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Chapter 1: Problem 103

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

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

Step by step solution

01

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. \[5.4\,\text{L} \times \frac{1000\,\text{mL}}{1\,\text{L}}\]
02

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.
03

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.
04

Solve for the total mass of cholesterol

Now we can solve for x by cross-multiplying: \[250\,\text{mg} \times 5400\,\text{mL} = 100\,\text{mL} \times x\,\text{mg}\] \[x\,\text{mg} = \frac{250\,\text{mg} \times 5400\,\text{mL}}{100\,\text{mL}}\]
05

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.
06

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: \[\frac{13500\,\text{mg}}{1000\,\text{mg/g}}\]
07

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.

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