The arrangment and location of what subatomic particles determine the chemical properties of an atom?
I don't know that the location is as much a determining factor as is the number of subatomic particles available. The subatomic particle, of course, is the electron, which orbit the nucleus of the atom by traveling in energy levels, two in the first, 6 in the second, and 10 in the third. It is the number of electrons available in the outer energy level that determine the atoms chemical properties. For example, hydrogen has the simplest atomic structure on the periodic chart of elements, with one proton in the nucleus and one electron circling in the first energy level about the nucleus. One of the chemical properties used to classify atoms is their ability to combust, to combine chemically with oxygen. Oxygen has 6 electrons in its outer energy level, with room for two electrons. Hydrogen will combine quickly and explosively with oxygen to form water, as the lone electron from each of two hydrogen atoms joing together chemically with one oxygen atom to form one molecule of water, H2O. It is this number of electrons available, or number of vacancies available, that determine both the ability and rate of an atom to combine chemically with other atoms.
The arrangment of electrons determine everything that you have to know about the chemical proerties.
By 1913,when during experiments are especially with spectrum light of hydrogen it was discovered that the electons spin around the Nuclei in fixed motions creating a so called orbital, later on subatomic orbitals where discovered.Therefore it was essential to arrage the elements by the Electonic Configuration.But before starting to make an Electonic Configuration, a new way of doing this was discovered called quantum numbers (Ill suggest you ask someone in physic or chemistry about these numbers) there are four of these numbers which tell excatly the configuration of an atom and it's position in the Periodic Table.
The position of an element in a Group tells it's Chemical Properties so keep in mind for excample the first group is called Alkali-Metals (Group) and all of the elements share the same chemical Properties but the properties increase as you go down the group excample Lithum is less reactive than Sodium etc.
So The Arrangment and location of Electons (which is a subatomic particle) determines the chemical properties of an atom.
Hope this helps.