Yes, you are right. I seems to have goofed. In (2), it looks like a result of previous action:
Hydrogen and oxygen unite, and water formed as a result of it.
At first I thought that infinitives (in the second type) is used as Present Participle in this sentence:
A girl sat reading a book.
That equals A girl was seating and reading a book. That is, these two actions happens simultaneously.

Thank you, bitpicker & sperk.