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Chapter 14

Chapter 14. Rates Equations and Order of Reactions. 14.1 Rates Equations and Order of Reactions 14.2 Zeroth, First and Second Order Reactions 14.3 Determination of Simple Rate Equations from Initial Rate Method. 14.4 Determination of Simple Rate Equations

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Chapter 14

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  1. Chapter 14 Rates Equations and Order of Reactions 14.1 Rates Equations and Order of Reactions 14.2 Zeroth, First and Second Order Reactions 14.3 Determination of Simple Rate Equations from Initial Rate Method

  2. 14.4 Determination of Simple Rate Equations from Differential Rate Equations 14.5 Determination of Simple Rate Equations from Integrated Rate Equations 14.6 Carbon-14 Dating

  3. Unit: mol dm-3 s-1 14.1 Rates Equations and Order of Reactions (SB p.25) Rate Equations Consider a reaction: aA + bB  C Rate of reaction = k[A]x[B]y (a rate law) k is called the rate constant Note: unit of k depends on x and y 1. x and y can only be determined experimentally and bear NO direct relationships with a and b (stoichiometric ratios) 2. x = order of reaction with respect to reactant Ay = order of reaction with respect to reactant Bx + y = overall order of reaction

  4. 14.2 Zeroth, First and Second Order Reactions (SB p.26) A product Rate = k[A]º = k Zeroth Order Reactions

  5. 14.2 Zeroth, First and Second Order Reactions (SB p.27) At high pressure, gold surface saturated with adsorbed HI(g) 2HI(g) H2(g) + I2(g) Example of Zeroth Order Reaction gold surface Rate = k[HI(g)]n (where n = 0) ∴ Rate = k Hence, the rate is independent of the concentration of HI(g) and is a constant.

  6. 14.2 Zeroth, First and Second Order Reactions (SB p.27) A product Rate = k [A] First Order Reactions

  7. 14.2 Zeroth, First and Second Order Reactions (SB p.27) 2H2O2(aq) 2H2O(l) + O2(g) Rate = k[H2O] Examples of First Order Reaction Reaction Rate equation 2N2O5(g) 4NO2(g) + O2(g) SO2Cl2(l) SO2(g) + Cl2(g) (CH3)3CCl(l) + OH-(aq) (CH3)3COH(l) + Cl-(aq) Rate = k[N2O5(g)] Rate = k [SO2Cl2(l)] Rate = k [(CH3)3CCl(l)]

  8. 14.2 Zeroth, First and Second Order Reactions (SB p.28) A products Rate = = k[A]2 2NOCl(g) 2NO(g) + Cl2 Rate = k[NOCl]2 Second Order Reactions (Case 1) Example:

  9. 14.2 Zeroth, First and Second Order Reactions (SB p.28) A + B products Rate = k[A][B] H2(g) + I2(g) 2HI(g) Rate = k[H2(g)][I2(g)] Second Order Reactions (Case 2) Examples

  10. 14.3 Determination of Simple Rate Equations from Initial Rate Method (SB p.29) By determining the initial rates of reactions with different initial concentrations of reactants experimentally: For a reaction between two substances A and B, experiments with different initial concentrations of A and B were carried out. The results were as follows:

  11. 14.3 Determination of Simple Rate Equations from Initial Rate Method (SB p.29) (a) What is the order of reaction with respect to A and with respect to B? Let m be the order of reaction with respect to A, and n be the order of reaction with respect to B. Then, the rate equation for the reaction can be expressed as: Rate = k[A]m[B]n Therefore, 0.0005 = k(0.01)m(0.02)n ………………(1) 0.0010 = k (0.02)m(0.02)n………………(2) 0.0020 = k(0.01)m(0.04)n……………….(3) Dividing (1) by (2), 0.0005/0.0020 = (0.01/0.02)m ∴ m =1 Dividing (1) by (3), 0.0005/0.0020 = (0.02/0.04)n ∴n = 2 Answer

  12. 14.3 Determination of Simple Rate Equations from Initial Rate Method (SB p.29) (b) Calculate the rate constant using the result of experimental 1. Using the result of experiment (1), Rate = k[A][B]2 0.0005 = k x 0.01 x 0.022 k = 125 mol-2dm6s-1 Answer (c) What is the rate equation for the reaction? Answer Rate = 125[A][B]2

  13. 14.4 Determination of Simple Rate Equations from Differential Rate Equations (SB p.32) Reactions Involving More Two Reactants Consider aA +bB  products By keeping B in large excess, we have rate = k[A]n i.e. log(rate) = nlog[A] + logk

  14. 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.37) A product Rate = = k0 Zeroth Order Reaction [A] = -k0t + [A]0

  15. 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.37) A product Rate = = k1[A] First Order Reaction Integrating the above equation gives In A = -k1t + In[A]0

  16. 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.38) In( ) = k1t In( ) = k1t In 2 = Half-life for First Order Reactions In A = -k1t + In[A]0 Rearranging, we have The time taken for half of the reactant to be converted to the product is known as the half-life of the reaction (t½) t1/2 = In 2/ k1 = 0.693/ k1

  17. 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.38) Half-life of a first order reaction Remark: All radioactivity decays are 1st order reaction and thus have constant half-lives.

  18. 14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.40) A product Rate = = k2[A]2 Half-life for Second Order Reactions Integrating the above equation gives

  19. As long as an organism is alive, the ration of carbon-14 to carbon-12 remains constant. When the organism dies and incorporation of carbon ceases, the ratio of carbon-14 to carbon-12 decreases. Thus the age of fossil can be deduced by comparing the carbon-14 to carbon-12 with that in living tissue. 14.6 Carbon-14 Dating (SB p.44) +  + Carbon-14 Dating In the upper atmosphere

  20. The END

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