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Chapter 14 – Chemical Kinetics • How fast a chemical A. Factors that affect reaction occurs rate • Only need to consider 1. Concentration of the forward reaction reactants 2. Temperature 3. Catalysts 4. Surface Area [conc] R t B. Reaction Rates 1. Rate is determined in the lab by experiment 2. Rate determined by measuring (-) disappearance of reactants (+) appearance of products Example 1 – Rates of… A+B C +D RA [ Af Ai ] (t f ti ) RC [C f Ci ] (t f ti ) Rate of disappearance of A Note the NEGATIVE sign!! Rate of appearance of C Note the POSITIVE sign!! C4H9Cl + H2O C4H9OH + HCl Data Table 14.2 – Disappearance of C4H9Cl Time (sec) 0.0 50.0 [C4H9Cl] (M) 0.100 0.0905 0.0820 0.0741 0.0671 [0.0741 M 0.0905 M ] R (150 s 50 s ) 100.0 150.0 = 1.64 x 10-4 M/s 200.0 Example 2 – Rates with Coefficients aA + bB cC + dD 1 [ A] RA a t 1 [C ] RC c t Note that the coefficient becomes a reciprocal value for rate comparison Example 3 – Rate Comparison 2 N2O5 4 NO2 + O2 RN 2O5 1 [ N 2O5 ] 2 t Given: RN O 2 5 = 4.2 x 10-7 M/s RNO2 1 [ NO2 ] 4 t RNO2 4 1 RN 2O5 1 2 RNO2 2(4.2x107 M / s) 8.4x107 M / s Calculate the rate of appearance of NO2 1 1 RNO2 RN 2O5 4 2 Example 3 – Rate Comparison 2 N2O5 4 NO2 + O2 RN 2O5 1 [ N 2O5 ] 2 t Given: RN O 2 5 = 4.2 x 10-7 M/s [O2 ] RO2 t The rate of O2 appearance is ½ the rate of N2O5 disappearance 1 RO2 (4.2 x107 M / s) 2.1x107 M / s 2 Rate Law Expression R = k [reactant]m • R = rate law expression • k = rate constant units are M-1s-1 Note: k depends upon temperature and nature of reaction • m = order of reaction – m=0 rate is independent of [ ]0 – m=1 rate is directly related to [ ]1 – m=2 rate is directly related to [ ]2 aA + bB products • R = k [A]m[B]n m = order with respect to A n = order with respect to B Overall order of reaction is = m + n Note: order of reaction must be determined experimentally in the lab and cannot be simply concluded from the equation coefficients!!!! • 2 N2O5 4 NO2 + O2 R = k[N2O5] • CHCl3 + Cl2 CCl4 + HCl R = k [CHCl3][Cl2] • H2 + I2 2 HI R = k [H2] [I2] Method of Initial Rates A +BC EXP [A] [B] Initial Rate (M/s) 1 2 3 0.100 M 0.100 M 0.100 M 0.200 M 0.200 M 0.100 M 4.0 x 10-5 4.0 x 10-5 16.0 x 10-5 First Order Reactions [ A] RA k[ A] t • Using Calculus… ln [A]t – ln [A]0 = -kt or ln [A]t /[A]0 = -kt [A]0=original conc [A]t=conc @ time, t k = rate constant t = time RA k[A] Graphing First Order Reactions ln [A]t = -k t + ln [A]0 [A] y = mx +b ln [A] t This is NOT a linear plot…. Scientists like linear plots t Example – 1st Order • The decomposition of an insecticide in H2O is first order with a rate constant of 1.45 yr -1. On June 1st, a quantity of 5.0x10-7 g/cm3 washed into a lake. insect product R = k [insect] What is the concentration on June 1st next year? ans. [insect]t=1yr = 1.17x10-7 g/cm3 How long will it take for the [insect] to drop to 3.0x10-7 g/cm3? ans. t = 0.35 years = 4 months a) b) 1st Order Reactions, Half-Life 1 [ A]0 ln 2 kt1 2 [ A]0 The time that it takes for Original concentration to Drop to ½ of its original concentration. 1 ln kt1 2 2 1 ln 2 t 1 2 k 0.693 t1 2 k Second Order Reactions RA k[ A] 2 y = mx +b slope=k • Using Calculus… 1 1 kt [ A]t [ A]0 [A]0=original conc [A]t=conc @ time, t k = rate constant t = time 1 [A] t 2nd Order Reactions, Half-Life t1/2= 1 k[A]0 To Determine Order You Must Graph the Data y = mx +b y = mx +b slope=k 1st Order 1 ln [A] [A] 2nd Order t t Activation Energy, Ea 1. Molecules must collide to react 2. Not all collisions result in a reaction 3. The higher the collision frequency, the faster the reaction rate a. increase temperature b. increase pressure or decrease volume (for gas only) c. catalyst d. increase [conc] Activation Energy, Ea 4. Activation energy, Ea – the minimum energy needed to start a reaction 5. Activated complex – intermediate product forming before the reaction is completed Activated Complex A* Ea E B The bigger Ea, the slower the rate Energy A Reaction progress For A B For B A exothermic E (-) endothermic E (+) + Ea Arrhenius Equation – Rate and Temperature k Ae Ea / RT Ea ln k ln A RT k=rate const A=frequency Ea=Activation energy R=gas const 8.31 J/mol K T=Temperature (Kelvin) Solving Arrhenius for Two Temperatures Ea ln k1 ln A RT1 Ea ln k 2 ln A RT2 Ea Ea ln k1 ln k2 ln A ln A RT RT 1 2 k1 Ea 1 1 ln k2 R T2 T1 Graphing Arrhenius Yintercept= ln A ln k Slope = - Ea R Note: to obtain Ea, you must multiply slope by the gas constant 1/ T k1 Ea 1 1 ln T T k2 R 2 1
"Chapter 14 – Chemical Kinetics"