On dissolving \(NaCl\) in water there occurs

increase in entropy

The correct answer is option 2. increase in entropy.

When NaCl dissolves in water, several thermodynamic changes occur, each related to fundamental concepts in physical chemistry. Let's analyze each aspect in detail:

1. Gibbs Free Energy (\(\Delta G\))

The Gibbs free energy change (\(\Delta G\)) determines the spontaneity of a process. The dissolution of NaCl in water is a spontaneous process, meaning that the Gibbs free energy change is negative (\(\Delta G < 0\)). This can be represented by the equation:

\(\Delta G = \Delta H - T\Delta S \)

where:

\(\Delta H\) is the enthalpy change.

\(T\) is the temperature.

\(\Delta S\) is the entropy change.

Since the process is spontaneous, \(\Delta G\) decreases.

2. Entropy (\(\Delta S\))

Entropy (\(\Delta S\)) is a measure of disorder or randomness in a system. When NaCl dissolves in water, it dissociates into sodium (\(\text{Na}^+\)) and chloride (\(\text{Cl}^-\)) ions:

\(\text{NaCl} \rightarrow \text{Na}^+ (aq) + \text{Cl}^- (aq) \)

This dissociation increases the number of particles in the solution, which increases the disorder of the system. Therefore, the entropy increases.

3. Enthalpy (\(\Delta H\))

The enthalpy change (\(\Delta H\)) of dissolution involves two main steps:

Breaking the ionic bonds in the solid NaCl (endothermic, requires energy).

Hydrating the ions in solution (exothermic, releases energy).For NaCl, the lattice enthalpy (energy required to break the ionic bonds) is relatively high. However, the hydration enthalpy (energy released when ions are surrounded by water molecules) is also significant but does not completely offset the energy required to break the lattice. Hence, the overall enthalpy change (\(\Delta H\)) is slightly positive, indicating that the process is slightly endothermic. However, this increase is small compared to the entropy increase, which drives the spontaneity.

4. Internal Energy (\(\Delta U\))

Internal energy (\(\Delta U\)) is the total energy contained within the system. It is related to enthalpy (\(\Delta H\)) and the work done by or on the system:

\(\Delta H = \Delta U + P\Delta V \)

For solutions, the volume change (\(\Delta V\)) is usually small, so \(\Delta U \approx \Delta H\).

Given the slight positive value of \(\Delta H\), the internal energy might increase slightly. However, since the enthalpy change is very small, the increase in internal energy is not significant and often negligible in this context.

Summary

Among the given options:

Gibbs energy: Decreases (not an increase).

Entropy: Increases (correct statement).

Enthalpy: Slightly increases, but this increase is small and depends on the balance of lattice and hydration enthalpy.

Internal energy: Does not significantly increase (depends on \(\Delta H\)).

Thus, the most accurate statement regarding the dissolution of NaCl in water is: (2) increase in entropy.