How was the diatomic nature of many common gaseous elements originally determined?

Question

How did scientists find out that $\ce{Cl2, H2, O2}$ atoms have a two-atomic molecular structure ?

Answer 1

Here I'll only provide the reasoning for $\ce{O2}$ and $\ce{H2}$ diatomic structure, I think similar reasoning was to deduce that of $\ce{Cl2}$.

The divalency of oxygen, shown by Avogadro's hypothesis.

It is known that two volumes of hydrogen gas and one volume of oxygen gas combine to form water. From Avogadro's hypothesis (equal volumes of gas contain equal numbers of molecules) it can be concluded that water must have two atoms of hydrogen and one atom of oxygen (or conceivably some multiple). Hence, oxygen is divalent (valence of 2) while hydrogen has a valence of 1:

$$\ce{2H + O \to H2O}$$

This would indicate that $\frac12$ gram of hydrogen atoms reacted with 8 grams of oxygen atoms. Since the atomic weight of hydrogen was defined as $H = 1$, then the respective atomic weights of hydrogen and oxygen would be $H = 1$ and $O = 16$ (the values accepted today).

The diatomic nature of hydrogen and oxygen, as shown by Avogadro's hypothesis.

It is observed that when two volumes of hydrogen gas and one volume of oxygen gas combine, two volumes of water gas are formed. If hydrogen and oxygen were monatomic (as shown in the equation above), then only one volume of water would be formed. The only explanation is that hydrogen and oxygen are diatomic: $$\ce{2H2 + O2 \to 2H2O}.$$

(Copied almost verbatim from this page)

Answer 2

The reason to form a bond is usually for stability, and so that is why some elements are diatomic.

In the case of chlorine, it is has -effectively- 7 electrons in its outer shell. The atom will be most stable when it has 8 electrons, and so it can share an electron with another chlorine atom, which will result in them both having 8 electrons in their outer shell.

Similarly, hydrogen has one electron in its outer shell. At this energy level, it needs 2 electrons in its outer shell, and so can share (in what's called a covalent bond) an electron with another hydrogen atom.

Oxygen has 6 electrons in its outer shell, and so needs two more electrons to achieve stability. To do this, it forms a double covalent bond with another oxygen molecule, and so it achieves a full outer shell and becomes stable.

Metals, such as sodium and potassium, are not actually single atoms, but atoms that are joined together in a lattice. It is made up of positive metal ions surrounded by a 'sea' of delocalised electrons. This means that they are as stable as they want to be, and so do not need to form covalent bonds with other atoms.

Edit After Comment Evidence for diatomic molecules can be seen in several different ways. One example is by looking at an electron density map of, for example, chlorine:

We can see that there are two atoms and these are sharing electrons.

Also, we can look at the mass spectrum of a chlorine molecule:

Here, the two peaks around 35 are the two isotopes of chlorine: chlorine-35 and chlorine-37. Further on, near 70, we see that there are three different peaks. These peaks are where a diatomic molecule of two chlorine isotopes has been formed. The peaks are of a 35-35 molecule, a 35-37 molecule, and a 37-37 molecule, respectively. This shows that chlorine forms a diatomic molecule with two of its isotopes. We can then extend this to saying that because it would be theoretically more stable, and that it is a gas at room temperature, it is likely that gases like chlorine are diatomic in standard conditions and so a covalent compound.

The evidence for the metallic structure which I described is effectively its characteristics. The fact that metals can conduct electricity implies that the delocalised electrons are free to move through the lattice when a potential difference is applied. Similarly, the way metals conduct heat can also be explained using this model, as the electrons move easily and so can transmit kinetic energy rapidly through the lattice.

The high melting and boiling temperatures suggest that the forces between metal atoms must be large because it takes a lot of energy to separate them. The metallic structure suggests that the lattice of positive ions are held tightly together by this electron 'glue'.

Lastly, metals are malleable and ductile, which indicates that the positive metal nuclei have room to move within the sea of electrons.

Answer 3

Hydrogen, oxygen, chlorine, etc, prefer to fill their valence electron shell by sharing electrons. Energy is released in the sharing a pair of electrons then individual atoms.

Sodium, potassium, etc, would rather give up an electron (to have a full valance electron shell), then to share electrons in an attempt to fill up the electron shell. In the case of bonding, a little energy is used to release an electron and a lot of energy is released when another atom pulls it into its valance shell.

Since the metal atom would use energy to take an extra electron, and the release uses energy, metal atoms will not take an extra electron.