Question

Ch 15 Extra credit opportunity. 10 pts max. Due By Exam 2 (11/14). 1)If you are enrolled in or have previously taken calculus, derive the integrated rate equations for oth, 1st and 2nd order reactions. (2 pt ea, 6 pts) Hint, start with the instantaneous rate law, expressed as differential rates, Such as d[A]/dt = k. Separate your variables, d[A] to one side, dt to the other. Integrate from time 0 to time t and simplify. Show every step. 2) Anyone else, show step-by-step how to convert from the integrated first order rate equation In ([R]/[R] ] = -kt to the following (2 pt ea, 6 pts). a. [R] - [R]ekt b. In[R]= -kt + In[R] c. In(2) = k112 Hint, review the rules of log algebra in Appendix D. Show how to transform from the starting equation to each final equation, showing all steps. 3)Anyone (calculus and non-calculus students), a, derive a half-life equation for oth order reaction, starting from integrated oth order rate equation. (1 pt) b. derive a half-life equation for 2nd order reaction, starting from integrated 2nd order rate equaiton. (1 pt) c. derive the expression (R)= [R] (0.5)tt12, starting from whatever equation or showing all steps, and equations you think are most appropriate (2pts).

Answer 1

Zro andr Rate = KTAJ as the conantrtion of reactant - dr41 [ve Mn i dieusring aepuatng variably -jedenlguatiny d lA = K dt Limst with AT - x (to) [AJ-FA= TA]= CAO-kt st ardu Rat = K[A] 4 dlA k[a] [apuating vaniabls7 d[A7 TAJ [AJ dr47 [AJ -kdt dra dSutegrating wh fopa tim A7 In(A) [A.J Kt _[A] [AT. -kt TA7 = [A1, E rdn 2 = K [A] K[AJ Rale dla7 dt [supnatiny vaiabe kdt [AT [Snigatiny with fropu Limits [AT TAlo -2+1 K lt-o) A.) kt CA7