Chem 402 Lecture 27: L27 3:31:17
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Department
University College - Chemistry
Course
University College - Chemistry Chem 402
Professor
Barnes Alexander
Semester
Spring

Description
31 March 2017 L27: 2 Order Rate Laws and Kinetic Parameters I. 2 Order Rate Laws A. From Chem 112 1. 2A οƒ  Products 1 𝑑 𝐴 a. Differential Rate Law: π‘Ÿπ‘Žπ‘‘π‘’ = βˆ’ = π‘˜ 𝐴 ]2 2 𝑑𝑑 β€’ Integrate:∫ [𝐴]𝑑 𝐴]= 2π‘˜ βˆ«π‘‘ 𝑑𝑑 [𝐴]0[𝐴] 0 1 1 b. Integrated Rate Law: [𝐴]= 𝐴 0 + 2π‘˜π‘‘ 1 c. Half life: 𝑑 = [ ] 2 2 𝐴 0 2. A + B οƒ  Products 𝑑 𝐴] 2 a. Differential Rate Law: βˆ’ 𝑑𝑑 = π‘˜ 𝐴 𝐡 = π‘˜ 𝐴 [ ] (if [A] = [B]) [𝐴]𝑑 𝐴] 𝑑 β€’ Integrate:∫[ ] 2 = βˆ’π‘˜ ∫ 𝑑𝑑 𝐴 0[𝐴] 0 b. Integrated Rate Law: 1 = 1 + π‘˜π‘‘ [𝐴] 𝐴 0 1 c. Half life: 𝑑2= [𝐴 0 d. Only works if [A] = [B] during reaction 3. Plot of 1/[A] vs. t for 2 Order reactions 1/[A] 1/[A]0 t a. Linear slope of k or 2k b. Y-intercept of 1/[A] 0 nd B. Deriving the 2 Order Rate Law 1. If [A] β‰  [B]: 𝑑 𝐴] a. – = π‘˜ 𝐴 [𝐡] [𝐴]𝑑 𝐴 ] 𝑑 b. ∫ = βˆ’π‘˜ ∫ 𝑑𝑑 = βˆ’π‘˜π‘‘ [𝐴0 𝐴 [𝐡] 0 𝑑 𝐴] β€’ Problem: 𝐴 [𝐡]οƒ  has 2 variables that change, but only one variable of integration β€’ Must change variable needed 2. Look at the stoichiometry a. [A] =[A] –0x β€’ Actual = initial – how much has gone (the progress of reaction) 𝑑 𝐴] β€’ = βˆ’1 or 𝑑 𝐴 = βˆ’π‘‘π‘₯ 𝑑π‘₯ b. [B] = [B] –0x 3. Re-write π‘₯ 𝑑π‘₯ a. ∫ = π‘˜π‘‘ 0 ( 𝐴0βˆ’π‘₯)( 𝐡 0π‘₯) β€’ Lose the negative because subbing in d[A] = -dx 4. Must split the integrand into partial fractions οƒ  method of partial fractions 1 𝐿 𝑀 a. ( 𝐴0βˆ’π‘₯)( 𝐡 0π‘₯) = ( 𝐴0βˆ’π‘₯) + ( 𝐡 0π‘₯) β€’ Must find L and M to make the RHS = LHS, x by denominator b. 1 = 𝐿 𝐡([ ] βˆ’ π‘₯ + 𝑀( 𝐴 [ ] βˆ’ π‘₯) 0 0 c. Gather and equate like powers of x: (set up equations LHS = RHS) β€’ X οƒ  1= 𝐡 𝐿 + 𝐴 𝑀 [ ] 1 0 0 β€’ X οƒ  0 = βˆ’πΏ βˆ’ 𝑀 d. Solve for L and M 1 1 β€’ 𝐿 = , 𝑀 = βˆ’πΏ = 𝐡 0 𝐴 ]0 [𝐴 0 𝐡 0 5. Substitute for integrand π‘₯ 𝑑π‘₯ 1 π‘₯ 𝑑π‘₯ 1 π‘₯ 𝑑π‘₯ a. ∫ = ( βˆ— ∫ ) + ( βˆ— ∫ ) 0 ( 𝐴0βˆ’π‘₯)( 𝐡 0π‘₯) [𝐡 0 𝐴 ]0 0 [𝐴0βˆ’π‘₯ [𝐴 0 𝐡 0 0 𝐡 0π‘₯ 𝑑π‘₯ 1 β€’ Using the standard i
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