Question

Which of the following phase transitions gives off more heat: (a) 1 mole of steam to 1 mole of water at \(100^{\circ} \mathrm{C}\), or (b) 1 mole of water to 1 mole of ice at \(0^{\circ} \mathrm{C} ?\)

Short answer

Condensing steam to water releases more heat (40.7 kJ/mol) than freezing water to ice (6.02 kJ/mol).

Step-by-step solution

Identify the Type of Phase Transition

In this exercise, we have two phase transitions: (a) the conversion of 1 mole of steam to 1 mole of water at 100°C, and (b) the conversion of 1 mole of water to 1 mole of ice at 0°C. Both transitions involve phase changes: condensation for (a) and freezing for (b).

Determine the Heat Released in Each Transition

For condensation: The heat released when converting steam to liquid water is known as the enthalpy of condensation, which is equivalent to the enthalpy of vaporization. At 100°C, the enthalpy of vaporization of water is approximately 40.7 kJ/mol. For freezing: The heat released when converting water to ice is the enthalpy of fusion, which is approximately 6.02 kJ/mol at 0°C.

Compare the Heat Released

Compare the two quantities of heat released: 40.7 kJ/mol for condensation and 6.02 kJ/mol for freezing. Since 40.7 kJ/mol is greater than 6.02 kJ/mol, the phase transition described in (a) releases more heat than that in (b).

Key concepts

Condensation

Condensation is the phase transition from a gas to a liquid. This process occurs when steam (gas) turns back into water (liquid). During condensation, heat is released into the surrounding environment. This is because the molecules in the gas phase release energy as they slow down and settle into a more structured liquid form.
When water vapor condenses at its boiling point, 100°C, it releases energy equal to the enthalpy of vaporization. This is why dew forms on cool surfaces; water molecules lose energy and change phase from gas to liquid. In our exercise, when 1 mole of steam becomes water, significant heat—approximately 40.7 kJ—is released.
Overall, condensation is a key process in the water cycle, crucial for forming clouds and precipitation.

Enthalpy of Vaporization

The enthalpy of vaporization refers to the amount of energy required to convert a liquid into a gas at its boiling point without changing its temperature. Conversely, it also equals the energy released when a gas condenses into a liquid.
For water, this value is about 40.7 kJ/mol at 100°C, illustrating how much energy is released when steam condenses to form water. This energy release is due to breaking and forming hydrogen bonds between molecules, a fundamental concept when examining phase changes. Understanding this helps explain why steam can scald more than boiling water; the steam carries additional energy.
In the exercise, recognizing these numbers helps in comparing heat released during phase transitions. The enthalpy of vaporization is central to understanding the heat dynamics of condensation.

Freezing

Freezing, the process of changing from a liquid to a solid, involves the release of energy. When water at 0°C becomes ice, it undergoes a transformation where its molecules arrange into a structured pattern. This ordered state has lower energy, so heat is released during this transition.
In our specific example, when 1 mole of water freezes, it releases approximately 6.02 kJ of energy. The shift to a solid state reduces energy, evident during the ice formation. This concept is why frosting forms in freezers; water molecules release heat as they transition to ice.
Understanding freezing is essential for applications such as food preservation, where controlling the phase transition plays a crucial role.

Enthalpy of Fusion

The enthalpy of fusion quantifies the energy required to change a solid into a liquid at its melting point without altering its temperature. It inversely equates to the energy released when a liquid solidifies into a solid.
For water, this energy is about 6.02 kJ/mol at 0°C, signifying the heat released when liquid water freezes into ice. Bonds between molecules need to form when transitioning from liquid to solid, releasing energy in the process.
In the context of the phase transition exercise, it's crucial to understand the enthalpy of fusion to comprehend how much less energy is released during freezing compared to other phase changes. The lower energy involved reflects the smaller temperature difference and structural energy change.

Heat Released in Phase Transition

Phase transitions, such as condensation and freezing, involve energy changes due to molecular rearrangements. The heat released during these changes reflects the attraction force adjustments between molecules. When comparing condensation and freezing for one mole of water, condensation clearly releases more heat. This is because the process requires significant rearrangement and bonding of water molecules, releasing approximately 40.7 kJ/mol.
In contrast, freezing involves less molecular change, releasing about 6.02 kJ/mol. This highlights that different transitions release or absorb varying heat amounts depending on molecular energy changes.
Comprehending the heat released in phase transitions is foundational for understanding natural phenomena and various applications, from meteorology to industrial processes.