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Rate of Reaction Analysis for First Order Reaction

Data analysis of a first-order reaction to determine rate and rate law expression, involving calculation of rate constants and reaction orders based on initial rate data.

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Rate of Reaction Analysis for First Order Reaction

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  1. Rate of Reaction Ken Rogers Miami Killian High

  2. 1. The following data were obtained for a first order rxn A a B + C time (seconds) [A] (molarity) 0 0.100 100 0.067 200 0.045 300 0.030 400 0.020 500 0.014 Make a graph and calculate the rate (slope) at time 100 s and 300 s.

  3. .10- .095M - .046M .09- D[A] Slope = ----------- = ------------------ .08- Dtime 0 - 200 s .07- = -2.45 x 10-4 M/s .06- .05- [A] .04- D[A] .03- .02- Dt D[A]/Dt = 1.1 x 10-4 M/s .01- 0 100 200 300 400 time (sec)

  4. Time (seconds)[A] (molarity) 0 0.100 100 0.067 200 0.045 300 0.030 400 0.020 500 0.014 Rate 2.45 x 10-4 M/s 0.067 2.45 x 10-4 M/s 1.1 x 10-4 M/s Rate = k [A]1 Rate = k [A]1 2.45 x 10-4 M/s = k [0.067M] 1.1 x 10-4 M/s = k [0.030M] 3.66 x 10-3/s = k 3.66 x 10-3/s = k

  5. Question 2 (a) What is the rate law expression for this reaction? 2 A + B a 3 C experiment initial initial initial rate number [A] [B] of B 1 0.10 0.10 4.0 x 10-4 M/min 2 0.10 0.30 4.0 x 10-4 M/min 2 0.30 0.30 1.2 x 10-3 M/min 2 0.20 0.40 8.0 x 10-4 M/min rate = k [A]x [B]y Solving for x and y means figuring out the order of each reactant.

  6. 2. 2 A + B a 3 C experiment initial initial initial rate number [A] [B] of B not changing 1 0.10 0.10 4.0 x 10-4 M/min 2 0.10 0.30 4.0 x 10-4 M/min 3 0.30 0.30 1.2 x 10-3 M/min 4 0.20 0.40 8.0 x 10-4 M/min 1 0.10 0.10 4.0 x 10-4 M/min 2 0.10 0.30 4.0 x 10-4 M/min x3 (3) x= 1 0 B is zero order

  7. 2. (a) 2 A + B a 3 C experiment initial initial initial rate number [A] [B] of B not changing 1 0.10 0.10 4.0 x 10-4 M/min 2 0.10 0.30 4.0 x 10-4 M/min 3 0.30 0.30 1.2 x 10-3 M/min 4 0.20 0.40 8.0 x 10-4 M/min 2 0.10 0.30 4.0 x 10-4 M/min 3 0.30 0.30 1.2 x 10-3 M/min x3 3 x = 3 1 A is first order

  8. rate = k [A]x [B]y 1 0 B is zero order, A is first order or just rate = k[A]

  9. 2. (b) value of rate constant? k = ? rate = k[A] Pick any experiment and substitute the info... experiment initial initial initial rate number [A] [B] of B 1 0.10 0.10 4.0 x 10-4 M/min rate = k[A] 4.0 x 10- 4 M/min = k [0.10 M]1 k = 4.0 x 10- 3/min or 4.0 x 10- 3 min-1

  10. 2. c) In experiment #1, what is the initial rate of appearance of product C? 2 A + Ba 3 C experiment initial initial initial rate number [A] [B] of B 1 0.10 0.10 4.0 x 10- 4 M/min 2 A + B a 3 C x 3 4.0 x 10- 4 M/min x 3 = 1.2 x 10- 3 M/min rate of B disappearing rate of C appearing

  11. 3. (a) A + B a C experiment initial initial initial rate number [A] [B] of B 1 0.10 0.10 6.0 x 10-3 M/s 2 0.20 0.20 4.8 x 10-2 M/s 3 0.10 0.20 1.2 x 10-2 M/s not changing x2 (2) x = 2 1 B is first order

  12. 3. (a) A + B a C experiment initial initial initial rate number [A] [B] of B not changing 1 0.10 0.10 6.0 x 10-3 M/s 2 0.20 0.20 4.8 x 10-2 M/s 3 0.10 0.20 1.2 x 10-2 M/s (2) x= 4 2 A is second order

  13. A is second order, B is first order….. rate = k [A]2 [B]1

  14. A + B a C experiment initial initial initial rate number [A] [B] of B 1 0.10 0.10 6.0 x 10-3 M/s 2 0.20 0.20 4.8 x 10-2 M/s 3 0.10 0.20 1.2 x 10-2 M/s 3. (b) value of rate constant? k = ? rate = k [A]2 [B]1 6.0 x 10-3 M/s = k [0.10M]2 [0.10M]1 6/M2.s or 6 M-2.s-1

  15. 3. c) What is the overall order for the reaction? 2 + 1 = 3 rate = k [A]2 [B]1 The reaction is 3rd order overall

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