Initial Rates Problems Key

INITIAL RATES PROBLEMS KEY F2(g) + 2ClO2(g)  2FClO2(g) 1. Given reaction rate data for: Experiment [F2](M) [ClO2](M) Initial Rate (M/s) 1 2 3 0.10 0.10 0.20 0.010 0.040 0.010 1.2 x 10-3 4.8 x 10-3 2.4 x 10-3 A. Determine the order of each reactant and the overall reaction order. From 1  3 [F2] doubles, ClO2 is constant, and Rate doubles: 2x = 2 x = 1 = order for [F2] From 1  2 [ClO2] quadruples, F2 is constant, and Rate quadruples: 4y = 4 y = 1 = order for [ClO2] Overall Reaction Order: 1 + 1 = 2 B. Write the rate law for the reaction. Rate = k[F2][ ClO2] C. Calculate the rate constant, k. k= 1.2x10 3 M / s Rate = = 1.2 M-1s-1 0.10 M0.010M [F2 ][ClO 2 ] 2O3(g)  3O2(g) 2. Given the rate data for: Run [O3] (M) Rate (M/s) 1 0.00600 5.03 x 10-7 2 0.00300 1.28 x 10-7 3 0.00150 3.08 x 10-8 A. What is the rate law for the reaction? Put larger concentrations and rates on top to avoid fractions!  5.03x10 7  0.00600M      1.28x10 7  0.00300M   From 2  1:  x     simplifies to 2x = 4 x = 2 = order for O3 Rate = k [O3]2 B. Calculate the rate constant, k. k= Rate [O3 ] 2 = 5.03x10 7 M / s 0.00600M2 = 0.0140 M-1s-1 C. What is the rate of reaction when [O3] = 0.00500 M? Rate = k [O3]2 = 0.0140 M-1s-1(0.00500 M)2 = 3.50x10-7 M/s 1 FIRST-ORDER KINETICS PROBLEMS KEY 1. The rate law for the decomposition of N2O5 is Rate = k[N2O5], where k = 5.0 x 10-4 s-1. What is the concentration of N2O5 after 1900 s, if the initial concentration is 0.56 M? ln [ A ]t = - kt [ A ]0 ln [ N 2 O5 ]t = - (5.0 x 10-4 s-1) (1900 s) = -0.95 (0.56 M ) [N2O5]0 = 0.56 M; k = 5.0 x 10-4 s-1; t = 1900 s Take anti ln both sides: [ N 2 O5 ]t = e-0.95 = 0.387 (0.56 M ) [N2O5]t = 0.560.387 = 0.22 M 2. The first order reaction, SO2Cl2  SO2 + Cl2, has a rate constant of 0.17 h-1. If the initial concentration of SO2Cl2 is 1.25 x 10-3 M, how many seconds does it take for the concentration to drop to 0.31 x 10-3 M? k = 0.17 h-1 ln [SO2Cl2]t = 0.31 x 10-3 M [ A ]t = - kt [ A ]0  0.31x10 3 M    ln 3  1 . 25 x 10 M   t= 0.17 h1  [SO2Cl2]0= 1.25 x 10-3 M   1.39   = 8.18 h = -  1   0.17 h   3600 s    2.9x104 s t = 8.18 h  1 hr   3. Cobalt-60 is a radioisotope that decays by first-order kinetics and has a half-life of 5.26 years. The Cobalt-60 in a radiotherapy unit must be replaced when the concentration of Co decreases to 75.0% of its initial value. When does this occur? 0.693 t1/2 = 5.26 yr k t1/2 = 0.693 k= = 0.132 yr-1 5.26 yr ln [ A ]t = - kt [ A ]0 [Co]t = 0.75[Co]0 ln 0.75 = -(0.132 yr-1) t  ln 0.75[Co]0 = -(0.132 yr-1) t [Co]0 -0.288 = -(0.132 yr-1) t  t = 2.18 yr 4. The first order reaction, CH3NC  CH3CN, has a rate constant of 6.3x10-4 s-1 at 230 C. A. What is the half-life of the reaction? t1/2 = 0.693 0.693 = = 1.1 x 103 s k 6.3x10 4 s 1 B. How much of a 10.0 g sample of CH3NC will remain after 5 half-lives? 5 1 10.0 g   = 0.313 g 2 C. How many seconds would be required for 75% of a CH3NC sample to decompose? 75% decomposed; 25% remains, so 2 half lives have passed. 21.1 x 103 s = 2.2 x 103 s 2 ACTIVATION ENERGY AND REACTION MECHANISMS KEY 1. Draw the potential energy profile for a reaction with H = -150 kJ and Ea = 100 kJ. Ea E H 2. A certain first order reaction has a rate constant of 1.75 x 10-1 s-1 at 20 °C. What is the value of k at 60 °C if Ea = 55.5 kJ/mol? k1 = 1.75 x 10-1 s-1 T1 = 293 K Ea = 55.5 kJ/mol k2 = ? k ln  1  k2  E  = a R  J Kmol  1k J   1000 J   = 8.314 x 10-3 kJ/(Kmol)  T2= 333 K R = 8.314  1 1     T2 T1  kJ 55 .5  1.75 x10 1 s 1  mol  = ln  k2   8.314 x10 3 k J Kmol  1 1      333 K 293 K   1.75 x10 1 s 1   = 6.68x103 K(-0.000410 K-1) = -2.74 ln  k2   1.75 x10 1 s 1 = e-2.74 = 0.0646 k2 1.75 x10 1 s 1  k2 = = 2.71 s-1 0.0646 1. The following mechanism has been proposed for the reaction: 2SO2 + O2  2SO3 Step 1: 2NO + O2  2NO2 slow Step 2: 2NO2 + 2SO2  2NO + 2SO3 fast A. Which is the rate determining step? step 1 is slow step B. What is the molecularity of the rate determining step? termolecular C. Identify the catalyst. NO D. Identify the intermediate. NO2 E. Write the rate law for the reaction. Rate = k[NO]2[O2] F. What is the overall reaction order? 2 + 1 = 3 3