I seem to be unsure about a discrepancy in energy conservation utilizing the equipartition theorem. Let's say I have a molecule within a thermal reservoir. For example, I will use a molecule of $NH_3$. I will assume that the temperature of reservoir is sufficiently high enough that the high temperature limit can be assumed for the thermodynamical ensembles and molecule's internal energy will be share equally among its degrees of freedom. Specifically, I will focus on its translational, vibrational, and rotational motions.
According to the equipartition theorem, $NH_3$ should have three translational degrees of freedom (each of which gives $\displaystyle \frac{1}{2} k_B T$
$$U_{tr}=\frac{3}{2} k_B T$$
Similarly for rotational energy
$$U_{rot}=\frac{3}{2} k_B T$$
And for a polyatomic molecule such as $NH_3$, there are $3N-6$ vibrational degrees of freedom each of which give energy $k_B T$ which gives
$$U_{vib}=6 k_B T$$
Therefore the total energy of the $NH_3$ molecule is
$$U_{tot}=9 k_B T$$
Now what if the $NH_3$ molecule completely dissociates so that
$$NH_3 \rightarrow N + 3H$$
Now we only have 3 translational degrees of freedom for each of the 4 atoms. This gives a total internal energy of the system to be
$$U_{tot}=6 k_B T$$
Of course due to energy conservation this energy must have gone somewhere. My question therefore is, where did the extra $3 k_B T$ worth of energy go? My best guess would be that it either was lost as heat to the surroundings when the bonds were broken or it went into the actual dissociation of the molecule. Would I be correct in any of these assumptions?