Question

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

Short answer

The large difference in molar volumes of water between its liquid state at room temperature and its gaseous state at 105°C and 1 atm pressure can be attributed to the change in the arrangement and motion of water particles. In the liquid state, water particles are held together by strong hydrogen bonding, resulting in a lower molar volume. As the temperature increases to 105°C, the water particles gain more kinetic energy, breaking free from the hydrogen bonding and moving farther apart, resulting in a significantly larger molar volume in the gaseous state.

Step-by-step solution

Understanding Molar Volume

Molar volume is defined as the volume occupied by one mole of a substance in any given state (solid, liquid, or gas). It's generally expressed in units of liters per mole (L/mol) or milliliters per mole (mL/mol). The molar volume of a substance depends on its state, temperature, and pressure.

Understanding States of Matter

Matter can exist in different states: solid, liquid, and gas. The state of matter is determined by the arrangement and motion of the particles (atoms, ions, or molecules) that compose the substance. In a solid, the particles are held tightly in a well-ordered structure, whereas in a liquid, the particles are more loosely held and can move around. In a gas, the particles are far apart and move freely, leading to the gas taking the shape and volume of its container.

Understanding the Relationship between Temperature, Pressure, and Volume for Gases

The behavior of a gas in terms of its volume, temperature, and pressure can be described by the Ideal Gas Law equation, given as: \(PV = nRT\) Where: - P is the pressure of the gas. - V is the volume of the gas. - n is the number of moles of the gas. - R is the Ideal Gas Constant (8.314 J/(mol K)). - T is the temperature of the gas in Kelvin. According to the Ideal Gas Law, if the moles and pressure of a gas remain constant, the volume of the gas is directly proportional to its temperature. This means that as the temperature of a gas increases, so does its volume.

Comparing Molar Volumes of Water in Liquid and Gaseous States

At room temperature (around 25°C), water exists as a liquid with a molar volume of 18 mL/mol. In its liquid state, the water particles are closer together and are held in place by strong hydrogen bonding, causing the relatively low molar volume. At 105°C (which is above the boiling point of water) and 1 atm pressure, water exists as a gas. In this gaseous state, the water particles have more kinetic energy, causing them to move farther apart and break free from the hydrogen bonding, resulting in a larger molar volume. At these conditions, the molar volume of water is over 30 L/mol.

Conclusion

The large difference in molar volumes of water between its liquid state at room temperature and its gaseous state at 105°C and 1 atm pressure can be explained by the change in the arrangement and motion of the water particles. As the temperature increases, the water particles have more kinetic energy, causing them to move farther apart and take up more volume in the gaseous state. This results in a much larger molar volume when water is a gas compared to its liquid state.