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 \((\mathrm{b}) 1\) mole of water to \(1 \mathrm{~mole}\) of ice at \(0^{\circ} \mathrm{C} ?\)

Short answer

The transition of 1 mole of steam to 1 mole of water at 100°C gives off more heat.

Step-by-step solution

Identify the enthalpy changes of each phase transition

The enthalpy of vaporization (∆Hvap) for water is 40.7 kJ/mol. This value is positive because heat is absorbed when water is vaporized to steam. However, in this problem steam condenses to water (reverse process), so ∆H would be -40.7 kJ/mol because heat is released. \nThe enthalpy of fusion (∆Hfus) for water is 6.01 kJ/mol. This value is positive because heat is absorbed when ice melts to water. In this problem, water is freezing to ice (reverse process), so ∆H would be -6.01 kJ/mol.

Compare the ∆H values of the transitions

The enthalpy change when steam condenses to water is -40.7 kJ/mol indicating the heat released is 40.7 kJ for each mole. The enthalpy change when water freezes to ice is -6.01 kJ/mol indicating the heat released is 6.01 kJ for each mole.

Conclude which transition gives off more heat

Because the absolute value of -40.7 kJ/mol is larger than -6.01 kJ/mol, more heat is given off in the transition of 1 mole of steam to 1 mole of water at 100°C.

Key concepts

Enthalpy of Vaporization

The process in which a substance changes from a liquid to a gas state is accompanied by the absorption or release of heat. This heat amount involved in transforming 1 mole of liquid to its vapor is known as the enthalpy of vaporization (H_{vap}). It is crucial to understand that when a liquid vaporizes, it absorbs heat from the surroundings, making H_{vap} a positive value as the system gains energy. Conversely, when the process is reversed, and a gas condenses into a liquid, as in the example of steam turning into water, the same amount of heat that was absorbed during vaporization is then released. This release makes the H for condensation negative, indicating that the system is losing energy to the surroundings. In the given problem, steam turns to water releasing 40.7 kJ/mol, illustrating the exothermic nature of condensation.

Understanding H_{vap} is not only essential for comprehending heat changes during phase transitions but it also plays a significant role in various real-world applications such as in refrigeration and distillation processes where control of vaporization and condensation is key.

Enthalpy of Fusion

The enthalpy of fusion (H_{fus}) is associated with the change of a substance from a solid to a liquid state at its melting point. This heat of fusion is the energy required to change 1 mole of a solid into a liquid without a temperature change. It's an endothermic phase transition, meaning that the substance absorbs heat during the melting process, hence the positive sign of H_{fus}. However, analogous to vaporization, when the phase change is from liquid to solid, or freezing, the process is exothermic; the same amount of energy absorbed during melting is released. For instance, when water transitions to ice, the H becomes negative (in this case, -6.01 kJ/mol) because the liquid releases heat to the environment during freezing.

Learning about H_{fus} helps students in fields like cryogenics, metallurgy, and even in understanding the natural phenomena such as the formation of ice on lakes during winter, since the principle revolves around the heat transfer during the phase change.

Heat Transfer in Phase Changes

The underlying principle that governs phase changes is heat transfer, a concept fundamental to thermodynamics. During phase transitions, substances absorb or release heat, but do not change temperature. For example, when a liquid heats up to its boiling point, additional heat (known as latent heat) is used solely to change the phase to gas, while the temperature remains constant, demonstrating this critical aspect of phase changes.

Phase changes typically involve transfers of significant amounts of energy, as reflected in the concepts of enthalpy of vaporization and fusion discussed earlier. The energy involved can be calculated and compared, as seen in the given exercise where steam condensing to water at 100°C releases more heat, specifically, -40.7 kJ/mol, compared to water freezing to ice at 0°C, which releases -6.01 kJ/mol. These calculations are not just academic exercises but are applied in designing heating and cooling systems, in weather patterns prediction, and in explaining how energy is distributed or absorbed during the changing states of matter in everyday life.