Question

A kilogram of lead occupies a much smaller volume than a kilogram of water because _______ has a much higher density.

Short answer

A kilogram of lead occupies a much smaller volume than a kilogram of water because lead has a much higher density.

Step-by-step solution

Define density

Density is the measure of mass per unit volume of a substance. It can be represented mathematically as: Density = \(\frac{Mass}{Volume}\) Higher density means more mass in the same volume, resulting in a smaller volume occupied by a substance with a higher density, as long as the mass remains constant.

Compare the densities of lead and water

We need to determine which of the two substances, lead or water, has a higher density. The densities are approximately: Lead: 11,340 kg/m³ Water: 1,000 kg/m³ Comparing these two values, we can see that lead has a much higher density than water.

Fill in the blank

Since lead has a much higher density than water, it occupies a smaller volume for the same mass. Therefore, the correct word to fill in the blank is "lead." The sentence will read: A kilogram of lead occupies a much smaller volume than a kilogram of water because lead has a much higher density.

Key concepts

Mass

Mass refers to the amount of matter that an object contains. It acts as a measure of an object’s resistance to acceleration under the influence of an external force. The unit for mass in the International System of Units (SI) is kilograms (kg). When considering materials like lead and water, mass remains constant regardless of volume.
Understanding mass is crucial in calculating density, as density is determined by dividing the mass of a substance by its volume. For example, if you have 1 kilogram of lead and 1 kilogram of water, their masses are equal.
However, because lead is denser, the volume it occupies is smaller compared to the volume occupied by the same mass of water.

• A simple way to comprehend this is by imagining dense materials— they "pack" more closely together, resulting in less space occupied.
• Mass remains consistent, but the volume changes for different substances.
• This concept helps distinguish between the size and weight of objects.

Understanding mass helps in the assessment of various substances and their densities.

Volume

Volume describes the amount of space that a substance or object occupies. It’s often measured in cubic meters (m³) or liters in the metric system. Volume helps differentiate how tightly matter is packed into a space.
When comparing lead to water, despite having the same mass, lead occupies a smaller volume because its particles are more tightly packed. This means that more lead can fit into a smaller space compared to water, which has less tightly packed particles.

• The concept of volume is critical in measuring density— which is mass divided by volume.
• A smaller volume doesn’t always mean less mass. Rather, it signifies a higher density.
• When two substances have the same mass but different volumes, the one with the smaller volume has a higher density.

Grasping the interplay between mass and volume helps in understanding a substance's density.

Lead

Lead is a heavy and dense metal, well-known for its high density among common materials. It is often used in applications where its weight and density are beneficial, such as in batteries and radiation shields.
The density of lead is approximately 11,340 kg/m³, much greater than that of water, which has a density of about 1,000 kg/m³. This significant difference in density explains why a kilogram of lead occupies much less space than a kilogram of water.
Lead's high density is due to its tightly packed atomic structure, allowing a substantial mass to fit into a small volume.

• High density materials like lead are heavier per unit volume compared to less dense materials.
• In everyday terms, it takes fewer lead atoms to fill up a specific space compared to water molecules.
• This property of lead makes it ideal for uses and applications where compact weight is essential.

Recognizing the properties of lead helps to appreciate why it is such a distinct and heavily applied material in various industries.