In the book, I have seen that it is written that in an isothermal change, $$\Delta H =\Delta U + \Delta n_\mathrm{g}RT$$ I can clearly understand the derivation where $\Delta H = \Delta U +\Delta (PV)$ And as $PV=nRT$, $\Delta (PV)=\Delta(n_\mathrm{g}RT)$
And as $T=\text{const.}$
$\Delta (PV)=\Delta n_\mathrm{g}RT$
We plunge this value in the above equation. But what my question is, if the process is isothermal, internal energy must be constant i.e. $\Delta U=0$.
Then the equation must be $$\Delta H = \Delta n_\mathrm{g}RT$$
I want to know where is my concept wrong?