Lecture Note
University
California State UniversityCourse
CHEM 100 | Principles of ChemistryPages
10
Academic year
2023
ronidalbo298 Roniwahyudi
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No.: Date Spontaneous Change Entropy t Gibbs energy Spontaneous Process - occurs naturally without any outside help non ( spontaneous Process - will not occur with an 1 external Source of energy A process which Is Spontaneous in one di rection is non- - SPontaneous in the other direction. SPortuneous Processes proc eg to equilibrium An extend Example SPontaneous ; aMa(s) + C12 C91 2 Non- 1 Spontaneous ; amacl (s) -) Establishing Criteria for Sponta Meaus charge H2°ce) H2°ccg) (25c,11 Nociss, Na+ (aq) tcl caap Arti°=3.9 kj/mol (25°c 1bar) N2°5(3) 2NO2 cg, + 1/2 O2 (97 ArH 110KS/MOLL 254.11 (KKY) Dore to dream, Dare to achieve CS Dipindai dengan CamScanner
No.: Date: A molecule has 3N types OF random motion called modes j N = # otoms ( 3 Trans lational modes ? linear molecules 2 rotational moves; 3N-5 Non- Linear 3 rotational modes; 3N - 6 Example ; H2O mole Cules Translational ; 411 atorno in one directions together (can move in X, Y,2 directions ) H H Rotational; Also 2 H H H H axis Vibrational ; 1,9A H H H H H H +symetric t symetric Stretch Bending Motion Streteh Solid State Moleceules can only vibrate about their equilibilan Position KIKY Dare to dream, Dare to achieve
No.: Date: The liquid State Molecules can move around each other (translation) d have limited amount OF Totational d Vibrational move ment. The gaseous State molecules have virtually unrestricted translational rotational d vibrational movement Statistical Entropy - An interpretation of entropy at the molecular level - A measure of the degree to which thermal energy is dispers ad in availal energy \ levels - assoc ated with random molecular Matton Entlopy is a State function ; changes is entropy are Pathway Indepen Entropy d Available Quantized Energy levels moleculla Populate a 9 realor # of energylevels Lenorgy is more Spread out) when the energy gap AE between adjacent energy levels is small This results ing reater entropy For the sample of molecut AE fn instational = Gx10-19 s/mol Approximal values AE rotational = G S/mol at any given i notant AE vibrational = 6 000 s/mol in time A E Vibrational \ 000 A Erotational DE translational (KKY) You can If you think you can
No.: Date: Energy is mainly dispersed into translational rotational energy levels where the energy gaps are extremely small. Most molecules at 250care in the lowest energy Vibrational level OF each OF its Vibrational modes. Fairly high t temperatures are needed to give molecules enough energy to give Populate higher energy vibrational energylevels. Single Particle Microstate Any Particular energy State for a Single niolecule that describes that molecule at a given instant in time. It is a Combination OF its quantized translational, rotational t Vibrational energy lev els. N- Particle Microstate Any qu antized State of a whole system OF molecutes. consists OF the collection of the single Particle microstutes ofallits malecules Statistical EntPopy + the #OF N particle Nicrostates 1. At only given instant in time, the total energy OF the system is disperse throughout a single M-Particle microstate 2. in the next instant in time ,the total energy oFthe System is dispersedt- throughout adifferent N-Particle microstate of equal energy 3. Each accessible N-particle miscrostate is equally Possible For the system. KKY You can if you think you can
No.: Date: under a given set OF conditions (P,T) the number OR acce ssible N-Particle microstates is the number OF ways its thermal energy can betige ersed a Moung the tr anslational, rotational d vibrational energy levels of all its moleculed Ludwig Boltzmonn's equation for calculating Entropy S=K enw K = Boltzman's Constant W = # of accessible N-Particle Microstates OF equal energy (given T,P) K= B NA k = 0.314 JK mg = 1.3806 X1023 J/K G.022 X1023 ma Entrapy change ; As = S (stated) - S(Statel) IF As has a Positive value, the system has Changed From a State OF lower Entropy state 1, which has a greater # OF accessible N. - Particle microstates 4where thermal energy is more Spread out. . obvious increases in entropy: Pruse Solid liquid gas solution Formation I onic solid solution of ions Chemical changes Solid / liquid gases less moles gas more moles OF gas KKY Dare to dream, Dare to achieve
No.: Date: Evaluating W For Simple Systems consider a system with 4 Particles d3 energy \ levels. 3 Partisles occupy the lowest level. I Particle O (coples the middle level. Q. : What is the number OF equal energy 4 Particle arrangement ? Level #: 3. 2. 1 2 3 R 1. 23 4 D 3 4 1 2 4 I 0 3 A : 4 possible equal energy arrangements w=4 W = N! M = total H Particles nj = H Particles which OCCUPYA givenlevel II nil 11 = Product of Fortorials For all a coupled levels m = occupied levels w = 4! = 4.3.2.1 = 9 3!1! 3.2.1 .1 S tatistical Entropy ITemPacture as T increases, molecule as have more thermal energy dcan Populate higher energy levels, T the N - Particle microstates. Energy SPread out d entropy increases KKY Dare to dream, Dare to achieve
No.: Date: consider a system with sparticles a 3 energy levels at a low T1 d high T2 - calculate WForeach . level It 3 2 I Law TI High T2 N (LOWT) = S! 5 4!1! 3 thight T) = 5! = 30 2.121.1, Entropy d the concept of Disorder / order Entropy increases as a system goes From an ordered, motion restricted State to a disordered less motion restricted State. The concept of disorder /order can be used to Predict whether a process res ults in an increase of decrease in intropy. However ; entropy is not disorder. O bs ervation: A gas will Sportaneously expand form a Small volume V1 to a larg of volume V2 KKY You can if you think you can
No.: Date: Q : can we show why the expansion occurs SP ontaneoly using statistical entropy ? consider the ex Pansion OF an ideal gas From a small Volume V1 fa a large volume V2: This occurs at constant temperature ;eg: 150 thermally (AT=0) because there are no attrative or repussive Forus between the particles OF anideal gas. The Particles of an ideal gas have only transl ational kinetic energy. U (ideal gas ) = 3/2RT u= U2 - V1 = 3/2RT2 - 3/2 RT, U= 3/2 R (AT) =0 This means that the accessible microstates before I after expansion have the same energy. we assume that the container is a three dimensional (3D) box. A volume in crease results From an increase thelength OF the box dimensions (length, width d height? For simplicity, we use the energy levels of the particle inthe one dimensional (ID) but as an analogy For the energy levels OF a 3D (real) container. we must consider how Increasing the leyth OF the ID box at Pects the energy gap NE(n) between the energy levels. Equation For the allowed energy levels of the particles in a 10 Box: Ecns= n2h2 no particle 90 contum # OML h= Plants Constant m mass OF the Particle L : length OF the ID box KKY You can if you think you can
No.: Date: Determing the energy gap between the First two adj acent energy levels as a Function of the Length OF the box, L: AE = E2-E1 =2h2 - 12 h2 s.mc2 2 ml2 =4 (h2 ) - h2 = constant some Qmc Sm * The energy gap is Inversely Propational TO the Square of the length of the box Interferences : 1. An increase in the length OF the box decreases the energy gal between adjacent levels. 2. The energy levds crowd CLOST together. 3. we saj that the d ensity OF energy levels Incr eases. Result : The number OF equal energy accessible microstates increases d so does the entropy of the ideal gas. Using the analogy, CS we see that expansion OF an Heal gas IS spontaneous Since Teal gases closely behave like an ideal gas under Mast conditions 1 it explains why expansion of a real gas IS al sa Spontaneous KKY Dare to dream, Dore to achieve
No.: Date: A System with 6 particles d 3 energy levels which undeggoes an 1sot hermal volume increase. State 1. (small volume) Av=G State a Lange Volume) same energy Total wCStatel) = 6! - 20 energylevel 3131 urrangement w(State2) = G! = 40 212121 Statistical entropy Provides an ex Planation Forthe Spontaneous of Pansion of a gas infro a larger container volume as the HOF equal accessible energy microstates W incireasedue to the ex Pansion. Energy is more Spread out tentropy in creases Entropy Change (AS) As = SF - SL Thermo by namic Properties for the St stem donot have be directly Identified. . Always assume AS, All, Au, Acrefer to the System thermodynamic Properties Prom the surroundings must CS be directly indentified. since S is a State Function, As is Parkisway independent dengan Thermo definition of energy Change ; AS=glev grew= heat lost or gaided TA a reve risible I Prosess, where direction can be ChangeD by a system Property KIKY Dare to dream, Dare to achieve
Spontaneus Cange Entropy
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