Physical Chemistry Terminology

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Microstate
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the instantaneous positon,momentum and internal state of all the particles in a system or the wave function for the entire system
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Ensemble
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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
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Microcanonical Ensemble
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Ω(NVE) Ensemble, fixed # of particles, volume and energy
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Canonical Ensemble
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Q(NVT) Ensemble, fixed # of particles, volume and Temperature
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Isothermal-Isobaric Ensemble
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∆(NPT) Ensemble, fixed # of particles, pressure and temperature
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Grand Cononical
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Ξ(μ,V,T) Ensemble, fixed chemical potential, volume and temperature
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Time Average
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measure a property of the system as a function of time Γbar = lim 1/T int(0,T) Γ(t)
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Ensemble Average
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Sum of all Microstates weighted by the probability that each microstate will be visited.
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Microstate Postulate 1
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Ergodic Hypothesis: Given enough time each micro state will be visited
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Microstate Postulate 2
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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
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Boltzmann Distribution
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The Probability of finding a system in the ith microstate
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1 Microstate
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Zero Entropy
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Adding Heat or Work does what to the microstates
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Heat: Changes the probability distribution over energy levels, Work: Changes the amount of energy levels with the same distribution.
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Distinguishable
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Particle which can tell the difference when counting them for example, q^(n) number of particle partition funtions
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Indistinguishable
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Particle which can not tell the difference when counting them. q^(n)/N! number of particle partition function (N! to correct for over counting)
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Translational Cv, and E in the Classical Limit
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3D, ie 3 degrees of freedom Cv= 3/2nR E = 3/2nRT
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Classical limit
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Thermal Energies kT >>>>> Quantum Energy level spacing Θ
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Vibrational Cv and E in the Classical Limit
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2 Degrees of Freedom Cv = nR E = nRT
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Black Body Radiation
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Material composed of many harmonic oscillators each emititng light at wavelength λ Described best by Plank!
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UV Catastrophe
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Rayleigh-Jeans Law that when λ→0, Intensity.Energy →infinity, Plank’s Law Removed this by producing a curve that matched the experiment exactly
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Rotational Cv and E for linear (non-linear)
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Linear = Degrees of Freedom, Non-Linear = 3 Cv= nR (3/2nR) E=nRT (3/2nRT)
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Paramagnetism
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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
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Magnetic susceptibility
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Large χ: large magnet Positive χ: Paramagnetic Negative χ: Diamagnetic
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Permanent Magnets
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Dipole Interactions and Exchange Interactions – Depends on the material
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Dipole Interaction for PM
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favor Head to tail arrangement – affect structures
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Exchange Interactions for PM
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favor exchanging electrons with parallel spins or anti parallel – driving force for magnetism
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Ferromagnetism
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exchange interactions favor parallel spins, as temperature increases, it acts as a paramagnet
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Mean Field
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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
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Currie Temperature
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The temperature for which a ferromagnetic material is no longer magnetic
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Two-Dimensional Ising model
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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
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Anti-ferromagnetism
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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
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GMR
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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.
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Chemical Potential
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μ, Partial Molar Gibbs free Energy
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Standard State Pressure
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1 bar
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Molality
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mol/kg
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Molarity
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mol/L
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Activity coefficients
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The correction for non-ideal systems using the equation for ideality. Used to describe the behaviour of real systems.
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Henry’s Law
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Used for solutes, P(i)vap=xi(solute)k(i)
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Raoult’s Law
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Used for solvents.

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