## 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

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

Cv = nR

E = nRT

Black Body Radiation

Material composed of many harmonic oscillators each emititng light at wavelength λ

Described best by Plank!

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)

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

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

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

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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