山东大学：《物理化学》课程教学资源（讲义资料）9.3 Rate equation of simple order reaction-for students

89.3 The rate equation of reaction with simple order

§9.3 The rate equation of reaction with simple order

Teaching obiectives Acknowledge 1. Discriminate: reactions with/without definite order Reaction with simple order 2. Recite the fundamentals about the firs-/second-/third-/zeroth-order reactions differential and integration form of rate law half-life linear relation 3. Explain the way to determine reaction order. Integration method; differential method, partial order method and isolation method ability: 1. Make calculation and prediction based on rate law 2. Determine reaction order quality Be ware of the possible trap for making error judgement about the order of the reaction

Teaching objectives Acknowledge： 1. Discriminate: reactions with/without definite order. Reaction with simple order. 2. Recite the fundamentals about the firs-/second-/third-/zeroth-order reactions; differential and integration form of rate law; half-life, linear relation. 3. Explain the way to determine reaction order. Integration method; differential method, partial order method and isolation method Ability： 1. Make calculation and prediction based on rate law. 2. Determine reaction order. quality： Be ware of the possible trap for making error judgement about the order of the reaction

89.3 The rate equation of reaction with simple order Reactions with the same reaction order are usually of same kinetic characteristics therefore reactions are usually classified on the basis of reaction order Elementary reaction? verall reaction?

Reactions with the same reaction order are usually of same kinetic characteristics, therefore, reactions are usually classified on the basis of reaction order. Elementary reaction? Overall reaction? §9.3 The rate equation of reaction with simple order

89.3 The rate equation of reaction with simple order 9.3.1 Reaction with simple order The reaction whose rate only depends on H+I=2HI k[H2][2y the concentration of reactants. and both H,+C1=2 HCI r=K[H21[C12 ].5 the partial order and the reaction order is zero or plus integer is reaction with simple [H2]B2 H2+ Br2=2 HBr r=k order 1+k, HBr [Br2] Reaction with definite order Overall Reaction with reactions simple order Reaction without definite order

1 1 2 2 H r k = [H ] [I ] 2 + I2 = 2 HI H2 + Cl2 = 2 HCl 1 0.5 2 2 r k = [H ] [Cl ] H2 + Br2 = 2 HBr 0.5 2 2 2 [H ][Br ] [HBr] 1 ' [Br ] r k k = + Overall reactions Reaction with definite order Reaction without definite order Reaction with simple order §9.3 The rate equation of reaction with simple order 9.3.1 Reaction with simple order The reaction whose rate only depends on the concentration of reactants, and both the partial order and the reaction order is zero or plus integer is reaction with simple order

89.3 The rate equation of reaction with simple order 9.3.2 First-order reaction Example: 1)Decay of isotopes 8Ra>86Rn+2He 2)Decomposition N2O5=N2O4+O2 3)Isomerization

Example: 1) Decay of isotopes 2) Decomposition 226 226 4 88 86 2 Ra Rn He → + 2 5 2 4 2 1 N O N O O 2 = + 3) Isomerization 9.3.2 First-order reaction §9.3 The rate equation of reaction with simple order

89.3 The rate equation of reaction with simple order 9.3.2 First-order reaction Which can be integrated directhy Reaction:A→>P at t=0 Inc=Inco -k, att=t Differential rate equation In -=k,t k C dt can be rearranged into: C=Co exp(k,t) k dt

9.3.2 First-order reaction Reaction: A −→ P at t = 0 c0 at t = t c Differential rate equation: 1 dc k c dt − = can be rearranged into: 1 dc k dt c − = Which can be integrated directly 0 1 ln c k t c = 0 1 c c k t = − exp( ) §9.3 The rate equation of reaction with simple order 0 1 ln ln c c k t = −

89.3 The rate equation of reaction with simple order 9.3.2 First-order reaction c-t curve of first EEE 012 Inc x t curve of the first order reaction 08 order reaction 旨 0.6 04 02 00 10002000300040005000 1000 3000 4000 5000 t/s Inc=Inco -k,t C=Co exp(k, t)

lnc ~ t curve of the first￾order reaction 0 1 ln ln c c k t = − 9.3.2 First-order reaction §9.3 The rate equation of reaction with simple order 0 1 c c k t = − exp( ) c~t curve of first￾order reaction

89.3 The rate equation of reaction with simple order 9.3.2 First-order reaction Characteristics of the first-order reaction n k 1)Unit of k is s. Half-life 2) Inc is in linear proportion to t C 3)can not complete n 4)Half-life does not depend on Co 2k1

0 2 c c = Half-life 1 2 1 ln 2 t k = 9.3.2 First-order reaction §9.3 The rate equation of reaction with simple order Characteristics of the first-order reaction 1) Unit of k is s-1 2) lnc is in linear proportion to t 3) can not complete 4) Half-life does not depend on c0 0 1 ln c k t c =

89.3 The rate equation of reaction with simple order 9.3.2 First-order reaction Principle for dating: the age of life: 3.8-4.0 billion Archaeology radiatio Ocean 6 thousand-birth of christ 40 thousand salinit million-geology deposit 0. 22 billion-geology radiation >4.0 billion-geology radiation Earth: 4.6 billion -radiation -238U Cosmos: 13.82 billion-big bang

Principle for dating: the age of life: 3.8-4.0 billion Archaeology + radiation Ocean: 6 thousand – birth of Christ 40 thousand – salinity million – geology + deposit 0.22 billion – geology + radiation > 4.0 billion – geology + radiation Earth: 4.6 billion – radiation – 238U Cosmos: 13.82 billion – big bang 9.3.2 First-order reaction §9.3 The rate equation of reaction with simple order

89.3 The rate equation of reaction with simple order 9.3.2 First-order reaction The half-life of the first-order decay of radioactive 14C is about 5720 years. The natural abundance of C isotope is 1.1 x 10-13 mol% in living matter Radiochemical analysis of an object obtained in an archeological excavation shows that the 14C isotope content is 0.89x 10-14 mo1% Willard F. Libby 1960 Noble prize USA 1908/12/17~1980/09/08 14C for age determinations(radiocarbon dating

Willard F. Libby 1960 Noble Prize USA 1908/12/17 ~1980/09/08 14C for age determinations (radiocarbon dating) The half-life of the first-order decay of radioactive 14C is about 5720 years. The natural abundance of 14C isotope is 1.1  10-13 mol% in living matter. Radiochemical analysis of an object obtained in an archeological excavation shows that the 14C isotope content is 0.89  10-14 mol%. 9.3.2 First-order reaction §9.3 The rate equation of reaction with simple order