I just learned about spin in class and I recall my professor vaguely mentioning how the spin of an electron is what determines certain chemical properties. I have trouble seeing why. Suppose an electron had no spin (which I know can't happen since electrons are fermions) but if they did, can we determine if some elements were chemically inert?
If electrons had no spin and if they were, therefore, bosons instead of fermions, our entire universe would be much different. If the electron were a boson, chemistry would be completely different. For example, in a bosonic electron universe:
...the biggest atom by volume would be the Hydrogen atom and it would be the same size as the Hydrogen atom in our universe which is the Bohr radius, $r_B$. However, for all other atoms, the effective radius would be $r_B/Z$. where $Z$ is the atomic number = the number of protons in the nucleus. The reason for this is that when electrons are bosons it will be possible for all of the electrons of the atom to be in the 1S orbital of the atom. But in our universe, the Pauli exclusion principle only allows two electrons in each distinct orbital - one with spin up and one with spin down. So in the bosonic universe the only time any electron would be in any higher orbital would be when it is temporarily excited to a higher orbital by a photon or some other source of energy - it would then quickly transition back to the 1S orbital....
-- (from an answer I wrote on Quora - see the answer for many other interesting consequences, such as an explosion whenever two objects touch each other)
Now, if the electron has no spin and if it still is a fermion, then chemistry would also be very different. In our universe, every electron orbital in an atom can have two electrons, one with spin up and one with spin down. In this spin 0 fermionic electron universe, there could only be one electron in each orbital. Therefore the size of high $Z$ atoms in this universe would be much larger than our universe since twice as many orbitals would be occupied.
Further, the chemical bonding of atoms into molecules will also be quite different. The simplest possible molecule is $H_2$. In our universe, the $H_2$ molecule is tightly bound - in particular, the total energy of $H_2$ is significantly lower than the energy of two individual $H$ atoms. Each individual $H$ atom has a single electron in the 1S orbital. However, the 1S orbital can hold a second electron; and each electron would as tightly bound as the other (ignoring the fact that there is only one proton in the nucleus). If you bring two $H$ atoms close to each other, the two individual electrons can occupy one molecular "orbital" that encompasses both nuclei, and that one molecular "orbital" would contain 2 electrons with opposite spins.
In this spin 0 fermionic electron universe, the $H_2$ molecule will not be as tightly bound as $H_2$ in our universe. Consider placing the two protons (nuclei) near each other, one of the electrons can be in the first molecular "orbital," but the second electron will have to go into the second, higher energy molecular "orbital." Thus, the $H_2$ molecule in this universe will not be as tightly bound ad the $H_2$ molecule in our universe.
This the chemistry in this spin 0 fermionic electron universe would be very different than the chemistry in our universe. for example, some molecules that are stable in our universe may not be stable in this universe.
See, e.g, https://en.wikipedia.org/wiki/Spin_chemistry:
"bonds can only be formed between two electrons of opposite spin...Sometimes when a bond is broken in a particular manner, for example, when struck by photons, each electron in the bond relocates to each respective molecule, and a radical-pair is formed. Furthermore, the spin of each electron previously involved in the bond is conserved,... which means that the radical-pair now formed is a singlet (each electron has opposite spin, as in the origin bond). As such, the reverse reaction, i.e. the reforming of a bond, called recombination, readily occurs. The radical-pair mechanism explains how external magnetic fields can prevent radical-pair recombination with Zeeman interactions, the interaction between spin and an external magnetic field, and shows how a higher occurrence of the triplet state accelerates radical reactions because triplets can only proceed to products, and singlets are in equilibrium with the reactants as well as with the products."
Suppose an electron had ... spin ..., can we determine if some elements were chemically inert?
Historically at the beginning it was simply observed that some elements are inert and/or have other chemical properties (to be a metal, an acid and so on), Later the known elendes were arranged in tables by Mendeleev and Meyer. The mentioned scientists arranged the elements by weight (from top to bottom) and by there chemical properties (from left to right). These tables were called periodic tables because in each row the chemical properties of the elements from left to right have repeating chemical properties.
Later physics claims that the founded properties have to do with electron shells around the nucleus. According to the above excerptwise shown periodic table the first shell contains maximum 2 electrons and the rightest elements of the next two rows both have 8 electrons in the outer electron shell. These elements He, Ne and Ar are inert and called noble gases.
Furthermore it was empirical determined that the elements next to the noble gases in compounds like to fill there shells with electrons from other elements. And that Fluorine F is more aggressive than Chlorine Cl - because the electrons in F are tighter bonded to the nucleus.
Fluorine is a fascinating element, which takes - simply spoken - the electron wherever it has another element around it. Examples are HF, ClF3 or ClF5. A really aggressive element. In each of these examples the every Fluorine captures one electron to fulfill his electron shell to eight electrons and the other element loses so many electrons that the remaining electrons are an even number.
What you have to check is, always to get pairs of electrons. That electrons like to be pairwise was expressed by the Pauli exclusion principle. It is a principle and not an explanation why this happens this way in atoms. But if you need an imagination of how the electrons form pairs you could think for yourself of the electrons as tiny bar magnets (they indeed have a magnetic dipole moment) and two of them form a magnetic pair.
And one more remark. The noble gas Xenon Xe is not inert to Fluorine! See on Wikipedia about Xenon fluoride.