Question

The egg whites from four "large" eggs occupy a volume of \(112 \mathrm{~mL}\). The mass of the egg whites from these four eggs is \(1.20 \times 10^{2} \mathrm{~g}\). What is the average density of an egg white from one "large" egg?

Short answer

Given: - Volume of egg whites from 4 large eggs: \(112 \mathrm{ mL}\) - Mass of egg whites from 4 large eggs: \(1.20 \times 10^2 \mathrm{ g}\) Solution: Calculate the total density for the egg whites from the four large eggs: Total density for 4 large eggs = \(120 \mathrm{ g} / 112 \mathrm{ mL} = 1.0714 \mathrm{ g/mL}\) Calculate the average density of an egg white from one large egg: Average density = \(1.0714 \mathrm{ g/mL} / 4 = 0.26785 \mathrm{ g/mL}\) Answer: The average density of an egg white from one large egg is approximately \(0.26785 \mathrm{ g/mL}\).

Step-by-step solution

Write down the given information

We are given the following information: - Volume of egg whites from 4 large eggs: \(112 \mathrm{ mL}\) - Mass of egg whites from 4 large eggs: \(1.20 \times 10^2 \mathrm{ g}\)

Calculate the total density of the egg whites from the four large eggs

We will use the formula for density: Density = Mass/Volume Substitute the given values into the formula: Total density for 4 large eggs = \((1.20 \times 10^2 \mathrm{ g}) / (112 \mathrm{ mL})\)

Calculate the total density of the egg whites

Now calculate the total density: Total density for 4 large eggs = \(120 \mathrm{ g} / 112 \mathrm{ mL} = 1.0714 \mathrm{ g/mL}\)

Calculate the average density of an egg white from one large egg

To find the average density for one egg white, we will divide the total density by the number of eggs: Average density = (Total density)/4 Average density = \(1.0714 \mathrm{ g/mL} / 4\)

Find the average density of an egg white from one large egg

Now, calculate the average density: Average density = \(0.26785 \mathrm{ g/mL}\) Thus, the average density of an egg white from one large egg is approximately \(0.26785 \mathrm{ g/mL}\).

Key concepts

Understanding Density in Chemistry Education

Density is a foundational concept in chemistry education. It's an intensive property, meaning it does not depend on the amount of substance present. To put it simply, it is a measure of how much 'stuff' is packed into a given space. The 'stuff' we speak of here is mass, and the 'space' is volume. When students learn about density, they're equipped with the understanding of how different materials stack up against each other in terms of mass and space occupation, which has real-world implications, from understanding why oil floats on water to designing ships that can float on seas.

In the context of education, teaching students how to calculate density effectively requires reinforcing the concept of units. Mass is measured in grams (g) or kilograms (kg), while volume is measured in milliliters (mL) or cubic centimeters (cm³), among other units. The importance of using consistent units can't be overstated, as it ensures that the density calculations are accurate and meaningful.

Furthermore, making the concept engaging through hands-on activities, like measuring the density of various household liquids or solids, can cement the understanding of density in young minds. Clear, step-by-step instructions, akin to those provided in the example problem about egg whites, help make the concept of density approachable and digestible.

The Density Formula Applied

The density formula links mass and volume through a simple but powerful equation: Density = Mass / Volume. Such an equation is vital because it allows for consistent comparisons between different substances. For example, if we were to find the density of various materials such as wood, iron, and plastic, it would become evident why iron sinks in water, but wood and plastic might float.

Let's apply this formula to the given exercise about egg whites. We calculated the density of egg whites by dividing the total mass of the egg whites by their total volume. While the calculation is straightforward, understanding the principle behind it is crucial. It’s not just about finding a number; it's about understanding the relationship between the mass of the material and the space it occupies.

When utilizing the density formula, it’s also important to note the units used. Grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³) are common units for density, and students must convert their measurements to these units before doing the calculation to achieve the correct density value.

Mass and Volume Relationship

Mass and volume are two properties of matter that are interconnected, especially when it comes to calculations involving density. Mass refers to how much matter an object contains, while volume refers to the amount of space it occupies. Understanding the relationship between mass and volume is essential for practical applications in chemistry and everyday life.

Students often learn about this relationship through direct measurement—such as weighing a substance for its mass and using displacement methods or graduated cylinders to measure its volume. In the example of the egg whites, knowing both the mass and volume allowed us to find out the density. The key takeaway here is that a change in the mass or volume of a substance (assuming no chemical change occurs) will result in a different density. Heavy, compact objects have a high density because there is a lot of mass in a small volume, while lightweight, airy materials have a low density because the mass is spread out over a larger volume.

The mass-volume relationship highlights why objects float or sink and is crucial for industrial applications where materials are chosen based on their density, around their needs to be certain weights or volumes. Such a relationship is therefore not just a staple in chemistry education but also a cornerstone in fields such as engineering, materials science, and environmental studies.