Ideal Solution Properties Analysis

An ideal solution is defined by specific thermodynamic properties upon mixing components at constant temperature (T) and pressure (P). We need to identify which of the given properties are characteristic.

Evaluating Solution Properties

• Statement (i): $(\Delta_{mix} G)_{T, P}$ is negative
  The Gibbs Free Energy change for mixing ($\Delta_{mix} G$) determines the spontaneity of solution formation. For any spontaneous process, including the formation of an ideal solution, $\Delta_{mix} G$ must be negative. This is because the formation of a solution leads to increased randomness, which is thermodynamically favorable.
  Therefore, statement (i) is correct.
• Statement (ii): $(\Delta_{mix} S)_{T, P}$ is positive
  Mixing generally leads to a more disordered state compared to the separate components. Entropy ($S$) is a measure of this disorder. Thus, the entropy of mixing ($\Delta_{mix} S$) for an ideal solution is always positive, reflecting increased randomness.
  Therefore, statement (ii) is correct.
• Statement (iii): $(\Delta_{mix} V)_{T, P}$ is positive
  In an ideal solution, the intermolecular forces between solute-solute, solvent-solvent, and solute-solvent particles are identical. This means there is no net change in volume upon mixing. Therefore, the volume change ($\Delta_{mix} V$) is zero, not positive.
  Therefore, statement (iii) is incorrect.
• Statement (iv): $(\Delta_{mix} H)_{T, P}$ is negative
  Similar to volume change, the enthalpy change ($\Delta_{mix} H$) for mixing ideal components is zero. The energy required to overcome solute-solute and solvent-solvent interactions is exactly compensated by the energy released from forming solute-solvent interactions. Thus, $\Delta_{mix} H$ is not negative.
  Therefore, statement (iv) is incorrect.

Conclusion on Ideal Solution Characteristics

Based on the analysis, the characteristic properties of an ideal solution among the given options are:

• $(\Delta_{mix} G)_{T, P}$ is negative (statement i)
• $(\Delta_{mix} S)_{T, P}$ is positive (statement ii)

Therefore, statements (i) and (ii) correctly describe properties of an ideal solution.