Question

A person with high cholesterol has 250 mg of cholesterol per 100.0 mL of blood. If the total blood volume of the person is 5.4 L, what is the total mass (in grams) of cholesterol present in the person’s blood?

Short answer

The total mass of cholesterol present in the person's blood is 13.5 grams.

Step-by-step solution

Convert blood volume to milliliters

First, we need to convert the given blood volume from liters to milliliters. We know that 1 L = 1000 mL, so we can multiply the given blood volume (5.4 L) by the conversion factor to get the blood volume in milliliters. \[5.4\,\text{L} \times \frac{1000\,\text{mL}}{1\,\text{L}}\]

Calculate the volume of blood in milliliters

Now, we can carry out the multiplication from step 1: \[5.4\,\text{L} \times \frac{1000\,\text{mL}}{1\,\text{L}} = 5400\,\text{mL}\] So, the total blood volume of the person is 5400 mL.

Use the concentration to find the total mass of cholesterol

We are given that the concentration of cholesterol is 250 mg per 100.0 mL of blood. We can use this to find the total mass of cholesterol in the person's blood. We know the person has 5400 mL of blood, so we can set up the following proportion: \[\frac{250\,\text{mg}}{100\,\text{mL}} = \frac{x\,\text{mg}}{5400\,\text{mL}}\] where x is the total mass of cholesterol in the person's blood in milligrams.

Solve for the total mass of cholesterol

Now we can solve for x by cross-multiplying: \[250\,\text{mg} \times 5400\,\text{mL} = 100\,\text{mL} \times x\,\text{mg}\] \[x\,\text{mg} = \frac{250\,\text{mg} \times 5400\,\text{mL}}{100\,\text{mL}}\]

Calculate the total mass of cholesterol in milligrams

Now, we can carry out the multiplication and division to find x: \[x\,\text{mg} = \frac{250\,\text{mg} \times 5400\,\text{mL}}{100\,\text{mL}} = 13500\,\text{mg}\] So, the total mass of cholesterol in the person's blood is 13500 mg.

Convert the total mass of cholesterol to grams

Finally, we need to convert the total mass of cholesterol from milligrams to grams. We know that 1 g = 1000 mg, so we can divide the total mass of cholesterol in milligrams by the conversion factor to get the mass in grams: \[\frac{13500\,\text{mg}}{1000\,\text{mg/g}}\]

Calculate the total mass of cholesterol in grams

Now, we can carry out the division: \[\frac{13500\,\text{mg}}{1000\,\text{mg/g}} = 13.5\,\text{g}\] Therefore, the total mass of cholesterol present in the person's blood is 13.5 grams.

Key concepts

Unit Conversion

Unit conversion is a fundamental step in many calculations, especially in science and medicine. It's about transforming one unit of measurement into another, like liters to milliliters. This process involves using a conversion factor, which is a known value that bridges the two units. For our exercise, we needed to convert 5.4 liters of blood into milliliters. We did this by multiplying by 1000 since:

• 1 liter equals 1000 milliliters.

Conversion allows consistent units across a problem, ensuring accuracy in subsequent calculations. Remember, it is important to always double-check the units after conversion to avoid errors.

Blood Cholesterol Concentration

Blood cholesterol concentration is a measure of how much cholesterol is found in the blood. It is usually expressed in milligrams (mg) of cholesterol per deciliter (dL) or milliliters (mL) of blood. In our specific problem, the cholesterol concentration was given as 250 mg per 100 mL of blood. This concentration tells us how much cholesterol is present within a certain volume of blood, which is crucial for calculating total cholesterol in a larger volume of blood. To find the total cholesterol, we used this concentration value to set up a proportion with the total blood volume. By ensuring that the ratio of cholesterol to blood volume stays constant, we can figure out the mass of cholesterol in a different volume, which is useful for medical assessments and diagnostics.

Mass Calculation

Mass calculation lets us determine the weight of a substance, such as cholesterol in the blood, based on concentration and volume. The goal was to find out the total mass of cholesterol, using the given concentration and the blood volume that we converted to milliliters. The steps included setting up an equation based on the concentration equation from earlier, cross-multiplying, and solving for the unknown mass. Once we found the mass in milligrams, we converted it to grams:

• Remember, 1 gram = 1000 milligrams.

Thus, the total mass of cholesterol was calculated as 13.5 grams, providing a better understanding of the cholesterol level in the entire blood volume, which is significant for health insights and treatment decisions.