Problem 57 - Chemistry The Science in Context

Question

The Density of Blood The average density of human blood is \(1.06 \mathrm{g} / \mathrm{mL} .\) What is the mass of blood in an adult with a blood volume of 5.5 L? Express your answer in (a) grams and (b) ounces.

Step-by-Step Solution

Answer

Answer: The mass of blood in an adult with a blood volume of 5.5 L is 5830 g or approximately 205.73 ounces.

Step 1: Write the formula for density

Density=mass/volume

Step 2: Rearrange the formula to isolate mass

Mass=density*volume

Step 3: Substitute known values

We know that the average density of human blood is 1.06 g/mL and the blood volume of the adult is 5.5 L. To use these values in the formula, we need to convert the volume from liters to milliliters: 1 L = 1000 mL, so 5.5 L = 5.5 * 1000 mL = 5500 mL Now, substitute the values: Mass = (1.06 g/mL) * (5500 mL)

Step 4: Calculate the mass

Mass = 5830 g Step 2: Convert the mass in grams to ounces

Step 5: Write the conversion factor

1 ounce = 28.3495 grams

Step 6: Set up the conversion ratio

To convert the mass of blood in grams to ounces, we will use the following conversion ratio: mass(ounces) = mass(grams) * (1 ounce / 28.3495 grams)

Step 7: Substitute the mass in grams

mass(ounces) = 5830 g * (1 ounce / 28.3495 grams)

Step 8: Calculate the mass in ounces

mass(ounces) = 205.73 ounces (a) The mass of blood in an adult with a blood volume of 5.5 L is 5830 g. (b) The mass of blood in an adult with a blood volume of 5.5 L is approximately 205.73 ounces.

Key Concepts

Density Formula

The concept of density is essential in various scientific disciplines, including physics and chemistry. Density is defined as an object's mass per unit volume and is a measure of how much matter is packed into a given space. The density formula is expressed as:
\[ \text{Density} = \frac{\text{mass}}{\text{volume}} \]
In applications like calculating the mass of blood as in the provided exercise, the given density allows us to reverse the formula to solve for mass:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
Understanding how to manipulate the density formula is vital for solving such problems. Working through examples, such as finding the mass of blood in an adult, helps to solidify one's grasp of the concept.

Mass-Volume Relationship

The mass-volume relationship is an intrinsic aspect of the density concept. When considering this relationship, it's important to recognize that mass is a measure of the amount of matter in a substance (typically in grams or kilograms), while volume measures the amount of space that substance occupies (commonly expressed in liters or milliliters). In the context of our exercise calculating the density of blood:

• Mass refers to the actual weight of the blood in the body.
• Volume refers to the space that blood takes up inside the human body.

To find the mass of blood using its density, you multiply the volume of blood by the density. This relationship is crucial because the mass of a substance can be calculated if the volume and its density are known. Effective use of this relationship is particularly important in health and medicine, such as estimating blood mass for medical treatments.

Unit Conversion

Solving problems in the natural sciences often requires the conversion of units, either to comply with the International System of Units (SI) or to align with regional practices. Unit conversion is the process of changing the measurement from one unit to another without altering the actual amount of substance. In our exercise, we needed to convert:

• Volume from liters to milliliters because the density was given in grams per milliliter.
• Mass from grams to ounces to provide an answer in the customary units commonly used in the United States.

This process involved multiplying the given volume by the conversion factor between liters and milliliters and then using another conversion factor to change grams into ounces. Familiarity with these conversion factors is invaluable when working across different measurement systems.