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# Ideal Gas Behavior

If ideal gas behavior is assumed, for which of the following reactions does $$\Delta H = \Delta U$$?

(a) N$$_2$$O$$_4$$ $$\rightarrow$$ 2 NO$$_2$$ $$(g)$$

(b) CH$$_4$$ $$(g)$$ + 2 O$$_2$$ $$(g)$$ $$\rightarrow$$ CO$$_2$$ $$(g)$$ + 2 H$$_2$$O $$(l)$$

(c) SO$$_2$$ $$(g)$$ + $$\frac {1}{2}$$ O$$_2$$ $$(g)$$ $$\rightarrow$$ SO$$_3$$ $$(g)$$

(d) Br$$_2$$ $$(l)$$ + 3 Cl$$_2$$ $$(g)$$ $$\rightarrow$$ 2 BrCl$$_3$$ $$(g)$$

(e) Cl$$_2$$ $$(g)$$ + F$$_2$$ $$(g)$$ $$\rightarrow$$ 2 ClF $$(g)$$

The correct answer is (e), and I just want to make sure I understand why. For $$\Delta U = \Delta H$$, no work can be done as $$\Delta U = H - W$$ (where $$W$$ is work done by the gas).

This means that the total number of molecules can't change, otherwise a change in volume will occur, causing work to be done upon molecules or the molecules to do work. Likewise, phase changes will also require work to be done on the molecules. Thus, we rule out (a), (b), (c), and (d)?

I'm not sure if this is too simplistic or the correct way of thinking about this problem.

Any help would be greatly appreciated.