Question

\(\triangle S\) is positive for the change (1) mixing of two gascs (2) boiling of liquid (3) dissolution of substance (4) all

Short answer

All

Step-by-step solution

Identify the Meaning of \( \triangle S \)

Understand that \( \triangle S \) represents the change in entropy. Entropy is a measure of the disorder or randomness of a system.

Mixing of Two Gases

When two gases are mixed, the number of possible ways in which the molecules can be arranged increases. This leads to an increase in disorder, and hence, an increase in entropy \( ( \triangle S > 0 ) \).

Boiling of Liquid

Boiling a liquid converts it into a gas. Since gas molecules have more freedom of movement than liquid molecules, this process increases the disorder, thus increasing entropy \( ( \triangle S > 0 ) \).

Dissolution of a Substance

When a substance dissolves, its particles spread out in the solvent, increasing the number of possible arrangements and thus increasing the disorder. This results in an increase in entropy \( ( \triangle S > 0 ) \).

Conclusion

Each of the processes described (mixing of gases, boiling of liquid, and dissolution of a substance) leads to an increase in entropy. Hence, the change in entropy \( \triangle S \) is positive for all these processes.

Key concepts

mixing of gases

When two gases are mixed, the molecular distribution becomes more random. This means the particles of both gases spread out to occupy the combined volume. The mixing process increases the number of possible ways the gas molecules can arrange themselves.

Higher number of arrangements means higher disorder. Therefore, mixing gases always increases entropy.

We can understand this with the simple entropy formula for mixing gases:
\( \triangle S_{mix} = -R \sum x_i \ln x_i \)
where \( R \) is the gas constant and \( x_i \) is the mole fraction of each gas. This shows mixing of gases increases entropy \( ( \triangle S > 0 ) \).

boiling of liquids

Boiling transforms a liquid into its gaseous state. This phase change is crucial because it allows molecules to move freely and independently.

In the liquid state, molecules are somewhat constrained by intermolecular forces. But in the gas state, these forces are minimal. Molecules can move around in all directions.

The entropy or disorder of the system significantly increases when a liquid boils because the gas phase has many more possible microstates.
The mathematical change in entropy during boiling can be roughly associated with the latent heat of vaporization and temperature: \( \triangle S = \frac{ \triangle H_{vap} }{ T } \). Here \( \triangle H_{vap} \) is the heat required to change the state, and \( T \) is the temperature.
This results in \( \triangle S > 0 \) when liquid boils.

dissolution of substances

Dissolving a substance, such as salt in water, spreads the solute particles throughout the solvent.

This spreading increases the number of possible ways particles can be arranged in the new solution compared to the independent solute and solvent.

Thus, the dissolution process increases disorder and results in a positive change in entropy (\( \triangle S > 0 \)).
The dissolution can be better understood through enthalpy change (\( \triangle H dissolution\)), but the entropy change (\