Question

At room temperature, water is a liquid with a molar volume of 18 mL. At \(105^{\circ} \mathrm{C}\) and 1 atm pressure, water is a gas and has a molar volume of over 30 L. Explain the large difference in molar volumes.

Short answer

The large difference in molar volumes between liquid and gaseous water, 18 mL and over 30 L respectively, can be attributed to the significant change in density (ρ) when water changes from the liquid to the gaseous state. In the liquid state, water molecules are close together and form hydrogen bonds, leading to a higher density. In the gaseous state, water molecules are far apart from each other, and hydrogen bonds are nearly absent, resulting in a lower density. As molar volume (V) is related to density through the formula \( V = \frac{M}{ρ} \), where M is the constant molar mass of water, the dramatic decrease in density when transitioning from liquid to gas leads to an increase in molar volume.

Step-by-step solution

Understand the states of matter and their properties

Water can exist in three different states - solid, liquid, and gas. In each state, water molecules exhibit unique properties, mainly due to the interactions between them. In the liquid state, water molecules are close together and form hydrogen bonds, resulting in a relatively higher density than its gas state. In the gaseous state, water molecules are far apart from each other, and the hydrogen bonds are nearly absent, leading to a lower density.

Analyze the relationship between molar volume and density

Molar volume refers to the volume occupied by one mole of a substance, in this case, water. Density is the mass of a substance per unit volume. The relationship between molar volume (V) and density (ρ) can be given by the formula: Molar volume (V) = Molar mass (M) / Density (ρ) Molar mass (M) for water is constant (18 g/mol), so when the density (ρ) changes between the states of matter, the molar volume (V) will also change.

Relate the change in molar volume to the change in state of water

During the transition from the liquid state to the gaseous state, water molecules gain energy, which in turn loosens the hydrogen bonds and causes the water molecules to be further apart from each other. This results in a significant drop in the density (ρ) of water in the gaseous state and leads to an increase in molar volume (V) according to the formula mentioned in Step 2.

Explain the difference in molar volumes

The large difference in molar volumes can be attributed to the significant change in density (ρ) when water changes from the liquid state to the gaseous state. The shift in water molecules' behavior, from being closely packed with hydrogen bonds to being more distant from each other and nearly without hydrogen bonds, causes a dramatic increase in molar volume (V). This explains why water has a molar volume of 18 mL in the liquid state and over 30 L in the gaseous state at the given temperature and pressure conditions.

Key concepts

Molar Volume

Molar volume is a way of expressing how much space a given amount of a substance occupies. Specifically, it refers to the volume occupied by one mole of a substance.
For example, liquid water has a molar volume of 18 mL, meaning that each mole of water takes up 18 milliliters of space in its liquid form.

• In the gaseous state, this volume increases dramatically to over 30 liters.
• The change is due to the difference in how molecules are arranged in different states of matter.

Understanding molar volume helps us grasp how substances behave under different conditions, such as pressure and temperature.
This is crucial when studying transformations between states, like when a liquid becomes a gas, as the molar volume changes significantly due to molecule spacing.

Density

Density is a measure of how much mass is contained in a given volume. It's essentially the heaviness of a substance relative to the space it occupies. In terms of a formula, density is the mass of a substance divided by its volume.
For water, as it shifts from a liquid to a gaseous state, its density decreases significantly.

• In the liquid state, water molecules are tightly packed, which increases its density.
• In the gaseous state, molecules are more spread apart, resulting in lower density.

This decrease in density during the phase change from liquid to gas explains the increase in molar volume. As density drops, each mole of water occupies more space.

Hydrogen Bonds

Hydrogen bonds are a type of weak chemical bond that is particularly important in the behavior of water. These bonds occur when a hydrogen atom in one water molecule is attracted to the oxygen atom in a neighboring molecule.
In the liquid state, hydrogen bonds contribute to water's unique properties, like high surface tension and relatively high density.

• The presence of hydrogen bonds is why water molecules are closer together in liquid form.
• When water turns into vapor, these bonds are broken.

The breaking of hydrogen bonds means molecules can move farther apart, which leads to the significant increase in molar volume from liquid to gas, as seen in the low density of gaseous water.

Gaseous State

The gaseous state of matter describes substances whose molecules are far apart and move freely, unlike solids and liquids. For water, going from liquid to gas dramatically increases its volume due to these changes in molecular arrangement.
This transformation involves several key characteristics:

• In gases, molecules have higher kinetic energy.
• This energy causes them to overcome attractive forces like hydrogen bonds.
• As a result, gases expand to fill their container, leading to a much larger molar volume.

This ability to expand is why water vapor can occupy a larger space, illustrating why gaseous water has a molar volume over 30 liters compared to 18 mL in its liquid state.