Statistical mechanics predicts states of a large (macroscopic) system based on classical and quantum probabilities of a given particle in that system. For instance, a molecule is very likely to possess high energy and unlikely to possess low energy. We can say that a huge collection of those particles is virtually certain to be of high energy. Note that measurement of any particular particle in that collection is not necessary--this is the advantage of statistical mechanics. Further research into the field grows elaborate, but is based on entropy and irreversibility (one-way processes such as mixing hot and cold to get warm).
Quantum mechanics entails two concepts foreign to classical physics--particle wave functions and inherent uncertainty. A wave function straddles the line between mathematical abstraction and physical object. A wave function "collapses" upon observation to give a distinct measurement. There is the disquieting conclusion that prior to observation, the particle does not exist in a definite sense, only its wave function does. A large number of observations lead to a large number of concrete measurements that reveal overall shape of the underlying wave function. Physical chemistry must also consider the Heisenberg Uncertainty Principle. This concept is relevant since atomic-scale measurements are inevitably marred by unavoidable error in, for instance, particle location measurement given particle momentum.
It is important to know features of gases, solids and liquids. Gases are defined by a changing volume. Density statements about gaseous systems must be accompanied by a temperature that specifies conditions under which a certain gas has a certain density. Liquids have a definite volume, but no definite shape. Gases and liquids are both described by fluid flow, with fluid existing as Newtonian (constant viscosity) or non-Newtonian (variable viscosity). Solids have a definite shape and density. Solid-state dynamics deals with surface interactions, internal molecular structure, and usually elements of crystal symmetry. Phase diagrams summarize under what temperature and pressure a substance exists as a solid, liquid, or vapor and are useful in relating energetic and physical properties of reaction products.