Thermodynamics
An intresting preface: Personally, as an unqualified individual with ready access to the world-wide web, I think that just as physics can sometimes be thought of as applied mathematics, Chemistry, for a large part of it, is largely thermodynamics.
From what I've seen, there's a lot of insight to be gained from this one subject, so I find its thorough and comprehensive understanding quite important if you are to fundamentally capture the concepts in later sections. I may be incorrect, but the ability to model physical systems like molecules with a basis in energy lets you, at its core, acquire a vast degree of knowledge on the probablities and seeming inevitabilities of the subject, be it through expected bonds or equillibrium states of many kinds.
The subjects of equillibrium and solubility (which can go hand-in-hand) are very dependent on this in particular for certain analyses.
Laws of Thermodynamics:
If we talk about thermodynamics, it's helpful to get its basis out of the way. While I won't cover the rich and contextually important history that leads to many of these understandings and aids in the proper comprehension of the subject (I strongly advice reading into this!), I hope to cover some more basic fundamental ideas that are sufficient to be used in the understanding of larger and more complex models through the lens of abstraction.
What we would like to do in this section is show many of these relations we can make, but in order to do that, its relevant to talk about the so-called laws of thermodynamics, starting not with the first but the zeroth law: the transitivity of temperature.
Zeroth Law: Temperature and Transitivity
Put very briefly, we know that molecules and particles can become agitated. We will now create a property called temperature to set values relating to this measure of agitation. There are many ways to measure the value of temperature for an object, but the Celcius, Farrenheit, and Kelvin scales are the most common. If you plan on taking this test, it seems you are to familiarize yourself with freely converting between all of these by yourself; be careful! Amen
Historical Footnote and Fun Fact: The Farrenheit, despite rightly critized for its non-comformance to SI units, has a wonderfully rich history! I don't remember all parts of it, but on research I found that it's baseline zero point was chosen as the freezing point of a stable brine solution, which made measuring easier than with water at the time!
Aside from this, unlike the Celcius scale which sets the boiling point of water as a target, the target for Farrenheit was 96 degrees for the standard body temperature (which, with later, more precise meaurements, is now closer to 98.6 degrees Farrenheit, about 2.6 degrees off, which was not bad!). 96 was chosen instead of 100 because it is the sum of 64 and 32, two powers of two, which made finding it with bisections easier.
Overall, despite the many criticisms, I find joy in looking at the historical and experimental reasons/considerations that made this wonderful scale come to be :) OH! DID I MENTION IT HELPED DEVELOP THE USE OF MERCURY FOR CALORIMETRY??
No matter what scale we use to measure this property, the zeroth law of thermodynamics simply states that for any object A, with a given temperature \( \theta_A \), if it is in thermal equillibrium with another object B--which is to say, they have the same temperature, aka \( \theta_A = \theta_B \)--that is itself in equillibrium with yet another object, C, A will be in equillibrium with C, thus making temperature transitive. This is the basis for a lot of things, and while it might seem self-evident, many things in nature don't follow this pattern so its interesting to note!