Lecture 9a - Leonor Michaelis (1875-1949) Maude Menten...

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1 Frederick Lindemann (1886-1957) Svante August Arrhenius (1859-1927) 1903 Chemistry Nobel Leonor Michaelis (1875-1949) Maude Menten (1879-1960) The reaction rate and rate laws
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2 [] 22 2 The rate of a reaction is given by: Rate () Definition: Examples: Rate ( 11 (1) (2 )( ) 2 ( ) 1 ) 1 R N O gC O g N O O g dd d d NO CO NO CO dt dt dt dt NO g F g NO F cC dD dC dD aA bB dA dB a g dt b dt cd t dd t =− = = = +→+ = = +→ + + U 2 1 ate 2 d NO F NO F dt dt dt == = Comments: (1) No intermediate species (unless their concentration is constant). (2) The definition depends on the way of writing the chemical reaction [ ] [ ] [ ] 21 00 lim lim tt NO NO dNO NO dt t t t ∆→ ∆−
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3 Rate laws The rate law provides a relationship between the reaction rate and the concen Def tra inition: tions. [] [] [] [ ] [ ] [ ] 25 2 2 26 3 2 1 2 11 1 6 22 2 2 1/ 2 2 2 1 ( 1 ) () 2 () (); 2 (2) ( ) 2 ( ) ; 1 (3) ( ) ( ) 2 ( ) ; 2 1 (4) ( ) ( ) 2 ( ) ; 2 Many (but not all!) Examples: Observation: re d NO g O g NO dt d CH g CH dt d Hg Ig H Ig H I H I dt d H g Br g HBr g HBr H B k dt k r k k →+ = →− = +→ = = [][] and are the "reaction orders" wit actions have rate laws of the form: h respect to and , respective is th ly (can be zero, fractional or negative). e "reaction rate con is t stant ; " t ra e . nm k AB k = + he "overall reaction order". 1. How to make predictions based on the rate law? 2. What is the relationship between the rate law and the reaction mechanism? 3. What happens on a molecular scale when a chemical reaction takes place? The basic questions of kinetics and chemical dynamics
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4 How to use rate laws in order to make predictions ??? [] 32 2 33 -1 1 () (0) Example: Decomposition of amonia on a tungsten surface 13 at 100% coverrage (NH N + H ). 22 ;. Units o Zero order reacti f k: (separation of variable ons: s). ct c dd NH c c NH dt dt mol L kk k s dc dt dc −= = = ⇒= 0 ( ) (0) (integration). (0 ) ( ) 0 at (0) / (which implies that all the amonia has decom Note th pose . at d) t dt c t c kt ct c t t c k k k =− =≥
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5 [][] [] [][ ] 25 2 2 1 () (0) 0 1 () 2 ; 2 ; ; Units of k: . (separation of variables). ln ( ) ln (0) ln ( ) (0) ( First order reactions The ) : (0) k ct t c t d NO g O g NO dt d cccN O s dt dc dt c dc dt c t c kt c ct c t k k k k k c e →+ = ⇒− = = ⇒= = = ∫∫ 1/2 1/2 Definition: (0) / 2 ln 2 ln ln 1/ 2 ln (2) (0) is independent of the initial concentration (unique for 1-st order reactions reaction half-time (t ) ): . t t tt cc c c k t k = ⎡⎤ = = = ⎢⎥ ⎣⎦ 2 22 2 2 2- 1 1 2 2 2 0 1d (); 2d t d ; ; Units of k: . dt (separation of variables) Second order reactions with . 11 ( one reactan )( 0 ) 1 ( t: t c k k k NO g NO g O g NO NO cN O c c L m o l s dc dt c dc dt kt k tc c = = ⎛⎞ −= ⎜⎟ ⎝⎠ 1/2 1( ) 1 0 ) ( 0 ) 1 ( 0 ) Definition: (0) / 2 1 1 1 ( ) (0) (0)/ 2 (0) (0) Th 1 (0) depends on the initial e reaction half concentration. -time (t ) : kt c c k t k c c t t t t t c kc =+ ⇔= + = −== 1 2 N Og N Slope=k
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6 [] {}[] {} 24 48 1 2 2( ) ( ) 1 ln ( ) ln (0) Ex 2 2 11 1 2 ) ( 0 ) ample CF g d CF kCF CF t k t dt d k t dt C F t C F −= = = + [] [] () 00 0 dd ; dt dt This differential equation can be solved subject to the initial condi Second order reactions wit tions (0 h two different reactants ) ; ( 0) and the solution is: 1 ln : AB P A B AB B B At Bt k A +→ = = == 0 0 ;if 1 t t A k
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This note was uploaded on 06/13/2009 for the course CHEM 260 taught by Professor Staff during the Spring '08 term at University of Michigan.

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Lecture 9a - Leonor Michaelis (1875-1949) Maude Menten...

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