Name TA Name Lab Section # ALL work must be shown to receive full credit. Due at the beginning of lecture on monday, October 8, 2001.

Transcription

1 hem 55 Problem Set #5 Fall 200 Name TA Name Lab Section # ALL work must be shown to receive full credit. Due at the beginning of lecture on monday, October 8, 200. PS5.. The following data was collected for the reaction 2N 2 O 5 (g) 4NO 2 (g) + O 2 (g) Experiment # Experiment #2 time (sec) onc.(m) time (sec) onc.(m) a) Plot the data for Exp. # and graphically estimate EM 55 Fall 200

2 .6.4 Initial rate Data for Experiment # [N2O5].2.0 Instantaneous 00 s Instantaneous 800 s Instantaneous 2000 s Time (sec) Data for Experiment #2 [dinitrogen pentoxide] Initial rate Instantaneous 00 sec Instantaneous 800 sec Instantaneous 2000 sec Time (sec) EM 55 2 Fall 200

3 PS5.. (ontinued) i) the initial rate y x x 0 3 M s ii) the instantaneous rate at 00 sec? 800 sec? 2000 sec? at 00 s instantaneous rate is.02 x 0 3 M s at 800 s instantaneous rate is 4.33 x 0 3 M s at 2000 s instantaneous rate is.69 x 0 4 M s iii) the time it takes for half of the N 2 O 5 to react half-life is approximately 50 s b) Repeat a) for Exp #2 i) the initial rate y x x 0 4 M s ii) the instantaneous rate at 00 sec? 800 sec? 2000 sec? at 00 s instantaneous rate is 4.3 x 0 4 M s at 800 s instantaneous rate is 2.6 x 0 4 M s at 2000 s instantaneous rate is 7.8 x 0 5 M s iii) the time it takes for half of the N 2 O 5 to react half-life is approximately 800 s c) By what factor did the initial concentration change in going from Exp # to Exp #2?.48 M M.54 d) By what factor did the initial rate change in going from Exp # to Exp #2?.20 x 0 3 M s 5.20 x 0 4 M s 2.3 EM 55 3 Fall 200

4 PS5.. (ontinued) e) What is the order of the reaction with respect to N 2 O 5? rate 2 rate k 2[N 2 O 5 ] m 2 k [N 2 O 5 ] m 2.3 (.54) m m 2 f) ow did the half-life change for the two experiments? The half-life increased by a factor of about.54. g) Determine the rate constant for the reaction including units. rate k[n 2 O 5 ] 2 initial rate k [N 2 O 5 ] 2.20 x 0 3 M s (.48 M) x 0-4 M -. sec - h) What would the initial rate be if the initial concentration of N 2 O 5 is.225 M? M? rate k[n 2 O 5 ] x 0-4 M -. sec - [.225] x 0 4 M. sec - rate k[n 2 O 5 ] x 0-4 M -. sec - [0.475] 2.24 x 0 4 M. sec - EM 55 4 Fall 200

5 PS5.2. The following initial rate data were collected for the reaction r( 2 O) 6 2+ (aq) + SN (aq) r(2 O) 5 SN 2+ (aq) + 2 O(l) at 25. Exp. # [r( 2 O) 6 2+ (aq) ] [SN ] initial rate M s.85 x 0 4 M 0.25 M 9.25 x x 0 4 M 0.25 M 2.28 x x 0 4 M 0.0 M 9.25 x 0 a) Determine the reaction order for r( 2 O) 6 2+ (aq) and SN. The reaction is first order for r( 2 O) 6 2+ and first order for SN. To determine the order with respect to r( 2 O) 6 2+ experiments and 2 will be used since the concentration of SN is constant. rate 2 rate k 2[r( 2 O) 6 2+ ] m 2 [SN ] n 2 k [r( 2 O) 6 2+ ] m [SN ] n the rate constant and [SN ] are constant x 0 0 M s 9.25 x 0 M 4.56 x 0 4 M m.85 x 0 s 4 M 2.46 (2.46) m m To determine the order of the reaction with respect to SN experiments 2 and 3 can be used. rate 2 rate 3 k 2[r( 2 O) 6 2+ ] 2 [SN ] n 2 k 3 [r( 2 O) 6 2+ ] 3 [SN ] n x 0 0 M s 9.25 x 0 M n s n n b) Determine the overall order of the reaction. The reaction is second order overall. overall order m + n 2 c) Write the specific rate law for the reaction. rate k[r( 2 O) 6 2+ ] [SN ] d) Determine the rate constant for the reaction (include units). rate k [r( 2 O) 6 2+ ] [SN ] 9.25 x 0 - M s [.85 x 0 4 M] [0.25 M] 2.00 x 0 6 M - sec - EM 55 5 Fall 200

6 PS5.3. The following initial rate data were collected for the reaction 2NO 2 (g) + O 3 (g) N 2 O 5 (g) + O 2 (g) at 00. Exp. # [NO 2 ] [O 3 ] initial rate M s.65 M.80 M 2.6 x M.8 M 4.40 x M.55 M.32 x 0 5 a) Determine the reaction order for NO 2 and O 3. The reaction is first order for NO 2 and first order for O 3. To determine the order with respect to NO 2 experiments and 2 will be used since the concentration of O 3 is effectively constant. rate 2 rate k 2[NO 2 ] m 2 [O 3] n 2 k [NO 2 ] m [O 3] n the rate constant and [O 3 ] are constant x 0 4 M s 2.6 x 0 4 M.0 M 0.65 M m s.68 (.69) m m To determine the order of the reaction with respect to O 3 experiments 2 and 3 can be used. rate 3 rate 2 k 3[NO 2 ] 3 [O 3] n 2 k 2 [NO 2 ] 2 [O 3] n 2.32 x 0 5 M s 4.40 x 0 4 M n s n n n The reaction is second order overall. overall order m + n 2 c) Write the specific rate law for the reaction. rate k[no 2 ] [O 3 ] d) Determine the rate constant for the reaction (include units). rate k [NO 2 ] [O 3 ] 2.6 x 0 4 M s [0.65 M] [0.80 M] 5.02 x 0 4 M - sec - EM 55 6 Fall 200

7 PS5.4. The reaction SO 2 l 2 (g) SO 2 (g) + l 2 (g) follows simple first order kinetics. If the [SO 2 l 2 ] 0 is M, a) calculate the rate constant for the reaction if it takes.25 x 0 2 s for the concentration of SO 2 l 2 to fall to M. ln [SO 2l 2 ] [SO 2 l 2 ] 0 kt ln [0.309 M] [0.582 M] 0 k(.25 x 0 2 ) ln 0.53 k(.25 x 0 2 ) k(.25 x 0 2 ) k 5.06 x 0 3 s b) calculate the half-life for the reaction. (When the [SO 2 l 2 ] M.) t / k t / x 0 3 s 37 s c) how long will it take for the [SO 2 l 2 ] to fall to 0.29 M? ln [SO 2l 2 ] [0.29 M] [SO 2 l 2 ] kt ln 5.06 x 0 0 [0.582 M] 3 s - (t) 0 ln x 0 3 s (t) x 0 3 s - (t) t 93 s d) what is the [SO 2 l 2 ] after 350 s? (When [SO 2 l 2 ] M.) ln [SO 2l 2 ] [SO 2 l 2 ] 0 kt ln [SO 2l 2 ] [0.56 M] x 0 3 s - (350 s) ln [SO 2 l 2 ] ln[0.56 M] 0.77 ln [SO 2 l 2 ].77 + ln[0.56 M] ln [SO 2 l 2 ] 3.63 [SO 2 l 2 ] e M e) calculate the fraction of SO 2 l 2 that remains after 60 s. ln [SO 2l 2 ] [SO 2 l 2 ] 0 kt ln [SO 2l 2 ] [SO 2 l 2 ] x 0 3 s - (60 s) ln [SO 2l 2 ] [SO 2 l 2 ] [SO 2 l 2 ] [SO 2 l 2 ] 0 e 0.80 [SO 2 l 2 ] [SO 2 l 2 ] [SO 2 l 2 ] t 0.445[SO 2 l 2 ] 0 EM 55 7 Fall 200

8 PS5.5. The reaction 3 O(g) 4 (g) + O(g) follows simple second order kinetics. When the [ 3 O] M the half-life is 8.75 s. a) alculate the rate constant for the reaction. t /2 k[ 3 O] 0 k t /2 [ 3 O] 0 k 8.75 s(0.020 M) 9.52 s M b) ow long will it take for the [ 3 O] to fall from M to 2.45 x 0 3 M? [ 3 O] [ 3 O] kt x 0 3 M M 9.52 M- s- (t) t 34. s c) What is the [ 3 O] after 7.0 minutes if [ 3 O] M? [ 3 O] [ 3 O] kt 0 [ 3 O] M 9.52 M- s- (7 min) 60 s min [ 3 O] 3998 M M [ 3 O] 2.50 x 0 4 M d) ow long will it take for the [ 3 O] to decrease to 0.66 of its original concentration when the [ 3 O] M? [ 3 O] [ 3 O] kt M M 9.52 M- s- (t) t 2.5 s EM 55 8 Fall 200

9 PS re-arranges from a cyclic structure to a straight chain structure according to the following equation; 3 6 (g) 3 6 (g) the rate constant for the decomposition is 5.5 x 0 4 s at 500. a) What is the order of the reaction? st order based on the unit of the rate constant b) ow long would it take for 5.00 % of a sample of 3 6 to decompose at 500 and atm? Since the reaction is first order we do not need to know the initial concentration of 3 6 (g). The time required for 5% of a sample to reacted is equivalent to the time when the concentration of 3 6 (g) is 85% of the initial 3 6 (g) concentration. That is, [ 3 6 ] t 0.85 [ 3 6 ] o n [ 3 6 ] t [ 3 6 ] o -kt n 0.85[ 3 6 ] o [ 3 6 ] o 5.5 x 0-4 sec - (time) ln x 0-4 sec - (time) x 0-4 sec - (t) 295 sec time If the students need a concentration it can be calculated using PVnRT recall PV nrt or n V P RT atm M L. atm (298 K) mol. K [ 3 6 ] o M So 5% reacting leaves 85% unreacted [ 3 6 ] t M n x 0-4 sec - (time) ln x 0-4 sec - (time) ln x 0-4 sec - (time) 295 sec time EM 55 9 Fall 200

10 c) What is the half-life of the reaction? The half-life of the reaction is t / k x 0-4 sec.26 x 0 3 sec d) ow long would it take for 5.00 % of a sample of 3 6 to decompose at 500 and 0 atm? For first order reactions, the time required for a specific amount of reaction to occur is independent of the initial concentration. Therefore, the time is identical to part b). If the [ 3 6 ] o is determined it should be M P RT 0 atm L. atm (298 K) mol. K M Performing the same calculations as used in part b) will yield the same answer as part b). PS5.7. The second-order thermal decomposition of hydrogen bromide, Br(g), has a half-life of 2.74 s at a given temperature when the initial concentration of Br is M. a) What is the concentration of hydrogen bromide after 3.6 s? t /2 k[br] 0 k t /2 [Br] 0 k 2.74 s(0.074 M) 5. s M [Br] [Br] kt 0 [Br] M 5. M- s- (3.6 s) [Br] 4.0 M M [Br] 3.32 x 0 2 M b) ow long will it take for 20.0 % of the sample to decompose? [Br] t 0.80[Br] (0.074 M) M [Br] [Br] kt M M 5. M- s- (t) t s EM 55 0 Fall 200

11 PS5.8. The rate constant for the gas phase decomposition of ozone 2O 3 (g) 3O 2 (g) is M sec at 80. a) ow long will it take for 90 % of a sample of ozone to decompose given that the initial concentration is 6.00 x 0 3 M? [O 3 ] t [O 3 ] 0 kt x 0 3 M 6.00 x 0 4 M remaining [6 x 0 4 M] 6 x 0 3 M M- s- (t) 500 M M - s- (t) 500 M t M - s-.9 x 0 5 seconds b) What is the half-life of the reaction for this initial concentration? t /2 t /2 k[o 3 ] M s (6.00 x 0 3 M).9 x 0 4 s EM 55 Fall 200

12 PS5.9. In the reaction NO 2 (g) NO(g) + 2 O 2(g) the [NO 2 ] was followed with time and the data shown below was obtained. Time(s) [NO 2 ](M) Determine the order of the reaction and its half-life. (Include graphs of your data to support your conclusion. Be sure all plots are included.) EM 55 2 Fall 200

13 EM 55 3 Fall 200 PS5.0a. Draw the Lewis structure and name the following compounds; i) 3 ( 3 )( 3 ) , 3, 3-trimethylhexane ii) 3 ( 3 ) 2 2 ( 3 ) ( 3 ) 3 2, 5, 5, 8-tetramethylnonane PS3.0b. Draw the structure which corresponds with each of the following names. i) 3-ethyloctane ii) 2,2,4,4-tetramethylhexane iii) 2,3-dimethyl-4-propylnonane