Physical Chemistry Terminology

Microstate
the instantaneous positon,momentum and internal state of all the particles in a system or the wave function for the entire system
Ensemble
a collection of microstates with a given macroscopic state of a system. One can also imagine a very large number of replicas of the system, all with the same macroscopic initial conditions. At any instant in time, the collection of microstates taken from all the replicas represent the members of the ensemble
Microcanonical Ensemble
Ω(NVE) Ensemble, fixed # of particles, volume and energy
Canonical Ensemble
Q(NVT) Ensemble, fixed # of particles, volume and Temperature
Isothermal-Isobaric Ensemble
∆(NPT) Ensemble, fixed # of particles, pressure and temperature
Grand Cononical
Ξ(μ,V,T) Ensemble, fixed chemical potential, volume and temperature
Time Average
measure a property of the system as a function of time Γbar = lim 1/T int(0,T) Γ(t)
Ensemble Average
Sum of all Microstates weighted by the probability that each microstate will be visited.
Microstate Postulate 1
Ergodic Hypothesis: Given enough time each micro state will be visited
Microstate Postulate 2
Principle of Equal Priori Probabilities: All microstates with fixed NVT having equal energy have equal probability. No knowledge of how a system passes from one microstate to another is needed
Boltzmann Distribution
The Probability of finding a system in the ith microstate
1 Microstate
Zero Entropy
Adding Heat or Work does what to the microstates
Heat: Changes the probability distribution over energy levels, Work: Changes the amount of energy levels with the same distribution.
Distinguishable
Particle which can tell the difference when counting them for example, q^(n) number of particle partition funtions
Indistinguishable
Particle which can not tell the difference when counting them. q^(n)/N! number of particle partition function (N! to correct for over counting)
Translational Cv, and E in the Classical Limit
3D, ie 3 degrees of freedom
Cv= 3/2nR
E = 3/2nRT
Classical limit
Thermal Energies kT >>>>> Quantum Energy level spacing Θ
Vibrational Cv and E in the Classical Limit
2 Degrees of Freedom
Cv = nR
E = nRT
Black Body Radiation
Material composed of many harmonic oscillators each emititng light at wavelength λ
Described best by Plank!
UV Catastrophe
Rayleigh-Jeans Law that when λ→0, Intensity.Energy →infinity, Plank’s Law Removed this by producing a curve that matched the experiment exactly
Rotational Cv and E for linear (non-linear)
Linear = Degrees of Freedom, Non-Linear = 3
Cv= nR (3/2nR)
E=nRT (3/2nRT)
Paramagnetism
noninteracting unparied electron system, in the absence of an an electric field there is no magnetic field. When placed in a magnetic field it reaches the state of ferromagnetism
Magnetic susceptibility
Large χ: large magnet
Positive χ: Paramagnetic
Negative χ: Diamagnetic
Permanent Magnets
Dipole Interactions and Exchange Interactions – Depends on the material
Dipole Interaction for PM
favor Head to tail arrangement – affect structures
Exchange Interactions for PM
favor exchanging electrons with parallel spins or anti parallel – driving force for magnetism
Ferromagnetism
exchange interactions favor parallel spins, as temperature increases, it acts as a paramagnet
Mean Field
2 Contributions to the total magnetic field, the external field B and the internal field. The internal field feeds back and creates a mean field
Currie Temperature
The temperature for which a ferromagnetic material is no longer magnetic
Two-Dimensional Ising model
Spins affect the neighbouring spins only, in a square lattice arrangement. This equation is more accurate than the mean field description because it has a steeper magnetic relationship with the Curie temperature. Predicts a phase transition
Anti-ferromagnetism
antiparallel spin alignment, B=0 →M=0
B>0 and T→0 This never adopts ferromagnetic ordering

Temperatures above Tc for these allow it to act as paramagnetic

GMR
Giant Magnetoresistance
Ferromagnetic/Antiferromagnetic/Ferromagnetic Material

If ferromagnetic ordering in the layers are the same direction you have less resistance than when you have the layers facing opposite directions. This is because the parallel spins will ignore the passing flow, increasing conductivity and the antiparallel will scatter the oposite spins, lowering conductivity.

Chemical Potential
μ, Partial Molar Gibbs free Energy
Standard State Pressure
1 bar
Molality
mol/kg
Molarity
mol/L
Activity coefficients
The correction for non-ideal systems using the equation for ideality. Used to describe the behaviour of real systems.
Henry’s Law
Used for solutes, P(i)vap=xi(solute)k(i)
Raoult’s Law
Used for solvents.
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