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Integrated Rate Equation

C. Y. Yeung (CHW, 2009). Physical Chemistry: Chemical Kinetics. Colorimetry. Chemical Method. Physical Method. Volume measurement. Differential Rate Equation. Integrated Rate Equation. AL CHEM REVIEW. C. Y. Yeung (CHW, 2009). p.01.

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Integrated Rate Equation

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  1. C. Y. Yeung (CHW, 2009) Physical Chemistry:Chemical Kinetics Colorimetry Chemical Method Physical Method Volume measurement Differential Rate Equation Integrated Rate Equation AL CHEM REVIEW

  2. C. Y. Yeung (CHW, 2009) p.01 Chemical Methodfor Studying the Variation of[A]withTime

  3. sampling, quenching, and titration p.02 Chemical Method = … Monitoring the change of conc. along with time by:

  4. p.03 Example 1: O O + + R’OH OH- O- R C OR’ R C (aq) (aq) (aq) (aq) Step1: Known amounts of ester and NaOH in beakers are placed in a thermostatic bath at known temperature. Step2: Start the reaction by mixing the reactants rapidly. The time is noted. Step3: At regular time intervals, a fixed volume of the mixture is pipetted into about 5 volumes of ice-water to quench the reaction.

  5. p.04 Example 1 (continued): O O + + R’OH OH- O- R C OR’ R C (aq) (aq) (aq) (aq) Step4: Remaining [OH-] in the reaction mixture is determined by titration against standard HCl using phenolphthalein. Step5: Repeat steps 3 and 4 to obtain variation of [OH-] against t.

  6. p.05 Example 2: MnO2(s) O2(g) 2H2O(l) 2H2O2(aq) + Step1: Known amounts of H2O2 is mixed with a small amount of MnO2(s) catalyst in a beaker placed in a thermostatic bath at known temperature. Step2: At regular time intervals, a fixed volume of the mixture is pipetted into excess dilute H2SO4(aq) to quench the reaction by removing the MnO2(s) catalyst.

  7. p.06 Example 2 (continued): MnO2(s) O2(g) 2H2O(l) 2H2O2(aq) + Step4: Remaining [H2O2] in the reaction mixture is determined by titration against standard KMnO4(aq). 5H2O2 + 2MnO4- + 6H+ 2Mn2+ + 8H2O + 5O2 Step5: Repeat steps 3 and 4 to obtain variation of [H2O2] against t.

  8. Examples: Br2 + HCOOH  2Br- + 2H+ + CO2 H2O2 + 2I- + 2H+ I2 + 2H2O p.07 Physical Methodfor Studying the Variation of[A]withTime < COLORIMETRY > < COLORIMETRY >

  9. measuring the variation of absorbance by colorimeter p.08 Colorimetry = … Monitoring the change of conc. along with time by: absorbance  [coloured substance] [colour intensity]

  10. p.09 Procedures: Calibration of Colorimeter + Measurement (I) Calibration of Colorimeter Step1: Use distilled water as sample, the absorbance is set to zero. Step2: A standard solution of Br2(aq) [e.g. 1.0M] is put into the sample cell in the colorimeter. Step3: Record the absorbance of 1.0M Br2(aq). Step4: Repeat steps 2 and 3 with different [Br2(aq)].

  11. Absorbance [Br2(aq)] p.10 Calibration of Colorimeter (continue) Step5: Plot a Calibration Curve of “Absorbance” versus “[Br2(aq)]”.

  12. Absorbance time p.11 (II) Measurement Br2 + HCOOH  2Br- + 2H+ + CO2 Put the Br2 containing reaction mixture in the sample cell and put into the colorimeter. Step1: Start the stop watch to monitor the variation of absorbance with time. Step2:

  13. Absorbance Absorbance time t1 [Br2]t1 [Br2(aq)] p.12 Monitoring the change of conc. along with time … Measurement Calibration A1 A1 [Br2]t1 t1

  14. measuring the volume of gas formed by syringe p.13 Another Physical Method … Monitoring the change of conc. along with time by:

  15. Example: p.14 Mg + 2HCl  MgCl2 + H2 (no colour change!)

  16. p.15 Rate Eqn. & Order of Rxn

  17. order of rxn w.r.t. [A] order of rxn w.r.t. [B] p.16 Rate Equation (Rate Law) the mathematical equation relating the rate of rxn to the [reactants]. Examples: 3A + 2B  C rate [A]x[B]y

  18. rate constant p.17 k[A]x[B]y rate= (varies with temp.!!) * usually, order of reaction = 0, 1 or 2. Therefore, the rate equation shows that:  rate of rxn is affected by [reactants]  rate of rxn is affected by temperature

  19. How to do it? [A] [A]03 [A]02 [A]01 kept constant t p.18 If [B] and temp. are kept constant, when [A] doubles, rate of reaction increases 4 times. initial rate method Repeat expt. with constant [A] and different [B], find n!

  20. rate m = 1 m = 2 m = 0 [A] Determination of k, m and n by graphical method p.19 Plot rate vs [A] : rate = k’ [A]m Only m could be found!

  21. log (rate) m = 2 m = 1 m = 0 log [A] p.20 rate = k’ [A]m log (rate) = m log [A] + log k’ y = mx + c log k’ i.e. Both k (=k’/[B]) and m could be found!

  22. p.21 Key Points Rate Equation shows that the rate of rxn is affected by conc. (order) & temp (k). Find the order of rxn (m, n) by Initial Rate Method (many combinations of [A] & [B]!) Plot log (rate) = m log[A] + log k’, both m, k’ and k could be found.

  23. p.22 Integrated Rate Equation

  24. [A] [A]0 t p.23 Zeroth OrderRxn Monitor the variation of conc. along with time by Chemical / Physical Method,  [A] = - k’t + [A]0 slope = - k’

  25. p.24 To study Integrated Equation, e.g. : [A] = -k’t + [A]0(zeroth order) During the reaction, both [A] and [B] decrease! In order to ensure that the decreasing rate is due to decreasing [A], not [B] … large excess of [B]should be used. i.e. keep [B] as “effectively constant”.

  26. First OrderRxn ln [A] ln [A]0 t p.25 ln [A] = - k’t + ln [A]0 slope = - k’

  27. Second OrderRxn [A]-1 [A]0-1 t p.26  [A]-1 = k’t + [A]0-1 slope = k’

  28. m = 0 m = 1 m = 2 p.27 Summary … 3 Integrated Rate Eqns [A] = - k’t + [A]0 ln [A] = - k’t + ln [A]0 [A]-1 = k’t + [A]0-1

  29. 10cm3 1.00 mol dm-3 H2O2 50cm3 borate buffer 10cm3 diluted KMnO4 Titrate against dilute KMnO4 10cm3 sample Flask A (150cm3 water) (around 5 mins) 10cm3 1.0M H2SO4 Flask B start stop watch! p.28 Kinetics Expt.:Decomposition of H2O2

  30. × 3 × 2 MnO2 2H2O2 O2 + 2H2O Flask A Flask B p.29 What happens in Flasks A and B …? H2O2 + 2OH- O2 + 2H2O + 2e-` MnO4- + 2H2O + 3e- MnO2 + 4OH- 3H2O2 + 2MnO4- 3O2 + 2H2O + 2OH- + 2MnO2 MnO2 is killed by H2SO4. 2MnO4- + 5H2O2 + 6H+ 2Mn2+ + 8H2O + 5O2

  31. For 1st order rxn, ln [A] = - k t + ln [A]0  ln ([A]0/[A]) = k t p.30 Date Treatment … As vol. of MnO4- used  [A],  ln (V0/V) = k t If a straight line is plotted [ln(V0/V) vs t]  1st order, and slope = k!

  32. Chemical Kinetics Colorimetry Chemical Method Physical Method Volume measurement Differential Rate Equation Integrated Rate Equation Differential / Integrated Rate Eqn? One Combination? (Continuous Method) Many Combinations? (Initial Rate Method) Physical/Chemical Method? p.31 Set Conc. + Collect Data + Plotting  Order of Rxn + “k”

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