Dynamics and Control PDF

dynamics &  Lecture 1 Innotes en equations impractice...

dynamics &  Lecture 1 Innotes en equations impractice 8/07 Chemicals the A-> B · can change structure but keep same formula ; ATP A C+ D hydrolysis +B > · : - Myoglobin > oxymyoglobin : A +z > ( - · - · unfolded - > folded protein : A + B · Rate is how fast concentrations change over time produced aA - + bB + c + dD reaction rate : - - consumed Stoichiometric Loeff. Reactants of · need to collide to react ; conc. needs to be sufficiently high so chances reaction are also high · In a mixture of molecules A and B, the freg · w/ which A-B collisions occur is proportional to the concs. [A] and [B] · Elementary reactions are single-step reactions w/ one transition state & no intermediates Transition State : Short-lived, unstable, single bond vibration - - Intermediate : product for one elem reaction, reactant for the next in a complex reaction Molecularity # of mols in the · taking part reaction : - bimolecular - unimolecular is one , bimolecular 2 , etc. /reactants) - H z(y) + [2(g) > - 2HI(g) < since alr balanced, this is elem. ~ still bimolecular Chemical equilibrium of change reactions& products > no let in IHI(g) Ha(g) E2y · : concs. - + = k k = equil const H z(q) In()IHI - + Fea · Law of mass action : aA + bB5cC + AD > - K = BJD 10-3) 31KI10") mostly K (k significant of both intermediate (10 mostly products large · small amt. - < = reactants = = , , (((03) ? ENH37 N2(y) + 3 Hz(y)= 2NHj(g) Kea = 20(q) + E02()202(9) Kea = " 2 (02(g) = 2(0(g) + 02(g) Rea = [Cocs2 · The reaction quotient can be used to determine dir, for when - reactions equilibrium :o If QCK , reaction goes right if Q3K , reaction left , if Q K system is at equil. goes - = , , If Q is undef , are consumed , and reaction irreversible reactants completely is - P - k= smaller for > = Kszic , for higher P = Kaso,  any chemical species involved A : in read. react S VA = Stoichiometric coeff (t)for prod -) for. ,. HA - A * moles of beginning = Na species A at · Extent of reaction : progress of a chemical reaction = VA E NA = moles of species A when by reached mz noNz nNH2-n0Hz Koky-HONHy - = 213HlgLNITo E - N = - I - 3 2 nc + n°c my + no - + E = - 2 - 6 3 I 0. 003 - 0. 004 p a. 5 = - 2 = 0 000S M. 006 nB - 0. b = 6 0 000SM - -.. 0 003. = NB - 0 006. -+ NB = 0 003M. Lecture 2 inotes expictures eequations in practice /10 TS 2 elem-rxus TS2 ER1-17 U > I- ERI endgt Er ERz ERI-ERI Treaction Mechanism I run progress · Reaction mechanism needs to be experimentally determined rans zelem I & (y) - 02(g) + &O : reaction intermediate &+ Oz(g) - 202(g) 203 (g) > 302(g) overall rxn mechanism -. Carson in this u/ most complex, it ↓ start Balancing chemical equations : (Hig(e) + 0z(y) > - (02(g) + H20(9) 4) Hio(e) + Oz(y) > - 7(02(g) + H20(g) 2) Hib(e) + 02(g) > T(02(g) + 8Hz0(g) - G Hio(e) (g) > z(02(g) - balanced 1102 + 8H2o(g) - + a. 2Hg(e) +o - Hg20c(s) = balanced. b 2202(g) + 2 Hz0(y) = not balanced c Mg(NOs)y(s) + 2(i (s) > - Mg(s) + 2 LiNOz(s) = balanced a - Nz(g) + 02(q) + NO < - 2NO < (g). b Pb(NOz)y(a) + Fells (aq) > - Fe(Noshy(aq) + PbC12(s) 3 Ph (NOs) = (aq) + Felly (aq) > - 2 Fe(NOs(z(aa) + Pb(lz (ag] 3 Pb (Noj zlag) + Feels (ag] > - IFC(NOj]y(a) + 3Pb(12 (aq) 3 Pb (NOs) < (aq) + 2 Fe(ly (ag) > - IFe(NO3) >(aq) + 3Pb(12 (aq). C (H , y(e) + 0z(g) (oz(g) + H- o(g) 2gH , y() + 02(g) - (02(g) + 2H20(g) (6H , y(e) + 02(g) > - 6102(g) + THz0(g) 2 (6 H , y(e) + 190c(g) + 12102(9) + 14420(g) · stoichiometric factor : N2(g) + 3 H2(g) > - INHy(g) - molar ratio of Nitz to Hz(SF) : 2Al + 312 > - 2Allz , 0. 429 mol Al 0. 429 mul = Mr : mol > + 2 x = 1. 287 > - X = 0 643 mol. In 32a(OH) z + 2HyPOn > - (dz(POy)2 + 6H20 - X = MR : 2 1- 36 > - X = 2 04.. mol C3Hg + So 2 - 3202 + YH20 X -202 = 1 Hg smal > - X = 2 25. mollo2 · 6. 62x1023 = 1. 35x10""Co2 molecules Mg(12 (aq) + 2 NaOH(09) > - Mg(OH) z(s) + 2 NacI(aq) - 9 2 NaOH = 79 8 mol. Mg(OH) z = 58 3. mol Imol log Mg10H)2 gimolMgH 2744 mol Mg(OH) = 0. NaOH x 2 mol - = 2744 mol > X S488mol NaOH (mol Mg(OH)2 0 gNaOH -. = 0. 22 · Law of Conservation of mass - mass cannot be created or destroyed gen input output mass of the reactants = mass of the products accumemp - - within consumed within sys. > prod sys M - · General balance equation : input +gen-output-consumption = accumulation - - - What enters what leaves built up within through system through system sys boundaries boundaries accum = input-output > - if balanced quantity is total mass , gene cons. = 0 · If input& output are diff , could mean : some other waste product - - consumption/accumulation - leak - equipment failure 50 , 000 + 22 , 000 75 , 000 19 , 000 22 , 000 = population decreasing - - - = 450k9 B/h xxg + my & steady state , accumulation = o 0 gen = sooky consump 0 = B/u input-output > - 500 Benzene kgT/m balance : 500 = 450 + X - y So kg B/h = - yky B/. 475kg Tlu Tolvene balance : 500eYTs + X > X = IS The by - Reaction rates & chemical key to understanding physical changes - be things that might want to known : - · what are steps involved · error rate · how fast is each step A P Hypothetical : B > elem + - ·. rxn v = rate · Rate Law : diff - eg. that describes ROC of cone Wr. time : V = KCAJ"B3 v = E rate of formation of product over time · Rate const.: K , characteristic of the rxn. being studied , depends on temp D not concs, veratel, always M/s , rate laws are experimentally determined · The dependence of the rate law on the cores of reactants defines the order of the reaction - Sum of exponents of the concentrations in a rate law is known as the reaction order [A] - first-order : t = - k[A] - second-order : A = - 2 + 1 = 3 B : I A) - third-order -k[A] [B] · order of reaction is the sum of exponents to which the conc terms of the reactants are raised  - order can be associated w/ eleme complex - theoretical value of mols Molecularity : # taking part in reaction · - - Always whole # for only elem rxns -. empirical - coeff > 2 - cona · Beer-Lambert's Law : A =Eed - - abs Pet 0 2. = (0400761( - c = S = 0. 00008333M > - 2 = 0. 0209M" am + 10. 201 = EC10cmi(km)) A = 0. 0209(SM)(km) > - A = 0. 1095 (10) (Scm((0 0209). = 1 045. Units · of rate coust. depend on order of rxn. - Rate is always on Always has+ value - · Reactant cons - decrease while product cones - increase CA + bB-cC + &D rxn-rate = - - Rate coust. K for 1st - order rxn. has units of s · Ary rate : occurs over a time period found by slope of line by joining 2 points any. , found of · Instantaneous rate : rate at a particular instant during rxn. , by slope a line tangent to the a curve a particular point · Initial rate : inst. rate & time t = 0. Tangent to curre + =. 0 Gives best Kinetic data Lectures 01/14 notes mequations In drawings mexamples · Rate of formation of product for AcKfCA]" = 1-> - rate of consumption of reactant - K(A)" = - Ky0 More · knowns for consumption @dCAJ = - Kdt -k SaCAl -kSdt [A]+-[A]o - 0) slope = & = > - = - k (t ③ CASt - = opeCAZ - T integratedrate kn for o-order uxni time  · Half-life of a zero-order reaction & Define conc of CAJ@ +2 CAJEyc = ECAJo CAM o a f · cone of a reactant decreases exponentially ws time for a 1st-order run. A -P d [P] : - Rate of formation of product : #t = k+ [A]' -K + (A)' > - > - Reat- 1 kSat S As = -Sat integrated rate law for 1st - order rxn. Cayl ? 10 - integrate : In = -x + > - InCAJe - InCASo = - R (t - 0) > - InCAle-InCAbo = -kt ↓ shope = -k Plotting 1st-order reactions : In [A]o = -kt + In CATo Increactant) vs. time E = k = 0 316 time. - == I k 1 -.. = k= 2 16. (n(A)t = - kt + (n(A)o & InCAlz Ke +In (Abo e - C --- [A]t = [A]oe - it time Mun aa n · umit of rate constant, K , depend on rate law and are always order M 5 · Half-lives of first-order rxns- & define (A) e + 12 = [CA]o ② In CAJo-In[A]o = - Kt ③ quotient rule :In x-iny = In - o = - k t[A] o =tin half-life of ⑦ subst. (A2 tyn : In CAJO = - 1E-InE = key2 apply reciprocal rule (In = -1nx) - > ist-order rus. · Zero and first-order rxns · In medicine : elimination kinetics · Pharmacokinetics : used to determine the rate at which a drug is removed from the body · Most drugs follow ist-order elimination Kinetics - Elimination rate const : Ke = In (2)/tisa - Once elim. Const. is known , can solve for drug in plasma at specific time t : [drug] = [druger follow zerth-order (rare alcohol) Some drugs · ,  Pharmacokinetics case study ↓ we want linearity , Ist-order What is the order of this process ? Plot tvs. In (c) Half-life of this drug in bloodstream ? Find Kr : InCA] = InCAJo-nowthis slode 01s min - t 1 = = 91 min Practice 1 InCAJt-InCAJo = -It In 10 036). - In 10 22). = - k(. 22x10") - 2 88. + 1 5. = - 1. 22x10"k k = 0 00011. 5'. 2 tyn = 135s Ato = 1. 28x10 M t 1/2 = I 138 e = > - K = 0 005s :. In [0 04 x10-3] In (1 28x103 MJ 00st > z 6935 - - = =.. 0. unimolecular reactions often · are 1st-order : ex, radioactive decay Practice 1 = 0. 138d- CAJo = 0 SM. [AJE = 0. OSM + = In 10. 01) - In (0 5). = - 0. 138t > - t = 16 7. days Lecture 4 mequations chexamples 01/17 muotes endrawings · Bimolecular reactions are often second-order - Example : nucleophilic substitution (electron donor ) · Rxn. order = theoretical , molecularity = empirical O bichol. 2A - P - rate O act unimol.  · Reactants decay more slowly for a 2nd-order run. than 1st-order , but details depend on type of rxn. - 2A-pGrate of consumption : - KCAS law for int-rate rxn ② integrate assuming (A) CAJoet. 0 Hand-order = = IA ↓ - The T ↓ & = - p(a + > - ( a(A) = xSat - + = - xt + (a) - Cas = x - units of K : Ms - If[A] is doubled , quadruples ↓ form Plot of linear To graph turn into y mxth time + vs [A] is - =.. , · Half-life for a 2nd-order rxn : DCA]tyz = ICA]o Inz-Cazo ↓ ② = + & substrato - To = Ke >- - = + - > 50 = Kityn + ty = To · For A + B-> P rate law : r= K[A][B] , · Pseudo Ist-order rxns. (CA] = (BJ) : A B - P let's that [ASox (BJo that [AJe [A]o - + approx = can say.