Question

Which occupies the grearest volume: 1 gram of ice, 1 gram of liquid water, or 1 gram of water vapor?

Short answer

1 gram of water vapor occupies the greatest volume.

Step-by-step solution

Understand Density and Volume Relationship

To find which substance occupies the greatest volume, we need to understand that volume can be determined using the relationship between mass and density: \[ V = \frac{m}{\rho} \]where \( V \) is volume, \( m \) is mass, and \( \rho \) is density. Since the mass of 1 gram is the same for ice, liquid water, and water vapor, the volume depends on their densities.

Know the Densities of Ice, Liquid Water, and Water Vapor

The densities of these substances are typically: - Ice: approximately 0.92 g/cm³ - Liquid Water: approximately 1 g/cm³ - Water Vapor: about 0.0006 g/cm³ (varies with temperature and pressure, but is significantly less than that of ice and liquid water).

Calculate the Volume for Each Substance

Using the formula \( V = \frac{m}{\rho} \):- Ice: \( V = \frac{1}{0.92} \approx 1.09 \) cm³- Liquid Water: \( V = \frac{1}{1} = 1 \) cm³- Water Vapor: \( V = \frac{1}{0.0006} \approx 1666.67 \) cm³

Compare the Volumes

Comparing the calculated volumes, we have: - Ice: 1.09 cm³ - Liquid Water: 1 cm³ - Water Vapor: 1666.67 cm³ Thus, 1 gram of water vapor occupies the greatest volume of the three.

Key concepts

Water Density Comparisons

Density is a fundamental concept in chemistry that refers to the mass of a substance per unit volume. It's commonly represented by the symbol \( \rho \) and is calculated using the formula \( \rho = \frac{m}{V} \). By comparing the densities of different substances, we can infer which one occupies more space given equal masses.

For water, its density changes notably with each phase: solid (ice), liquid (water), and gas (vapor). Ice has a density of about 0.92 g/cm³, making it less dense than liquid water, which has a density of approximately 1 g/cm³. This anomaly is why ice floats on water. Water vapor has a drastically lower density—around 0.0006 g/cm³—because molecules in the gaseous state are spread far apart. These density differences are key when comparing how much space 1 gram of each phase will occupy.

Phase Changes in Water

Water is unique in its ability to naturally exist in three distinct phases: solid, liquid, and gas. Each phase has unique properties that influence the density and volume of the water.

• **Ice (Solid)**: In its solid form, water expands and takes up more volume per gram than when it is a liquid. The hydrogen bonds create a crystal lattice structure, which is less dense than the liquid phase.
• **Liquid Water**: This phase has the highest density under normal atmospheric conditions, meaning molecules are closely packed together. This phase takes up less space per gram compared to ice.
• **Water Vapor (Gas)**: The gaseous state has molecules that are very spread out, leading to its extremely low density. Consequently, water vapor will occupy much more volume than the other two phases if you have 1 gram of each.

As water undergoes phase changes, interactions between molecules are what cause the shifts in density and volume.

Volume Calculation

Understanding how to calculate volume is essential for determining which state of water occupies the most space. The formula \( V = \frac{m}{\rho} \) helps calculate volume when you know both mass and density.

Starting with 1 gram of a substance:

• For **Ice**, given the density of 0.92 g/cm³, using the formula allows us to calculate that it occupies approximately 1.09 cm³.
• For **Liquid Water**, with a density of 1 g/cm³, the volume is 1 cm³.
• For **Water Vapor**, with its much smaller density of 0.0006 g/cm³, the volume expands significantly to about 1666.67 cm³.

These calculations illustrate that despite having the same mass, water vapor occupies the greatest volume due to its sparse molecular arrangement.