Thermodynamics of a spontaneous isothermal chemical reaction.
The internal energy and enthalpy of a pure ideal gas depends only on temperature.  But, the internal energy and enthalpy of an ideal gas mixture depends both on temperature and on the amount of each chemical species that is present.  To be more precise, it is equal to the internal energy and enthalpy per mole of each component as if it were a pure species times the number of moles of that species present, summed over all the species in the mixture:  $$U=\sum{n_iu_i}$$and$$H=\sum{n_ih_i}$$So, even at constant temperature, $$\Delta U=\sum{(\Delta n_i)u_i}$$and$$\Delta H=\sum{(\Delta n_i)h_i}$$You should have been taught this when they were covering the thermodynamics of mixtures and chemical reactions.