Referring to Pentcho Valev's question, I recall some textbook knowledge:
In isobaric processes which proceed in systems neither exchanging any matter
with their surroundings nor exchanging work except volume work, the change in
enthalpy gives the exchanged H E A T (rather than work).
The change in Gibbs free energy indicates, if negative, the maximum work the
system can perform, and, if positive, the minimum work one has to perfom on
the system to force the process to proceed.
Both quantities do depend on concentrations. What is independent of
concentrations are the molar standard enthalpy and molar standard Gibbs free
energy.
These are sufficient points to resolve the paradox, I think.
Stefan Schuster