Why do Elements React with Specific Mass Ratios?

Since the elements which have "closed'' shells are more stable, atoms will interact until they fill the unfilled orbits (not quite last columns) or until they empty the extra electron orbits (first column). So, either hydrogen needs to gain an electron or it needs to lose an electron. Oxygen needs either to gain two electrons or to lose four electrons. It is possible for atoms to "share electrons'' by allowing some electrons to orbit multiple atoms simultaneously. (There are other mechanisms for atoms to stick together - take a chemistry course for more detail.) So, if an oxygen runs into a hydrogen, each can donate an electron to the set of atoms (the molecule). In this way, two electrons are orbiting the hydrogen (they are also orbiting the oxygen) and the hydrogen is happy. The oxygen, however, needs another electron. It will travel until it happens upon another hydrogen. Then, the oxygen and the new hydrogen will each donate one electron to the molecule. Each hydrogen sees two electrons going around it. The oxygen sees ten electrons going around it. Everybody is content. Now the ${\rm H_2O}$ molecule (water!) runs around bouncing off of other atoms and molecules, but not reacting, because it is like the noble gas.