Question

Given the densities and conditions of ice, liquid water, and steam listed in Table \(14.1,\) calculate the volume of \(1.0 \mathrm{~g}\) of water under each of these circumstances.

Short answer

The volume of 1.0 gram of water in each state can be calculated using the formula Volume = Mass / Density and the given densities from Table 14.1: a) Ice: Volume of ice = \( \frac{1.0~g}{\rho_{ice}}\) cm³ b) Liquid water: Volume of liquid water = \( \frac{1.0~g}{\rho_{water}} \) cm³ c) Steam: Volume of steam = \( \frac{1.0~g}{\rho_{steam}} \) cm³ Substitute the given density values and calculate the volumes for ice, liquid water, and steam.

Step-by-step solution

Identify given densities.

We have the densities of ice, liquid water, and steam from Table 14.1. Let's assume the densities are as follows: - Density of ice = \( \rho_{ice} \) [g/cm³] - Density of liquid water = \( \rho_{water} \) [g/cm³] - Density of steam = \( \rho_{steam} \) [g/cm³]

Calculate the volume of water in each state.

We are given that the mass of water is 1.0 gram. We will now find the volume of water in each state using the formula: Volume = Mass / Density a) Ice: Volume of ice = \( \frac{1.0~g}{\rho_{ice}} \) b) Liquid water: Volume of liquid water = \( \frac{1.0~g}{\rho_{water}} \) c) Steam: Volume of steam = \( \frac{1.0~g}{\rho_{steam}} \)

Substitute the values and compute the volumes.

Now, we will substitute the given density values from Table 14.1 into the above volume equations and calculate the volumes of ice, liquid water, and steam. a) Ice: Volume of ice = \( \frac{1.0~g}{\rho_{ice}}\) cm³ b) Liquid water: Volume of liquid water = \( \frac{1.0~g}{\rho_{water}} \) cm³ c) Steam: Volume of steam = \( \frac{1.0~g}{\rho_{steam}} \) cm³ After substituting the given density values and calculating, you'll have the volume of 1.0 gram of water in the form of ice, liquid water, and steam.

Key concepts

Density of Ice

Understanding the density of ice is crucial when studying the properties of water in its solid state. Density, defined as the mass per unit volume of a substance, tells us how tightly packed a material's molecules are.

For ice, which is less dense than liquid water, the molecules are spaced relatively further apart because of the way they align in a crystalline structure when water freezes. This spacey arrangement makes ice float on water—a concept that has significant ecological consequences, such as insulating bodies of water and providing habitats for various species.

To find the volume of a 1.0 gram mass of ice, we simply divide the mass by the density of ice, using the formula: \[\text{Volume of ice} = \frac{1.0~\text{g}}{\rho_{\text{ice}}}\]. When this calculation is performed, it illustrates how much space this mass of ice occupies.

Density of Liquid Water

The density of liquid water is higher than that of ice, which explains why ice floats on water. At 4°C, liquid water reaches its maximum density, generally around 1 g/cm³, making it a standard for comparison in many scientific measurements.

When calculating the volume that 1.0 gram of liquid water occupies, we use the same formula for volume: \[\text{Volume of liquid water} = \frac{1.0~\text{g}}{\rho_{\text{water}}}\]. This calculation shows that 1.0 gram of water, at maximum density, will theoretically occupy a volume of 1 cm³. This ratio changes slightly with temperature as water expands and contracts with heating and cooling. Understanding this relationship between mass, volume, and density is fundamental to many disciplines including chemistry, physics, and engineering.

Density of Steam

When water turns into steam, its density decreases dramatically due to the substantial increase in volume with little change in mass. Steam, the gaseous form of water, has molecules that are far apart compared to liquid water or ice, making its density much lower.

Using the formula for volume calculation: \[\text{Volume of steam} = \frac{1.0~\text{g}}{\rho_{\text{steam}}}\], we can deduce how large a volume 1.0 gram of steam will occupy. This concept is vital, especially in the study of gases and their behaviors under different temperature and pressure conditions. Steam's low density compared to its liquid form is one of the reasons why it is so effective in carrying energy in industrial processes, such as power plants and distillation.

Volume-Mass Relationship

The volume-mass relationship is a fundamental concept in the science of materials, particularly evident in the study of density. The formula \[\text{Volume} = \frac{\text{Mass}}{\text{Density}}\] provides a clear mathematical representation of how the volume of a substance relates to its mass and density.

The practical application of this relationship allows for the determination of the volume that a given mass will occupy, which is essential for many scientific and industrial processes. For example, understanding the volume that a mass of oil will occupy is crucial for packaging and transport. In environmental science, it helps predict the spread of a pollutant. This volume-mass relationship also underpins various principles in buoyancy and is integral to designing vessels and structures that float.