Thermodynamics of solutions:\r When both the solute and the solvent are liquids, the heat effect upon forming the solution is specifically termed the __________.

Introduction:
Engineers often need to estimate the thermal effects when blending two liquids. The enthalpy change observed when a liquid solute and a liquid solvent are combined at the same initial temperature is a classic topic in solution thermodynamics. Knowing the correct term avoids confusion with gas–liquid or solid–liquid cases and helps in energy balance calculations for mixers and dissolvers.

Given Data / Assumptions:

• Both solute and solvent are in the liquid phase before mixing.
• No chemical reaction occurs; we consider physical mixing only.
• The process occurs at constant pressure typical of industrial mixing tanks.

Concept / Approach:
When two liquids are mixed, the enthalpy change is called the heat of mixing. This differs from heat of hydration (water binding to ions/molecules, usually relevant to dissolving solids or gases in water) and from heat of solvation (a broader term often used for dissolving a solute in a solvent, commonly in gas/solid–liquid contexts). The standard integral heat of solution refers to dissolving a specified amount of solute to form a standard concentration, not necessarily liquid–liquid blending. Hence, for liquid–liquid mixing without reaction, “heat of mixing” is the precise term.

Step-by-Step Solution:
Identify phases: solute (liquid) + solvent (liquid).Match the proper thermodynamic descriptor: heat of mixing.Eliminate terms associated with hydration/solvation specific to other phase combinations.

Verification / Alternative check:
Process design texts treat mixer heat duties via enthalpy-of-mixing correlations or excess enthalpy models for liquid mixtures, confirming the terminology.

Why Other Options Are Wrong:

• Heat of hydration/solvation: Emphasize solvent–solute interactions in dissolution (often non-liquid solute).
• Standard integral heat of solution: A standardized dissolution metric, not generic liquid–liquid mixing.
• Partial molar enthalpy of dilution: A differential property, not the named overall heat effect.

Common Pitfalls:
Using “heat of solution” generically for all cases; for two liquids, “heat of mixing” is preferred.

Final Answer:
heat of mixing.