Problem 40 - Chemistry and Chemical Reactivity

Question

Which occupies a larger volume, \(600 .\) g of water (with a density of \(0.995 \mathrm{g} / \mathrm{cm}^{3}\) ) or \(600 .\) g of lead (with a density of \(\left.11.34 \mathrm{g} / \mathrm{cm}^{3}\right) ?\)

Step-by-Step Solution

Answer

600 g of water occupies a larger volume than 600 g of lead.

Step 1: Understand the Problem

We need to determine which occupies a larger volume: 600 grams of water or 600 grams of lead. To do this, we'll calculate the volume for each using their respective densities.

Step 2: Recall the Formula for Volume Calculation

Volume is calculated using the formula: \[V = \frac{m}{\rho}\]where \(m\) is the mass and \(\rho\) (rho) is the density.

Step 3: Calculate the Volume of Water

Given the density of water is \(0.995\, \mathrm{g/cm}^3\), we use the formula:\[V_{\text{water}} = \frac{600\, \mathrm{g}}{0.995\, \mathrm{g/cm}^3} = 603.02\, \mathrm{cm}^3\]

Step 4: Calculate the Volume of Lead

Given the density of lead is \(11.34\, \mathrm{g/cm}^3\), we use the formula:\[V_{\text{lead}} = \frac{600\, \mathrm{g}}{11.34\, \mathrm{g/cm}^3} = 52.92\, \mathrm{cm}^3\]

Step 5: Compare the Volumes

Now that we have calculated the volumes, compare them:- Volume of water = 603.02 \(\mathrm{cm}^3\)- Volume of lead = 52.92 \(\mathrm{cm}^3\)The water occupies a larger volume than the lead.

Key Concepts

Volume Calculation

The concept of volume calculation is crucial when figuring out how much space an object takes up. Volume is a three-dimensional space occupied by a substance, and it can be calculated using the formula: \[V = \frac{m}{\rho}\]where \( V \) is the volume, \( m \) is the mass, and \( \rho \) (rho) is the density. When calculating the volume of both water and lead in this exercise, we used their masses and densities. By substituting the given values into the formula, we determined how much space 600 grams of each substance occupies. Remember:

• The calculated volume tells us how much room a given mass of material takes up in space.
• The density of the material affects the resulting volume.

Performing these calculations provides insight into how different materials can have vastly different space requirements for the same mass.

Mass and Volume Relationship

The relationship between mass and volume is foundational in understanding density, which is a measure of how much mass is present in a given volume. Density is defined as:\[\rho = \frac{m}{V}\]where \( \rho \) is density, \( m \) is mass, and \( V \) is volume.Understanding this relationship helps us predict how substances will behave when subject to different conditions.
In the exercise, we held mass constant at 600 grams for both water and lead:

• For water, with a lower density of 0.995 g/cm³, the volume occupied is greater.
• For lead, with a higher density of 11.34 g/cm³, the same mass occupies much less volume.

This direct relationship is crucial in various applications, from designing containers for liquids to understanding buoyancy in ships and objects.

Material Properties

Understanding material properties such as density is essential for making informed choices in real-world applications. Density is a characteristic property that determines how dense or compact a substance is. A higher density means that the particles of a material are closer together, which is why lead, a denser material, occupies less volume for the same mass compared to water. Different materials exhibit unique properties:

• Lead: Highly dense, making it suitable for applications needing weight and compactness, such as in batteries and radiation shielding.
• Water: With lower density, it's vital for life and is used in a wide range of domestic and industrial applications.

Knowing the properties of materials helps in selecting the right material for specific needs, affecting everything from engineering and construction to manufacturing and environmental science.