Question

At \(100^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\), if the density of liquid water is \(1.0 \mathrm{~g} \mathrm{~cm}^{-3}\) and that of water vapour is \(0.0006 \mathrm{~g} \mathrm{~cm}^{-3}\), then the volume occupied by water molecules in 1 litre of steam at that temperature: (a) \(6 \mathrm{~cm}^{3}\) (b) \(60 \mathrm{~cm}^{3}\) (c) \(0.6 \mathrm{~cm}^{3}\) (d) \(0.06 \mathrm{~cm}^{3}\)

Short answer

The volume occupied by water molecules in 1 litre of steam is 0.6 cm³ (option c).

Step-by-step solution

Determine Mass of 1 Litre of Steam

Since the density of water vapour is given as \(0.0006 \; \text{g/cm}^3\), we first need to calculate how much mass is contained in 1 litre of steam. Knowing that 1 litre is equivalent to 1000 cm³, we calculate:\[\text{Mass} = \text{Density} \times \text{Volume} = 0.0006 \; \text{g/cm}^3 \times 1000 \; \text{cm}^3 = 0.6 \; \text{g}\] So, the mass of 1 litre of steam is 0.6 g.

Calculate Volume Occupied by Liquid Water

Since the density of liquid water is given as \(1.0\; \text{g/cm}^3\), we need to know how much volume this mass (0.6 g) would occupy if the water were in its liquid form.Given:\[\text{Volume of liquid water} = \frac{\text{Mass}}{\text{Density}} = \frac{0.6 \; \text{g}}{1.0 \; \text{g/cm}^3} = 0.6 \; \text{cm}^3\]Thus, the volume occupied by water molecules in 1 litre of steam is 0.6 cm³.

Key concepts

Density of Water

Density is a measure of how much mass is contained in a given volume. For water, this property is crucial. At 100°C and 1 atm, the density of liquid water reaches about 1.0 g/cm³.
This means that every cubic centimeter of water has a mass of 1 gram.
Liquid water is quite dense compared to water vapor, which drastically decreases density when it transitions into its gaseous state.

• The factors affecting water's density include temperature and pressure.
• Understanding density allows us to calculate how much space a given mass of water would occupy.

When water is in its liquid form, it packs tightly, giving it its dense nature, but this changes significantly when it turns into vapor.

Density of Water Vapour

Water vapour has a much lower density compared to its liquid form. At the given conditions of 100°C and 1 atm, water vapour has a density of about 0.0006 g/cm³.
This means it's incredibly lighter than liquid water, which explains why steam rises and fills up the airspace.

• The low density of water vapor is a consequence of molecules being spread out in the gaseous phase.
• While liquid water maintains a compact molecular arrangement, water vapor's molecules are dispersed over a larger volume.

This low density is due to the increased energy levels and movement of molecules, which is important when considering phase transitions from liquid to gas.

Volume Conversion

Volume conversion is essential when dealing with different units or scales. In this exercise, we were required to convert litres to cubic centimeters (cm³). Since 1 litre equals 1000 cm³, this knowledge helped convert the volume efficiently.
Volume conversions are standard in different calculations.

• Accurate conversion is crucial to solving problems that involve measurements in different units.
• By ensuring accurate conversion, you maintain the integrity of your calculations.

In scientific calculations, understanding conversions can make complex problems easier to solve, as seen by our necessary conversion in solving this set.

Phase Transition

Phase transition refers to the change of a substance from one state to another, such as from liquid to gas.
In the given exercise, this occurs when water transitions into steam.
The transition depends on changes in temperature and pressure, which affect the movement and arrangement of molecules.

• A phase transition involves significant energy changes and alters the substance's properties, like density and volume.
• When water turns into vapor at 100°C, it requires energy to overcome molecular attractions, leading to less density and more volume.

Understanding these transitions explains the drastic change in density and physical properties, essential for accurately calculating the volume of molecules in water vapor.