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EQUILIBRIUM AND KINETICS

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Mechanical Equilibrium of a Rectangular Block Centre Of Gravity Potential Energy = f(height of CG) Metastable state Unstable Stable Configuration Lowest CG of all possible states

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Kind of equilibrium can be understood by making small perturbations Global minimum = STABLE STATE Local minimum = METASTABLE STATE Maximum = UNSTABLE STATE

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Intensive Properties Independent of the size of the system e.g. P, T Extensive Properties Dependent on the quantity of material e.g. V, E, H, S, G

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Some thermodynamic terms Internal Energy = E = KE + PE Interactions in the solid (bonds) Vibration / Translation / Rotation

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Enthalpy = H = E + PV Measure of the heat content of the system At constant pressure the heat absorbed or evolved is given by H Transformation / reaction will lead to change of enthalpy of system Work done by the system For condensed phases PV << E H ~ E H 0 represents energy released when atoms are brought together from the gaseous state to form a solid at zero Kelvin Gaseous state is considered as the reference state with no interactions

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Gibbs Free Energy = G = H TS Absolute Temperature Entropy For a transformation that occurs at constant temperature and pressure the relative stability of the system is determined by its GIBBS FREE ENERGY Entropy is a measure of the randomness of a solid G = H T S Even endothermic reactions are allowed if offset by T S

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Entropy ThermalConfigurational + other H,E –ve at zero K But thermal S is zero S thermal increases on melting at constant temperature Zero or +ve Boltzmann constant No. of different configurations of equal PE Actually these are two interpretations of Entropy Macroscopic Microscopic

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Configurational Entropy change due to mixing A and B (pure elements) S = S mixed state S pure elements (A & B) Zero Stirling’s approximation Ln(r!)=r ln(r) r

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Possible configurations of in an 1D system of 4 sites and two different species Due to the statistical nature of the configurational entropy the equation is valid for a large number of species

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Helmholtz Free Energy = A = E TS For a transformation that occurs at constant temperature and volume the relative stability of the system is determined by its HELMHOLTZ FREE ENERGY

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KINETICS

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Order wrt A ConcentrationsRate Constant Frequency factor Activation Energy Affected by catalyst T in Kelvin A is a term which includes factors like the frequency of collisions and their orientation. It varies slightly with temperature, although not much. It is often taken as constant across small temperature ranges. Arrhenius equation

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ln (Rate) → Fraction of species having energy higher than Q (statistical result) 0 K

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A + BC AB + C A + BC (ABC)* AB + C Activated complex Reactants Products

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Configuration Energy A + BC (ABC)* AB + C ΔHΔH Activated complex Preferable to use G

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The average thermal energy is insufficient to surmount the activation barrier (~ 1eV) The average thermal energy of any mode reaches 1eV at ~ 12000 K But reactions occur at much lower temperatures Fraction of species with energies above the activation barrier make it possible Lost species by reaction are made up by making up the distribution Rate fraction of species with sufficient energy Rate vibrational frequency (determines the final step) Rate n

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Chapter 11-2: How does temperature affect enthalpy and entropy?

Chapter 11-2: How does temperature affect enthalpy and entropy?

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