I have a question regarding this formula for Gibbs free energy of a system: $$\Delta G=\Delta H-T\,\Delta S$$
According to the second law of thermodynamics: $T\,\Delta S\ge\Delta Q$ and to my understanding, $\Delta H$ is just the same as $\Delta Q$.
Now, if $\Delta Q$ will be always smaller than (or equal to) $T\,\Delta S$ and $\Delta H=\Delta Q$, then looking at the first formula again it seems that $\Delta G$ can only be smaller than (or equal to) zero.
What am I doing wrong here?