Which of the following processes are spontaneous :

1. melting of ice at 2 atm and 273K.
2. melting of ice at ½ atm and 273K.
3. boiling of water at ½ atm and 373K.
4. boiling of water at 2 atm and 373K.

To determine whether a process is spontaneous, we need to consider the conditions under which the process occurs, particularly the temperature and pressure involved. Let's analyze each of the processes you've mentioned, focusing on the melting of ice and the boiling of water under different pressures and temperatures.

Understanding Spontaneity

A spontaneous process is one that occurs without needing to be driven by an external force. In thermodynamics, spontaneity is often assessed using the concepts of Gibbs free energy (G) and the conditions of temperature (T) and pressure (P). A process is spontaneous if the change in Gibbs free energy (ΔG) is negative.

Melting of Ice

Melting ice is a phase transition from solid to liquid. The spontaneity of this process depends on temperature and pressure:

• Melting of ice at 2 atm and 273 K: At this pressure, the melting point of ice is higher than 273 K. Therefore, ice will not melt spontaneously at this condition.
• Melting of ice at ½ atm and 273 K: At lower pressure, the melting point of ice decreases. Since 273 K is above the melting point at ½ atm, the ice will melt spontaneously in this scenario.

Boiling of Water

Boiling water involves a transition from liquid to gas. The spontaneity of boiling also depends on temperature and pressure:

• Boiling of water at ½ atm and 373 K: At this pressure, the boiling point of water is lower than 373 K. Therefore, water will boil spontaneously at this condition.
• Boiling of water at 2 atm and 373 K: At higher pressure, the boiling point of water increases. Since 373 K is at the boiling point for water at 2 atm, the process is not spontaneous; it requires additional energy to maintain the boiling state.

Summary of Spontaneous Processes

Based on our analysis, the spontaneous processes among the options you provided are:

• Melting of ice at ½ atm and 273 K
• Boiling of water at ½ atm and 373 K

In contrast, the melting of ice at 2 atm and 273 K, as well as the boiling of water at 2 atm and 373 K, are not spontaneous processes. Understanding these principles helps us predict how substances behave under varying conditions of temperature and pressure.