Question

A normal value for blood cholesterol is \(200 \mathrm{mg} / \mathrm{dL}\) of blood. If a normal adult has a total blood volume of \(5 \mathrm{~L}\) how much total cholesterol is present?

Short answer

The total cholesterol present is 10,000 mg.

Step-by-step solution

Convert Blood Volume to Deciliters

First, we need to convert the total blood volume from liters to deciliters. Since 1 liter equals 10 deciliters, multiply the blood volume in liters by 10. Total blood volume in deciliters: \(5 ext{ liters} \times 10 = 50 ext{ deciliters}\).

Calculate Total Cholesterol

Next, we calculate the total cholesterol content based on the concentration given. We use the formula: \\[\text{Total Cholesterol} = \text{Cholesterol Concentration} \times \text{Total Blood Volume in Deciliters}\]Substituting the given values:\[200 \text{ mg/dL} \times 50 \text{ dL} = 10,000 \text{ mg}\].

Key concepts

Blood Cholesterol Measurement

Cholesterol is a waxy, fat-like substance found in your blood. While essential for building cell membranes and producing certain hormones, excessive cholesterol can lead to health issues like heart disease.
Measuring blood cholesterol is crucial in monitoring and managing health. This measurement indicates how much cholesterol is present in a specific volume of blood.

• Cholesterol levels are usually reported in milligrams (mg) of cholesterol per deciliter (dL) of blood.
• A normal cholesterol level is considered to be around 200 mg/dL.

Understanding this measurement helps in assessing heart health and deciding on dietary or medicinal interventions if necessary. By knowing how much total cholesterol is present, it aids healthcare providers in creating effective treatment plans.

Unit Conversion in Chemistry

Unit conversion is a fundamental skill in chemistry and allows us to interpret and use measurements correctly. In the context of the exercise, the task is to convert the blood volume from liters to deciliters.

• 1 liter (L) is equivalent to 10 deciliters (dL).
• This conversion is necessary because the cholesterol measurement is given in mg/dL.

Thus, when given a blood volume measurement in liters, we can ensure compatibility with the cholesterol concentration's unit by converting liters to deciliters.
Such conversions are critical when performing calculations across different scales in chemistry, making sure results are accurate and consistent.

Calculating Concentrations

Concentration calculations are about determining how much of a substance is present in a mixture or solution. In the exercise, we calculate the total cholesterol in the blood.

Given:

• A cholesterol concentration of 200 mg/dL.
• A blood volume converted to 50 dL.

To find the total amount of cholesterol, we multiply the concentration by the total blood volume in deciliters:
\[\text{Total Cholesterol} = 200 \text{ mg/dL} \times 50 \text{ dL} = 10,000 \text{ mg}\]
This calculation provides a measurable quantity of cholesterol present in the blood, which is crucial for health assessments.

Chemistry Problem Solving

Solving problems in chemistry often involves a series of steps that break down complex processes into manageable pieces. In the given exercise, we followed a systematic approach:

• Identify the conversion needed: liters to deciliters.
• Apply the conversion factor to match the units.
• Use the formula for calculating total cholesterol.

This methodology illustrates how problem solving in chemistry often requires a keen eye for detail and a logical plan of action. These skills develop through practice and are a valuable asset when working with real-world chemical data.