Introduction
This is the branch with the equations in it. Ask an organic chemist what happens when you mix two things and you get a product. Ask a physical chemist and you get a number: how much, how fast, how much heat came out, and what happens if you warm it by ten degrees.
One distinction is worth getting straight early, because confusing it causes most of the trouble. Can the reaction go? That is thermodynamics. Will it go today? Kinetics. Take a diamond. Graphite is the more stable form of carbon at room temperature, so thermodynamically every diamond is on its way to becoming pencil lead. Kinetically the trip takes longer than the universe has existed. Nobody insures against it.
History and Development
Svante Arrhenius submitted a dissertation in 1884 arguing that dissolved salts split into charged particles. His doctoral committee at Uppsala was unimpressed and graded it fourth class, non sine laude approbatur, approved not without praise. He posted copies to chemists abroad instead; Wilhelm Ostwald read his, travelled to Uppsala that August and offered him a job. The same work won the 1903 Nobel Prize in Chemistry. Josiah Willard Gibbs supplied the other half of the foundation, the thermodynamic treatment of chemical equilibrium.
Quantum mechanics arrived in the 1920s and changed what the field could claim. Before it, bonding was a bookkeeping convention; after it, a bond was a calculable consequence of electron behaviour. The instruments mattered just as much. Spectroscopy let chemists infer structure from the light a substance absorbs, and calorimetry turned heat into a number you could put in a table, which is the unglamorous foundation the equations rest on.
Core Concepts
The first law says energy is conserved. True, and not much use alone. It says nothing about direction.
The second law supplies direction. Heat moves from hot to cold unprompted. Reverse it and you need a pump and an electricity bill.
Kinetics defeats intuition. Warm a reaction by ten degrees and the rate often doubles. That seems disproportionate. The reason is the fraction of molecules carrying enough energy to react, and that fraction climbs steeply with temperature. Concentration, surface area and catalysts pull the same lever.
Quantum chemistry underlies all of it and brings bad news. An electron has no position to report. It has a distribution of places it might be found.
Subtopics in Physical Chemistry
Electrochemistry is the trick of separating a reaction's two halves so the electrons have to travel through a wire to get from one to the other. That is a battery. Everything difficult about battery engineering follows from making that journey reversible a few thousand times without the electrodes degrading. Activation energy is the hill a reaction climbs before it can roll downhill, which is why a mixture can be wildly unstable and perfectly safe at room temperature.
The Schrodinger equation describes an electron exactly, and can be solved exactly for hydrogen. One electron. Everything beyond that is approximation, which is the honest state of quantum chemistry: enormously useful, never exact. Molecular orbitals come out of those approximations, and they explain something the dot-and-cross diagrams cannot, such as why oxygen is attracted to a magnet.
Applications of Physical Chemistry
Materials science is applied physical chemistry under another name. Whether a polymer is a rigid plastic or a stretchy one often comes down to how its chains pack and at what temperature they start sliding past each other, which is a thermodynamic question with a commercial answer. Enzyme kinetics moves the same mathematics into biology, and it is how pharmacologists describe what a drug does to an enzyme and how tightly it holds on.
Atmospheric chemistry is the case where getting the kinetics right mattered historically. CFCs are inert at ground level, which was the selling point. High in the stratosphere, ultraviolet light breaks them apart and the chlorine released destroys ozone catalytically, meaning one atom wrecks many molecules before it is removed. Nothing about that is visible from the compound's behaviour in a can.
Further Reading
For deeper study, explore these resources: