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

Chemical Method for Studying the Variation of [A] with Time C. Y. Yeung (CHW, 2009) p.01

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

Example 1: RC O OR’ (aq) + OH - (aq) RC O O-O-O-O- (aq) + R’OH (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. p.03

Example 1 (continued): RC O OR’ (aq) + OH - (aq) RC O O-O-O-O- (aq) + R’OH (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. p.04

Example 2: 2H 2 O 2 (aq) + O 2 (g) Step1: Known amounts of H 2 O 2 is mixed with a small amount of MnO 2 (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 H 2 SO 4 (aq) to quench the reaction by removing the MnO 2 (s) catalyst. MnO 2 (s) 2H 2 O(l) p.05

Example 2 (continued): Step4: Remaining [H 2 O 2 ] in the reaction mixture is determined by titration against standard KMnO 4 (aq). Step5: Repeat steps 3 and 4 to obtain variation of [H 2 O 2 ] against t. 2H 2 O 2 (aq) + O 2 (g) MnO 2 (s) 2H 2 O(l) 5H 2 O 2 + 2MnO H +  2Mn H 2 O + 5O 2 p.06

p.07 Physical Method for Studying the Variation of [A] with Time Examples: Br 2 + HCOOH  2Br - + 2H + + CO 2 H 2 O 2 + 2I - + 2H +  I 2 + 2H 2 O

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

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

Step5: Plot a Calibration Curve of “Absorbance” versus “[Br 2 (aq)]”. Calibration of Colorimeter (continue) [Br 2 (aq)] Absorbance p.10

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

p.12 timeAbsorbance [Br 2 (aq)] Absorbance Time [Br 2 ] t1t1 A1A1 A1A1 [Br 2 ] t1 t1t1 Measurement Calibration Monitoring the change of conc. along with time …

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

p.14 Mg + 2HCl  MgCl 2 + H 2 Example: (no colour change!)

Rate Eqn. & Order of Rxn p.15

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

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

p.18 If [B] and temp. are kept constant, when [A] doubles, rate of reaction increases 4 times. How to do it? [A][B]Initial rate Expt. 1[A] 01 [B]Rate 1 Expt. 2[A] 02 [B]Rate 2 Expt. 3[A] 03 [B]Rate 3 ….. kept constant t[A] [A] 03 [A] 02 [A] 01 initial rate method Repeat expt. with constant [A] and different [B], find n!

Plot rate vs [A] : p.19 Determination of k, m and n by graphical method rate = k’ [A] m [A][B]Initial rate Expt. 1[A] 1 [B]Rate 1 Expt. 2[A] 2 [B]Rate 2 Expt. 3[A] 3 [B]Rate 3 ….. rate[A] m = 0 m = 1 m = 2 Only m could be found!

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

Key Points p.21 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.

Integrated Rate Equation p.22

p.23  [A] = - k’t + [A] 0 Zeroth Order Rxn Monitor the variation of conc. along with time by Chemical / Physical Method, Timet1t1 t2t2 t3t3 t4t4 [A][A] 1 [A] 2 [A] 3 [A] 4 [A]t [A] 0 slope = - k’

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

p.25 Timet0t0 t1t1 t2t2 t3t3 …. [A][A] 0 [A] 1 [A] 2 [A] 3 …. ln[A]ln [A] 0 ln [A] 1 ln [A] 2 ln [A] 3 …. ln [A] = - k’t + ln [A] 0 ln [A] t ln [A] 0 slope = - k’ First Order Rxn

p.26 Timet0t0 t1t1 t2t2 t3t3 …. [A][A] 0 [A] 1 [A] 2 [A] 3 …. [A] -1 [A] 0 -1 [A] 1 -1 [A] 2 -1 [A] 3 -1 …. [A] -1 t [A] 0 -1 slope = k’  [A] -1 = k’t + [A] 0 -1 Second Order Rxn

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

p.28 Kinetics Expt.: Decomposition of H 2 O 2 Flask A (150cm 3 water) 10cm mol dm -3 H 2 O 2 50cm 3 borate buffer 10cm 3 diluted KMnO 4 start stop watch! 10cm 3 sample (around 5 mins) 10cm 3 1.0M H 2 SO 4 Flask B Titrate against dilute KMnO 4

What happens in Flasks A and B …? p.29 Flask A H 2 O 2 + 2OH -  O 2 + 2H 2 O + 2e -` MnO H 2 O + 3e -  MnO 2 + 4OH - × 3 × 2 3H 2 O 2 + 2MnO 4 -  3O 2 + 2H 2 O + 2OH - + 2MnO 2 2H 2 O 2 O 2 + 2H 2 O MnO 2 Flask B MnO 2 is killed by H 2 SO 4. 2MnO H 2 O 2 + 6H +  2Mn H 2 O + 5O 2

p.30 Date Treatment … For 1 st order rxn, ln [A] = - k t + ln [A] 0  ln ([A] 0 /[A]) = k t As vol. of MnO 4 - used  [A],  ln (V 0 /V) = k t If a straight line is plotted [ln(V 0 /V) vs t]  1st order, and slope = k!

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