In adsorption/solution thermodynamics, which “heat of solution/adsorption” depends on both temperature and adsorbate concentration (surface coverage)?

Introduction / Context:
In adsorption and in solution thermodynamics, heats can be defined in two ways: differential (at an incremental addition) and integral (average over the total amount). Distinguishing their dependencies is essential for interpreting calorimetric data and modeling isotherms.

Given Data / Assumptions:

• “Adsorbate concentration” refers to surface coverage or solution composition.
• Temperature affects intermolecular interactions and thus heats.

Concept / Approach:
The differential heat is defined as the incremental enthalpy change per incremental amount added at a specified composition/coverage. It varies with both temperature and current coverage (or concentration). The integral heat is the average from zero up to a given amount and is less sensitive as it averages the varying differential values, though it can change with composition due to averaging.

Step-by-Step Solution:
Define differential heat: q_diff = (∂H/∂n) at fixed T and fixed coverage state.Recognize its strong dependence on the instantaneous state variables (T and coverage).Select “differential” as the quantity explicitly dependent on adsorbate concentration and temperature.

Verification / Alternative check:
Typical adsorption isotherms show q_diff decreasing with increasing coverage for heterogeneous surfaces, confirming dependence on concentration/coverage.

Why Other Options Are Wrong:
Integral heat is an average and does not represent the instantaneous dependence in the same way; “both” overstates the equivalence; “neither” and “only at infinite dilution” are incorrect.

Common Pitfalls:
Confusing average (integral) with incremental (differential) measures; ignoring coverage effects in calorimetric interpretation.

Final Answer:
differential