Chemical Kinetics Problems and Solutions

1. 2C2H2(g) + 5O2(g) → 4CO2(g) + 2H2O(l) 2. 2CH3OH(l) + 3O2(g) → 2CO2(g) + 4H2O(l) 3. 4NH3(g) + 5O2(g) → 4NO(g) + 6H2O(g) 4. C6H12O6(g) + 6O2(g) → 6CO2(g) + 6H2O(l) 5. HC2H3O2(l) + 2O2(g) → 2CO2(g) + 2H2O(l) 6. CH4(g) + 2O2(g) → CO2(g) + 2H2O 7. 2H2S(g) + 3O2(g) → 2H2O(l) + 2SO2(g) 8. 2C2H6(g) + 7O2(g) → 4CO2 + 6 H2O 9. 2Al(s) + 3ZnO(s) → Al2O3(s) + 3Zn(s) 10. C3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(g) 11. 2Fe(s) + 2HCl(aq) → 2FeCl2(s) + H2(g) 12. MgCl2(s) + 2Na(l) → 2 NaCl(s) + Mg(s) 13. 2Al(S) + Fe2O3(s) → Al2O3(s) +2Fe(l) 14. 2NaHCO3(s) → Na2CO3(s) + H2O(l) + CO2(g) 15. Fe2O3(s) + 3H2(g) → 2Fe(s) + 3H2O(g) 16. 2 Al(s) + 3Cl2(g) → 2 AlCl3(s) 17. 3ZnS(s)+ 3O2(g) →2ZnO(s) + 2SO2(g) 18. 2H2(g) + 2CO2 → C2H5O2(l) 19. O2(g) + 2H2(g) → 2H2O(l) 20. H2(g) + Br2(l) → 2HBr(g)

Key to Correction 1. 2C2H2(g) + 5O2(g) → 4CO2(g) + 2H2O(l)

−1 Δ [C 2 H 2 ] −1 Δ [O2] 1 Δ[CO 2 ] 1 Δ [H 2 O] = = = 2 Δt 5 Δt 4 Δt 2 Δt 2. 2CH3OH(l) + 3O2(g) → 2CO2(g) + 4H2O(l)

−1 Δ [CH 3 OH ] −1 Δ [O2 ] 1 Δ [CO 2 ] 1 Δ [H 2 O] = = = 2 Δt 3 Δt 2 Δt 4 Δt 3. 4NH3(g) + 5O2(g) → 4NO(g) + 6H2O(g)

−1 Δ [NH 3 ] −1 Δ[O2 ] 1 Δ[ NO2 ] 1 Δ[ H 2 O] = = = 4 Δt 5 Δt 4 Δt 6 Δt 4. C6H12O6(g) + 6O2(g) → 6CO2(g) + 6H2O(l)

−Δ[ C6 H 12 O6 ] −1 Δ[O 2] 1 Δ[CO 2 ] 1 Δ[H 2 O] = = = Δt 6Δt 6 Δt 6 Δt 5. HC2H3O2(l) + 2O2(g) → 2CO2(g) + 2H2O(l)

−Δ [ H C 2 H 3 O2 ] −1 Δ[O 2 ] 1 Δ[CO2 ] 1 Δ[ H 2 O] = = = Δt 2 Δt 2 Δt 2 Δt 6. CH4(g) + 2O2(g) → CO2(g) + 2H2O

−Δ[ CH 4 ] −1 Δ [O2 ] 1 Δ[CO2 ] 1 Δ [H 2 O] = = = Δt 2 Δt 2 Δt 2 Δt 7. 2H2S(g) + 3O2(g) → 2H2O(l) + 2SO2(g)

−1 Δ [H 2 S ] −1 Δ [O 2 ] 1 Δ[ H 2 O] 1 Δ [SO 2 ] = = = 2 Δt 3 Δt 2 Δt 2 Δt 8. 2C2H6(g) + 7O2(g) → 4CO2 + 6 H2O

−1 Δ [C 2 H 6 ] −1 Δ[O2 ] 1 Δ[CO 2 ] 1 Δ [ H 2 O] = = = 2 Δt 7 Δt 4 Δt 6 Δt 9. 2Al(s) + 3ZnO(s) → Al2O3(s) + 3Zn(s)

−1 Δ [ Al] −1 Δ[ ZnO] Δ [ Al 2 O3 ] 1 Δ[ Zn] = = = 2 Δt 3 Δt Δt 3 Δt 10. C3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(g)

−Δ [C3 H 8 ] −1 Δ [O2 ] 1 Δ[CO2 ] 1 Δ[H 2 O] = = = 11. 2Fe(s) + 2HCl Δ t (aq) → 2FeCl 5 Δ t 2(s) + H2(g) 3 Δt 4 Δt

−1 Δ [Fe] −1 Δ[ HCl] 1 Δ[ FeCl 2 ] Δ[H 2 ] = = = 2 Δt 2 Δt 2 Δt Δt

12. MgCl2(s) + 2Na(l) → 2 NaCl(s) + Mg(s)

−Δ [ Mg Cl2 ] −1 Δ[ Na] 1 Δ[NaCl] Δ[ Mg] = = = Δt 2 Δt 2 Δt Δt

13. 2Al(S) + Fe2O3(s) → Al2O3(s) +2Fe(l)

−1 Δ [ Al] −Δ[Fe 2 O 3 ] Δ[ Al 2 O3 ] 1 Δ[ Fe] = = = 2 Δt Δt Δt 2 Δt 14. 2NaHCO3(s) → Na2CO3(s) + H2O(l) + CO2(g)

−1 Δ [NaHC O3 ] Δ [Na 2 CO3 ] Δ [H 2 O] Δ [CO 2 ] = = = 2 Δt Δt Δt Δt 15. Fe2O3(s) + 3H2(g) → 2Fe(s) + 3H2O(g)

−Δ[Fe 2 O 3 ] −1 Δ[ H 2] 1 Δ[Fe] 1 Δ[H 2 O] = = = Δt 3Δt 2 Δt 3 Δt 16. 2 Al(s) + 3Cl2(g) → 2 AlCl3(s)

−1 Δ [ Al] −1 Δ[Cl ] 1 Δ [ Al Cl 3 ] = = 2 Δt 3 Δt 2 Δt 17. 3ZnS(s)+ 3O2(g) →2ZnO(s) + 2SO2(g)

−1 Δ [ZnS] −1 Δ[O 2] 1 Δ [ZnO ] 1 Δ[SO 2 ] = = = 3 Δt 3Δt 2 Δt 2 Δt 18. 2H2(g) + 2CO2 → C2H5O2(l)

−1 Δ [H 2 ] −1 Δ [CO2 ] Δ [C 2 H 5 O2 ] = = 2 Δt 2 Δt Δt

19. O2(g) + 2H2(g) → 2H2O(l)

−Δ [O2] −1 Δ[ H 2 ] 1 Δ [ H 2 O] = = Δt 2 Δt 2 Δt 20. H2(g) + Br2(l) → 2HBr(g)

−Δ[ H 2] −Δ[Br 2 ] 1 Δ[HBr ] = = Δt Δt 2 Δt

1. What is the rate constant under first order where a 50 M reactant produced a 29 molar concentration after 10 minutes? 2. What is the value of the rate constant for a first order reaction for which half-life is 29.75 minutes? 3. A certain first order reaction is 53% complete in 30 min. at 20 ° C. What is its rate constant?

4. In a given first-order reaction A→B, the initial concentration is 0.385 molar. What will be the concentration after 45 seconds with half-life of 19 seconds? 5. An experimentation of 3M concentration and made react in its first order. After 3 seconds, the rate constant is 1.5/s. How much amount is decreased in the original amount that was observed? 6. An initial amount if 0.52 M decompose into half of the initial amount. Determine the length of time where the rate constant is 0.1x10-3s-1. 7. How much amount of concentration is produced after a second that a 0.81 M reacts, knowing the rate constant is 5.03x10-3s-1 and under the first order reaction? 8. Determine the K of the following first order reaction with the half-life of 26.54 hrs.

9. The rate constant at 75 ° C. for the decomposition of its first order is 0.636 per second. Determine the half-life of its reaction. 10. The decomposition that proceeds into two different type of gas under first order resulted in a certain amount of concentration from 0.397M in 274 ° C.. It was observed that its half-life is 19s. Determine the amount after 100s.

11. The reaction 2A→B is first order in A with a rate constant if 4.8x10-2s-1 at 65 ° C. How long will it take for A to decrease from 0.75M to 0.15M?s 12. How much of concentration is produced after 25 seconds that 0.75M reacts, knowing rhe rate constant is 3.7x10-2s-1 and under the first order reaction.

13. A certain reaction is under a first-order reaction with a rate constant of 5.3x10-4s-1 at 500 ° C. if the initial concentration of reaction was 0.38M. What is the concentration after 150 seconds? 14. What is the rate constant under first order where a 45M reactant produced a 17M concentration after 15 minutes? 15. What is the value of the rate constant for first order reaction if its half-life is 32.5 min? 16. In a given first-order reaction A→B, the initial concentration is 0.95 molar. What will be the concentration after 30 seconds if its rate constant is 3.2x10-2s-1?

17. The rate constant at 65 ° C for the decomposition at its first order is 2.42x10-2s-1. Determine the half-life of its reaction? 18. An initial amount of 1.5M decompose into half-life of the initial amount. Determine the length of time when the rate of reaction is 1.2x10-3s-1. 19. Determine the concentration of a certain first order reaction at 5.6 minutes. Given the rate constant equal to 4.8x10-2s-1 and its initial concentration is 0.37M. 20. What is the value of the rate constant for a first-order reaction for which its half-life is 34.5 minutes?

Key to Correction: 1. What is the rate constant under first order where a 50 M reactant produced a 29 molar concentration after 10 minutes? Given: [A]o = 50M [A]t = 29M t = 10min Required: k Formula: ln[A]t = -kt + ln[A]o Solution: ln[29M]=-k(10min)+ln[50M]

ln

29 M =−k (10 min) 50 M

k =0.054 /min 2. What is the value of the rate constant for a first order reaction for which half-life is 29.75 minutes? Given:

t1 2

= 29.75 min

Required: k Formula:

t1 2

=

0.693 k

Solution: 29.75min=

k=

0.693 k

0.693 29.75 min

k =0.023/min 3. A certain first order reaction is 53% complete in 30 min. at 20 ° C. What is its rate constant? Given: [A]o = 100M [A]t = 47M t = 30 min

Required: k Formula: ln[A]t = -kt + ln[A]o

47 M ln =−k (30 min) Solution: 100 M k =0.025/min 4. In a given first-order reaction A→B, the initial concentration is 0.385 molar. What will be the concentration after 45 seconds with half-life of 19 seconds? Given:

t1 2

= 19 s

t = 45 s Required: [A]t Formula: ln[A]t = -kt + ln[A]o

k=

Solution:

0.693 19 s

k =0.036/ s ln[A]t = -(0.036/s)(45 s+ ln[0.385M] = -2.57 [A]t = e-2.57 = 0.08 M 5. An experimentation of 3M concentration and made react in its first order. After 3 seconds, the rate constant is 1.5/s. How much amount is decreased in the original amount that was observed? Given: [A]o = 50M t = 10min Required: k Formula: ln[A]t = -kt + ln[A]o Solution ln[A]t =-(1.5/s)(3 s)+ln[3 M] =-3.40 [A]t=e-3.40 =0.03M 6. An initial amount if 0.52 M decompose into half of the initial amount. Determine the length of time where the rate constant is 0.1x10-3s-1. Given: [A]o = 0.52M [A]t = 0.26M k=0.1x10-3s-1 Required: t Formula: ln[A]t = -kt + ln[A]o

ln

Solution:

0.26 M =¿ 0.52 M

-(0.1x10-3s-1)t

t=6931.47 s 7. How much amount of concentration is produced after a second that a 0.81 M reacts, knowing the rate constant is 5.03x10-3s-1 and under the first order reaction? Given: k= 5.03x10-3s-1 [A]o = 0.81M t=1s Required: [A]t Formula: ln[A]t = -kt + ln[A]o Solution ln[A]t =-(5.03x10-3s-1)(s)+ln[0.81 M] =-0.26 [A]t=e-0.26 =0.77M 8. Determine the K of the following first order reaction with the half-life of 26.54 hrs. Given:

t1 2

= 26.54 hrs

Required: k Formula:

t1 2

=

0.693 k

Solution: 26.54 hr=

k=

0.693 k 0.693 29.75 min

k =0.026/hr 9. The rate constant at 75 ° C. for the decomposition of its first order is 0.636 per second. Determine the half-life of its reaction. Given:

k =0.636/ s

Required:

t1 2

t1

Formula:

=

2

t1

Solution:

2

0.693 k

0.693 = k k=

0.693 0.636 /s

t 1 =1.09 s 2

10. The decomposition that proceeds into two different type of gas under first order resulted in a certain amount of concentration from 0.397M in 274 ° C.. It was observed that its half-life is 19s. Determine the amount after 100s. Given:

t1 2

= 19 s

t = 100 s [A]o=0.397M Required: [A]t Formula: ln[A]t = -kt + ln[A]o Solution:

t1 = 2

0.693 19 s

k =0.036/ s ln[A]t = -(0.036/s)(100 s+ ln[0.397M] = -4.5 [A]t = e-4.5 = 0.01 M

11. The reaction 2A→B is first order in A with a rate constant if 4.8x10-2s-1 at 65 ° C. How long will it take for A to decrease from 0.75M to 0.15M?s Given: [A]o = 0.75M [A]t = 0.15M k=4.8x10-2s-1 Required: t Formula: ln[A]t = -kt + ln[A]o Solution:

ln

0.15 M =¿ 0.75 M

-(4.8x10-2s-1)t

t=3353 s 12. How much of concentration is produced after 25 seconds that 0.75M reacts, knowing rhe rate constant is 3.7x10-2s-1 and under the first order reaction. Given: k= 3.7x10-2s-1 [A]o = 0.75M t = 25 s Required: [A]t Formula: ln[A]t = -kt + ln[A]o Solution ln[A]t =-(3.7x10-2s-1)(25 s)+ln[0.75 M] =-1.21 [A]t=e-1.21 =0.30 M

13. A certain reaction is under a first-order reaction with a rate constant of 5.3x10-4s-1 at 500 ° C. if the initial concentration of reaction was 0.38M. What is the concentration after 150 seconds? Given: k= 5.3x10-4s-1 [A]o = 0.38M t = 150 s Required: [A]t Formula: ln[A]t = -kt + ln[A]o Solution ln[A]t =-(5.3x10-4s-1)(150 s)+ln[0.38 M] =-1.05 [A]t=e-1.05 =0.35 M 14. What is the rate constant under first order where a 45M reactant produced a 17M concentration after 15 minutes? Given: [A]o = 45M [A]t = 17M t = 15min = 900s Required: k Formula: ln[A]t = -kt + ln[A]o Solution: ln[17M]=-k(900 s)+ln[45 M]

ln

17 M =−k (900 s ) 45 M

k

=-1.08x10-3s-1

15. What is the value of the rate constant for first order reaction if its half-life is 32.5 min? Given:

t1 2

= 32.5 min

Required: k Formula:

t1 2

=

0.693 k

Solution: 32.5 min =

k=

0.693 k

0.693 32.5 min

k =0.021/min

16. In a given first-order reaction A→B, the initial concentration is 0.95 molar. What will be the concentration after 30 seconds if its rate constant is 3.2x10-2s-1? Given: k= 3.2x10-2s-1 [A]o = 0.95 M t = 30 s Required: [A]t Formula: ln[A]t = -kt + ln[A]o Solution ln[A]t =-(3.2x10-2s-1)(30 s)+ln[0.95 M] =-1.01 [A]t=e-1.01 =0.36 M 17. The rate constant at 65 ° C for the decomposition at its first order is 2.42x10-2s-1. Determine the half-life of its reaction? Given:

k = 2.42x10-2s-1

Required: Formula:

t1 2

t1 2

=

0.693 k

t1

Solution:

2

0.693 k

=

¿

0.693 2.42 x 102 / s

t 1 =28.88 s 2

18. An initial amount of 1.5M decompose into half-life of the initial amount. Determine the length of time when the rate of reaction is 1.2x10-3s-1. Given: [A]o = 1.5M [A]t = 0.75M k=1.2x10-3s-1 Required: t Formula: ln[A]t = -kt + ln[A]o

ln

Solution:

0.75 =¿ -(1.2x10-3s-1)t 1.5 M t=577.67 s

19. Determine the concentration of a certain first order reaction at 5.6 minutes. Given the rate constant equal to 4.8x10-2s-1 and its initial concentration is 0.37M. Given: k= 4.8x10-2s-1 [A]o = 0.37 M t = 5.6 min Required: [A]t Formula: ln[A]t = -kt + ln[A]o Solution ln[A]t =-(4.8x10-2s-1)(5.6 min)+ln[0.37 M] =-1.16 [A]t=e-1.16 =0.31 M 20. What is the value of the rate constant for a first-order reaction for which its half-life is 34.5 minutes? Given:

t1 2

= 34.5 min

Required: k Formula:

t1 2

=

0.693 k

Solution: 34.5 min =

k=

0.693 k

0.693 34.5 min

k =0.020/min

11. Given: 800s ; 0.031 M 0s ; 0.184 M Required: average rate Formula:

average rate=

−∆[reactant ] ∆t

12. 14. 13. 15.Given: Given:200s 500s 800s; ;0.129 0.069 0.031MM Solution: 1200s 1500s 800s 1500s ; ;0.031 ;0.016 0.019 0.016 MMM −( 0.031−0.184 )M Required: Required: average average rate rate average rate=

800 s−∆[reactant −∆[reactant] ] average average rate= rate= Formula: Formula: ∆∆t t Solution: Solution:

16. Given: 150s ; 0.010 M 0s ; 0.026 M Required: average rate Formula:

average rate=

−∆[reactant ] ∆t

19. 18. 17. 20.Given: Given:50s 100s 150s 50s; ;;0.020 0.020 0.014 0.010MM M Solution: 250s 200s 150s 200s; ;0.010 0.006 0.008 0.008MM −( 0.010−0.026 ) M Required: Required: average averagerate rate average rate=

150 s −∆[reactant −∆[reactant] ] average average rate= rate= Formula: Formula: ∆∆t t Solution: Solution:

−−( 0.019−0.129 0.016−0.069 0.031−0.129 ( 0.016−0.031) )MM

−−( 0.008−0.014 0.006−0.010 0.010−0.020 ( 0.008−0.020) M )M

1. A certain second order reaction, A→B, when performed at 25 ° C, is 53% complete after 47 min. What is the rate constant of this reaction? 2. The decomposition of NO2 into NO and O2 has rate constant of 7.8x10-2/M∙s. If the initial concentration is 0.56 M at 3.2 min, what is its final concentration?

3. The decomposition of Carbon Sulfide, CS, and Sulfur is second order with k=2.8x10-2/M∙s at 1000 ° C. If the initial concentration was 0.324M calculate the concentration after 5.90 min. 4. At a given temperature, a first-order reaction has a rate constant of 2.5x10-3/M∙s. Calculate the time required (in seconds) for the reaction to be 63% complete. 5. The half-life for a second-order reaction is 48s. What was the original concentration if its rate constant is 5.19x10-2/M∙s? 6. A certain second order reaction has a rate constant if 3.2x10-2/M∙s at 23 ° C. If the initial concentration

was 0.032M, calculate the concentration after 3 minutes. 7. Calculate the half-life of a certain reaction if its initial concentration is 0.54M and is 0.45/M∙s. 8. The reaction rate constant fir a particular second order reaction is 0.47/M∙s. If the initial concentration of the reaction is 0.53 M, how many seconds will it take for the concentration to decrease to 0.13M? 9. A second-order reaction has a half-life of 10.9 minutes. Calculate the rate constant for this in s-1 if the initial concentration is 0.36M. 10. The half-life of a radioisotope is found to be 6.5 min. If the decay follows second order kinetics, what is its initial concentration if it has a rate constant of 2.56x10-3/M∙s. 11. The reaction A→B is shown to be second-order reaction with the initial concentration of 1.8M. but after 35s, the concentration decreases in 0.73M. What is the rate constant of the reaction? 12.In a second-order reaction, if the rate constant is 1.9x10 -3/M∙s. How long will it take the concentration to fall from 2.8M to 0.8M? 13.The initial concentration of reactant in a second order reaction is 1.36M. The rate constant for the reaction is 0.7M-1s-1. What is the concentration after 3s? 14. If the reaction of ethyl chloride is second order with a constant rate of 0.845/M∙s. What is the concentration of the sample that will remain after 100s if the initial concentration is 0.32M? 15. A second-order reaction has a half-life of 15s when the initial concentration is 0.578M. What is the rate of the reaction? 16. A solution originally at 1.65M under second order reaction is found to be 0.65M after 14 min. What is the half-life? 17. In a second-order reaction of A→B wherein A is 0.4 M initially and becomes 0.02M after a certain time. How long does the reaction take if the constant rate is 0.1/M∙s? 18. Find the rate constant of the decomposition at 70 ° C if the initial concentration is 1.78M and its half-life is 15s. 19. Substance B decomposes by a second order reaction. Starting with 1.21M, after 10s, the produced concentration is 0.4M. What is its rate constant? 20. Calculate the half-life of a certain reaction if its initial concentration is 0.25M and is 0.35/M∙s.

Key to Correction: 1. A certain second order reaction, A→B, when performed at 25 ° C is 53 % complete 63 minutes. What is the rate constant of this reaction? Given: [A]o = 1.00 M [A]t = 0.47 M t = 63 min =3750 s Required: k Formula:

1 1 =k ( 3780 s )+ [0.47 M ] [1 M ]

Solution:

k=5.6x10-4s-1 2. The decomposition of NO2 into NO and O2 has a rate constant of 7.8x10-2M/s. If the initial concentration of reactant is 0.56M at 3.2 min, what is its final concentration? Given: [A]o = 0.56M k = 7.8x10-2/M∙s t = 3.2 min =192 s Required: k Formula:

1 1 −2 =7.8 x 10 /M ∙ s+ [ A ]t [0.56 M ]

Solution:

[A]t =0.06 M 3. The decomposition of Carbon Sulfide, CS2, to Carbon Monosulfide, CS, and sulfur is secondorder with k= 2.9x10-2/M∙s at 1000 ° C. If the initial concentration was 0.324M, calculate the concentration after 5.90 min. Given: [A]o = 0.324M k = 2.9x10-2/M∙s t = 5.90 min = 354s Required: k Formula:

(

)

1 2.9 x 10−2 1 = ∙ s (354 s)+ [ A ]t M [0.324 M ]

Solution:

[A]t =0.08 M 4. At a given temperature, a first-order reactionhas a rate constant of 2.5x10 -3/M∙s. Calculate the time required (in seconds) for the reaction to be 63% complete. Given: [A]o = 1.00 M Required: t [A]t = 0.37 M k= 2.5x10-3/M∙s Formula:

1 1 −2 =(2.5 x 1 0 / M ∙ s)t + [0.37 M ] [1 M ]

Solution:

t=2724s 5. The half-life for a second order reaction is 48s. What was the original concentration if its rate constant is 5.19x10-2/M∙s. Given:

t1

=48s

2

Required: [A]o

k= 5.19x10-2/M∙s Formula:

Solution:

t1 = 2

1 k [ A ]o

48 s=

1 (5.19 x 10 /M ∙ s)[ A ]o

[A]o=0.40M

−2

6. A certain second order reaction has a rate constant if 3.2x10-2/M∙s at 23 ° C. If the initial concentration was 0.032M, calculate the concentration after 3 minutes. Given: [A]o = 0.032M k = 3.2x10-2/M∙s t = 3 min = 180s Required: k Formula:

(

)

1 3.2 x 1 0−2 1 = ∙ s (180 s)+ [ A ]t M [0.032 M ]

Solution:

[A]t =0.03 M 7. Calculate the half-life of a certain reaction if its initial concentration is 0.54M and is 0.45/M∙s. Given: [A]o=0.54M k= 4.5x109/M∙s

t1

Required:

2

t1 =

Formula:

2

1 k [ A ]o

t1 =

Solution:

2

1 (0.45/ M ∙ s )[0.54 M ]

t1 2

=4.12x10-2s

8. The reaction rate constant fir a particular second order reaction is 0.47/M∙s. If the initial concentration of the reaction is 0.53 M, how many seconds will it take for the concentration to decrease to 0.13M? Given: [A]o = 0.53 M [A]t = 0.13M k= 0.47/M∙s Required: t Formula:

1 1 =(0.47 / M ∙ s)t + [0.13 M ] [0.53 M ]

Solution:

t=12.35s 9. A second-order reaction has a half-life of 10.9 minutes. Calculate the rate constant for this in s-1 if the initial concentration is 0.36M. Given:

t1

=10.9 min =654s

2

[A]o = 0.36M Required: k

t1 =

Formula:

2

1 k [ A ]o

654 s=

Solution:

1 (k )[0.36 M ]

k=4.25x10-3/M∙s 10. The half-life of a radioisotope is found to be 6.5 min. If the decay follows second order kinetics, what is its initial concentration if it has a rate constant of 2.56x10-3/M∙s Given:

t1

=6.5 min=390s

2

k= 2.56x10-3/M∙s Required: [A]o Formula:

Solution:

t1 = 2

1 k [ A ]o

390 s=

1 (2.56 x 1 0 /M ∙ s)[ A ]o

[A]o=1.00M

−3

11. The reaction A→B is shown to be second-order reaction with the initial concentration of 1.8M. but after 35s, the concentration decreases in 0.73M. What is the rate constant of the reaction? Given: [A]o = 1.8M [A]t = 0.73M t = 35s Required: k Formula:

1 1 =k ( 35 s )+ [0.73 M ] [1.8 M ]

Solution:

k=0.03/M∙s 12.In a second-order reaction, if the rate constant is 1.9x10 -3/M∙s. How long will it take the concentration to fall from 2.8M to 0.8M? Given: [A]o = 2.8M [A]t = 0.8M M k= 1.9x10-3/M∙s Required: t Formula:

1 1 −3 =(1.9 x 1 0 / M ∙ s )t + [0.8 M ] [2.8 M ]

Solution:

t=470 s 13.The initial concentration of reactant in a second order reaction is 1.36M. The rate constant for the reaction is 0.7M-1s-1. What is the concentration after 3s? Given: [A]o = 1.36M k = 0.7M-1s-1 t = 3s Required: k Formula:

1 1 −1 −1 =(0.7 M s )(3 s)+ [ A ]t [1.36 M ]

Solution:

[A]t =0.35 M 14.If the reaction of ethyl chloride is second order with a constant rate of 0.845/M∙s. What is the concentration of the sample that will remain after 100s if the initial concentration is 0.32M? Given: [A]o = 0.32M k = 0.845/M∙s t = 100s Required: k Formula:

1 1 =(0.845/ M ∙ s)(100 s)+ [ A ]t [0.32 M ]

Solution:

[A]t =0.011 M 15.A second-order reaction has a half-life of 15s when the initial concentration is 0.578M. What is the rate constant of the reaction? Given:

t1

=15 s

2

[A]o = 0.578M Required: k Formula: Solution:

t1 = 2

1 k [ A ]o

15 s=

1 (k)[0.578 M ]

k=0.115/M∙s 16. A solution originally at 1.65M under second order reaction is found to be 0.65M after 14 min. What is the half-life? Given: [A]o=1.65M [A]t=0.65M

t=14 min

t1

Required:

2

t1 =

Formula:

2

1 k [ A ]o

1

Solution: [ 0.65 M ]

=k (14 min ) +

1 [ 1.65 M ]

k=0.07/M∙min

t1 = 2

1 (0.07/ M ∙ min)[1.65 M ]

t1 2

=8.66 min

17. In a second-order reaction of A→B wherein A is 0.4 M initially and becomes 0.02M after a certain time. How long does the reaction take if the constant rate is 0.1/M∙s? Given: [A]o = 0.4 M [A]t = 0.02M k= 0.1/M∙s Required: t Formula:

1 1 =(0.1/ M ∙ s )t + [0.02 M ] [0.02 M ]

Solution:

t=475s

18.Find the rate constant of the decomposition at 70 ° C if the initial concentration is 1.78M and its half-life is 15s. Given:

t1

=15 s

2

[A]o = 1.78M Required: k Formula: Solution:

t1 = 2

1 k [ A ]o

15 s=

1 (k)[1.78 M ]

k=0.04/M∙s 19. Substance B decomposes by a second order reaction. Starting with 1.21M, after 10s, the produced concentration is 0.4M. What is its rate constant? Given: [A]o = 1.21M [A]t = 0.4M t = 10s Required: k Formula: Solution:

1 1 =k ( 10 s ) + [ 0.4 M ] [1.21 M ]

k=0.167/M∙s 20. Calculate the half-life of a certain reaction if its initial concentration is 0.25M and is 3.5x109/M∙s. Given: [A]o=0.25M k= 0.35/M∙s

t1

Required: Formula:

Solution:

2

t1 = 2

1 k [ A ]o

t1 = 2

1 (0.35/ M ∙ s )[ 0.25 M ]

t1 2

=11.43