Problem 19 - Chemistry The Central Science

Question

Consider a system consisting of an ice cube. (a) Under what conditions can the ice cube melt reversibly? If the ice cube melts reversibly, is \(\Delta H\) zero for the process?

Step-by-Step Solution

Answer

In conclusion, an ice cube can melt reversibly if it is heated infinitesimally slowly at the melting point (0°C or 273.15 K) while maintaining equilibrium with its surroundings, and the surrounding temperature is infinitesimally higher than the melting point. During this process, the enthalpy change (\(\Delta H\)) is positive and non-zero as the ice cube absorbs heat for the phase transition from solid to liquid.

Step 1: Determine conditions for reversible melting

A process can be considered reversible if it proceeds infinitesimally slowly, maintaining thermodynamic equilibrium between the system (ice cube) and its surroundings throughout the entire process. For the ice cube to melt reversibly, it must be heated at the same rate it is melting, keeping the system and surroundings in equilibrium. Let's consider an ice cube at its melting point, which is 0°C (273.15 K) at atmospheric pressure. To make the melting process reversible, the temperature of the surroundings should be infinitesimally higher than the melting point. This will provide a gradual supply of heat to the ice cube, allowing it to melt slowly while maintaining equilibrium with its surroundings.

Step 2: Calculate the change in enthalpy \(\Delta H\)

Enthalpy change, \(\Delta H\), is the amount of heat absorbed or released during a process at constant pressure. In the case of the ice cube melting, it absorbs heat from its surroundings, which is converted into internal energy, leading to a phase transition from solid to liquid. The enthalpy change for melting is also known as the enthalpy of fusion, which is the amount of heat required to convert 1 mole of a substance from the solid phase to the liquid phase at its melting point and constant pressure. For water, the enthalpy of fusion is approximately 6.01 kJ/mol. As the ice cube is absorbing heat to transform from solid to liquid during the reversible melting process, the enthalpy change, \(\Delta H\), is positive and non-zero.

Step 3: Conclusion

To sum up, an ice cube can melt reversibly if it is heated infinitesimally slowly, maintaining thermodynamic equilibrium between the system (ice cube) and its surroundings. The surroundings should have a temperature infinitesimally higher than the melting point of the ice cube (0°C or 273.15 K). During the reversible melting process, the enthalpy change, \(\Delta H\), is positive and non-zero, since the ice cube absorbs heat to transform from solid to liquid.

Key Concepts

Thermodynamic Equilibrium

Thermodynamic equilibrium is a state where a system and its surroundings are in complete balance. This means no net change is happening in the system without external influence. For an ice cube to be in thermodynamic equilibrium, it should exchange heat with its surroundings in a balanced manner.

• In practical terms, for reversible processes like melting an ice cube, the system and surroundings must be almost at the same temperature.
• This ensures the process occurs slowly, allowing equilibrium conditions to be maintained.

Imagine tipping a perfect balance scale by adding grains of rice one by one. As each grain is added very carefully, the scale tips ever so slightly, maintaining an equilibrium where it could easily tip back if even one grain is removed. Likewise, the temperature of the ice cube and the surroundings should be nearly identical. This way, the melting happens in such a way that you could almost say it could "tip back" into its solid form if conditions slightly changed.

Enthalpy of Fusion

The enthalpy of fusion refers to the heat required to change a solid into a liquid at its melting point. This is a key part of understanding phase transitions like melting.

• When we talk about the melting of an ice cube, the enthalpy of fusion is the energy needed to break the bonds holding the water molecules in a solid state.
• For water specifically, this value is about 6.01 kJ/mol.

What happens is that as the ice absorbs heat, this energy is used to disrupt the molecular bonds that keep it solid. But it does not cause an increase in temperature until the entire solid has transitioned into liquid.
Think of this energy as the ticket price for water molecules to journey from a tightly packed ice block to a freely flowing liquid. In a reversible process, this heat is carefully added, ensuring that every bit of added energy perfectly matches the energy needed to transition the next molecule.

Phase Transition

A phase transition refers to a change in the physical state of a substance, such as from solid to liquid, known as melting. This occurs when energy, in the form of heat, is added or removed.

• Melting is the phase transition from solid to liquid, occurring at the melting point when sufficient heat is added.
• In reversible processes, this transition is gradual and well-controlled.

During melting, the added heat doesn't immediately raise the temperature of the ice. Instead, it is utilized to change the state of water molecules, moving them from a fixed lattice in a solid to a free form in liquid.
Consider phase transition like a dance, where each molecule must find another partner (energy) before it can swap styles (states). The dance floor (the ice) won't change its form (temperature) until every dancer (molecule) is perfectly paired and ready to move.