mathrm{L}\). Therefore, a concentration of \(200 \, \mathrm{mg}/100 \, \mathrm{mL}\) is equivalent to \(2000 \, \mathrm{mg}/\mathrm{L}\) since \(\frac{200}{0.1} = 2000\).

Step 2: Unit Conversion for (b) µg/mL

1 milligram (mg) equals 1000 micrograms (\(\mu\)g). So, convert \(200 \, \mathrm{mg}/100 \, \mathrm{mL}\) to \(\mu \mathrm{g}/\mathrm{mL}\) by multiplying the 200 mg by 1000 to get \(200,000 \, \mu \mathrm{g}/100 \, \mathrm{mL}\), which simplifies to \(2000 \, \mu \mathrm{g}/\mathrm{mL}\) since \(\frac{200000}{100} = 2000\).

Step 3: Unit Conversion for (c) g/L

1 gram (g) equals 1000 milligrams (mg). Thus, to convert \(2000 \, \mathrm{mg}/\mathrm{L}\) to \(\mathrm{g}/\mathrm{L}\), divide by 1000 to get \(2 \, \mathrm{g}/\mathrm{L}\) since \(\frac{2000}{1000} = 2\).

Step 4: Unit Conversion for (d) ng/µL

1 milligram (mg) equals 1,000,000 nanograms (ng), and 1 microliter (µL) equals \(0.001 \, \mathrm{mL}\). So, convert \(200 \, \mathrm{mg}/100 \, \mathrm{mL}\) to \(\mathrm{ng}/\mu \mathrm{L}\) by converting mg to ng, which gives \(200,000,000 \, \mathrm{ng}/100 \, \mathrm{mL}\). This is equivalent to \(2000 \, \mathrm{ng}/\mu \mathrm{L}\) since \(100 \, \mathrm{mL} = 100,000 \, \mu \mathrm{L}\).

Step 5: Calculate Total Cholesterol in Blood for (e)

To find out how much total blood cholesterol a person has, multiply the concentration \(2000 \, \mathrm{mg}/\mathrm{L}\) by the blood volume, \(5 \, \mathrm{L}\). This results in \(10,000 \, \mathrm{mg}\), or \(10 \, \mathrm{g}\), since \(\frac{10000}{1000} = 10\).

Key Concepts

Mass Per Unit Volume

Mass per unit volume is a common way to express the concentration of a substance in a solution. Imagine you have a square piece of chocolate and cut it into small pieces. Each piece is a specific amount of chocolate mass spread over a unit of space, similar to how concentration measures the amount of a substance mass within a given volume of liquid. This is typically denoted as mass/volume, such as milligrams per liter (mg/L).
For example, with blood cholesterol levels, we typically use the concentration of milligrams per deciliter to understand how much cholesterol is present in a certain amount of blood. Knowing how to express this concentration accurately is crucial for medical assessments.
The main idea here is to understand how much of a substance is present in a specific space, which in this case, is the blood volume. It helps you compare and interpret different concentrations accurately.

Unit Conversion

Unit conversion is the process of changing one unit of measurement into another. This concept is vital in scientific computation and daily life, as it allows us to interpret and compare measurements using different systems of units.

Understanding Conversion Between Units

When dealing with cholesterol concentration, for instance, you might need to convert milligrams to micrograms, grams, or nanograms, depending on the context. These conversions rely on fixed numerical factors; for example, 1 milligram (mg) is equivalent to 1000 micrograms (µg), and 1 gram (g) is 1000 milligrams (mg).
To ensure accuracy in information, it's necessary to understand these conversion factors and apply them correctly, allowing you to express and interpret information effectively across different units.

Blood Cholesterol Concentration

Blood cholesterol concentration is an important health metric. It indicates the amount of cholesterol present in the blood, typically measured in milligrams per deciliter (mg/dL). Monitoring these levels helps assess cardiovascular health.
High cholesterol levels can lead to health issues such as heart disease, while too low levels can also be problematic. The concentration value provides a clear metric for healthcare providers to diagnose and manage cholesterol-related conditions. Sometimes, for precision's sake, conversions to more detailed units like micrograms per milliliter are needed for specific tests.
When converting blood cholesterol concentration from mg/dL to mg/L, understanding that 1 dL equals 0.1 L can help in making these calculations more accurate and accessible.

Microgram

A microgram, symbolized as µg, is a unit of mass equal to one-millionth of a gram. This tiny measurement is often used in scientific contexts where precision is key.

Why Micrograms Matter

In the conversion between units, like when changing milligrams to micrograms to understand better the concentration of substances like cholesterol in blood, knowing that 1 mg equals 1000 µg is essential. Such precision is important in medical testing to ensure accurate interpretation and diagnosis.
Micrograms offer a level of detail that can be critical in fields like pharmacology and nutrition, where even minute amounts of a substance can have significant biological effects.

Nanogram

A nanogram, represented as ng, is an even smaller unit of mass than a microgram, equal to one-billionth of a gram. This ultra-precise measurement is used when dealing with substances present in very low concentrations.

The Importance in Biological Contexts

In the exercise, converting blood cholesterol into nanograms per microliter (ng/µL) helps in dealing with the tiny scale of biological processes. It reflects how a small change in these measurements can indicate significant health changes.
Understanding that 1 mg equals 1,000,000 ng is crucial for professionals working with precise biochemical processes. It ensures that tiny quantities, significant in medical diagnoses or chemical reactions, are accurately represented and understood.