Question

According to the National Heart, Lung, and Blood Institute, LDL-cholesterol levels of less than \(130 \mathrm{mg}\) of LDLcholesterol per deciliter of blood are desirable for heart health in humans. On the average, a human has \(4.7 \mathrm{~L}\) of whole blood. What is the maximum number of grams of LDL- cholesterol that a human should have?

Short answer

A human should have a maximum of 6.11 grams of LDL-cholesterol.

Step-by-step solution

Convert LDL-Cholesterol Level to Grams Per Liter

First, convert the given LDL-cholesterol level from milligrams per deciliter to grams per liter. Remember that 1 deciliter (dL) = 0.1 liters (L) and 1 gram (g) = 1000 milligrams (mg). The given LDL-cholesterol level is 130 mg/dL. Convert this to grams per liter using the following steps: \(130 \text{ mg/dL} = 130 \frac{\text{mg}}{0.1 \text{ L}}\) Now convert milligrams to grams: \(130 \frac{\text{mg}}{0.1 \text{ L}} = \frac{130 \text{ mg} \times 1 \text{ g}}{0.1 \text{ L} \times 1000 \text{ mg}}\ = 1.30 \text{ g/L}\)

Multiply by Total Blood Volume

To find the total amount of LDL-cholesterol in grams, multiply the concentration (in grams per liter) by the total blood volume of a human, given as 4.7 liters. \(\text{Total LDL-cholesterol} = 1.30 \text{ g/L} \times 4.7 \text{ L}\)

Calculate the Result

Finally, perform the multiplication to find the maximum number of grams of LDL-cholesterol. \(\text{Total LDL-cholesterol} = 1.30 \times 4.7 = 6.11 \text{ grams}\)

Key concepts

Unit Conversion

Unit conversion is an essential skill in all scientific fields. For this exercise, you need to convert LDL-cholesterol levels from milligrams per deciliter (mg/dL) to grams per liter (g/L). Remember, 1 deciliter (dL) equals 0.1 liters (L), and 1 gram (g) equals 1000 milligrams (mg). By converting carefully, you ensure accurate and meaningful results. Here’s the conversion process:

Given LDL level: 130 mg/dL.
Using unit conversions: 130 mg/dL = 130 mg / 0.1 L = 130 mg/0.1 L × (1 g/1000 mg) = 1.30 g/L.

Converting units properly helps us communicate and use measures that are universal in scientific discussions.

Concentration Calculation

Concentration is a crucial concept in chemistry and biology. It tells us how much of a substance (like cholesterol) is present in a given volume of solvent (such as blood). Concentration can be expressed in different units, such as mg/dL or g/L.

In this exercise, after converting the unit, we found that the concentration of LDL-cholesterol is 1.30 g/L. This means every liter of blood contains 1.30 grams of LDL-cholesterol. Understanding concentration helps in various applications, like determining safe levels of substances in the blood and ensuring proper dosages of medications.

Blood Volume

Knowing the average blood volume of a human is necessary for many medical and health calculations. The volume of blood in an average human is about 4.7 liters. This value can be used to calculate the total amount of different substances in the blood by multiplying the concentration by the blood volume.

For LDL-cholesterol calculation: we multiply the concentration (1.30 g/L) by the total blood volume (4.7 L):

Total LDL-cholesterol = 1.30 g/L × 4.7 L = 6.11 grams.

Understanding blood volume and how it relates to concentration helps medical professionals assess health conditions accurately.

Cholesterol Levels

Cholesterol levels are critical indicators of heart health. LDL-cholesterol, also known as 'bad' cholesterol, is one type that needs monitoring. The National Heart, Lung, and Blood Institute states that an LDL-cholesterol level of less than 130 mg/dL is desirable for heart health.

High levels of LDL-cholesterol can lead to plaque buildup in the arteries, increasing the risk of heart disease and stroke. Managing cholesterol levels often involves a combination of diet, exercise, and sometimes medication.

For our calculation, the maximum LDL-cholesterol in a human's blood was found to be 6.11 grams, reinforcing the importance of keeping cholesterol levels within recommended limits to maintain cardiovascular health.