§ 9.2 Reaction rate and rate equation

1. §9.2 Reaction rate and rate equation

2. c c1 c c2 t1 t2 t t1 t 2.1 expression of reaction rate The rate (r) of a chemical reaction is defined as the change in concentration of a reactant or a product per unit time. There are two kinds of reaction rates: mean rate instantaneous rate: Physical meaning: the slope of the [A] ~ t curve at time t.

3. N2 + 3H2 == 2NH3 It is apparent that When expressed using different species, the rate of the reaction may attain different values, which is not convenient and sometimes may even cause confusion.

4. Definition: extent of reaction or advancement () where i is the stoichiometric coefficient of the reaction. aA + bB  gG + hH Definition: The true rate of the reaction or rate of conversion (J):

5. For general reaction: aA + bB  gG + hH When the extent of reaction is d When the reaction takes place in a container with constant volume Define rate

6. Unit: mol m-3 s-1

7. c Initial rate Rate at any time t = 0 t = t t 2.2 measurement of reaction rate Physical meaning: slope of the c ~ t curve kinetic curve The key subject of kinetic study is to measure the concentration of some species after arbitrary time intervals.

8. t = t1 t = t2 t = 0 The concentration of the species can be measured using either chemical or physical methods. For example: CH3COOC2H5 + NaOH  CH3COONa + C2H5OH The reaction can be stopped by removing of CH3COOC2H5, and the consumption of NaOH can be determined by chemical titration.

9. The change in physical properties of the reaction system which relates to the concentration of reactants or products can be usually chosen as indicator of the progress of the reaction. The first successful example for measuring concentration of reactant physically was made by Wilhelmy in 1850 . He determined the residual concentration of sucrose by measuring the change of the rotation angle of a beam of plane-polarized light passing through the hydrolysis solution (optical activity).

10. [] 66.5 []1 []2 20 t1 t2 t C12H22O11 + H2O  C12H22O11 + C12H22O11 glucose sucrose fructose The rotation angle of the 1:1 mixture of glucose and fructose is –20 o We still use in it in our physical chemistry laboratory

11. CH3COOC2H5 + NaOH  CH3COONa + C2H5OH the rate of which can be monitored using pH meter or conductometer. N2O5 = N2O4 + 0.5 O2 When this reaction takes place in a container with constant volume, the rate of the reaction can be monitored by measuring the pressure change. And when this reaction takes place under constant pressure, the advance of the reaction can be monitored by measuring the volume increase. dilatometer.

12. FTIR spectroscopy Stretch of epoxy group

13. Real time analysis • Quenching • Static method • 2) Flow method Analyzing methods: The physical parameters usually used for monitoring reaction process includes volume, pressure, electric conductance, pH, refractive index, thermal conductivity, polarimetry, spectrometry, chromatography, etc. All the above methods are valid only for reactions with half-lives of at least a few seconds, i.e., “slow” reaction. For fast reaction of half-lives ranging between 100 ~ 10-11 s, special methods are required.

14. Stable flow: l t Flow method Mixer detector Moving direction Difficulties in study on kinetics

15. 2.3 Rate equation and the law of mass action The concentration-dependence of rate: r = r(ci) = r(cA, cB, cC…) Where ci represents concentration of individual specie present in rate equation. In many instances, the rate of a reaction is proportional to the concentrations of the reactants raised to some power. rate equation Rate law

16. For example: H2 + I2 = 2 HI H2 + Cl2 = 2 HCl Where rate coefficient/constant (k) is a proportionality constant /coefficientindependent of concentration. The exponent shows the effect of concentration on the reaction rate. In 1895, Noyes defined them as partial order of the reactant.

17. , is the partial order of the reaction with respect to A or B, respectively. This implies that the reaction obeying rate law is first-order in H2 and 0.5-order in Cl2. the sum of the partial order n = + + +… is the overall order of the reaction, or more simply, the reaction order. The overall order is 1.5.

18. 2SO2 + O2 2SO3 is first-order in SO2, -0.5-order in SO3 and 0.5 order overall. n, , , , etc., different from the stoichiometric coefficient, may be integers, decimals, of plus or minus values. Rate law must be determined from measurements of reaction rate and cannot be deduced from the reaction stoichiometry.

19. For elementary reaction,  = a,  = b, etc. Partial order=stoichiometric coefficient Reaction order=number of molecules involved in the reaction For example: 2I + H2 = 2HI Law of mass action valid only for elementary reaction

20. An exercise

21. Group work: Write the differential form of rate equation and deduce the integration rate equations of reactions with simple orders. A member of a chosen group will be asked to deduce the equation on blackboard this Thursday.