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Chemical Kinetics Problems with solutions>Expressing rate of reaction>First-order reaction>Second-order reaction

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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) + 2H2O7. 2H2S(g) + 3O2(g) 2H2O(l) + 2SO2(g)8. 2C2H6(g) + 7O2(g) 4CO2 + 6 H2O9. 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)

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)

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 20C. What is its rate constant?4. In a given first-order reaction AB, 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 75C. 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 274C.. It was observed that its half-life is 19s. Determine the amount after 100s.11. The reaction 2AB is first order in A with a rate constant if 4.8x10-2s-1 at 65C. How long will it take for A to decrease from 0.75M to 0.15M?s12. 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 500C. 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 AB, 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 65C 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 = 29Mt = 10minRequired: kFormula: ln[A]t = -kt + ln[A]oSolution: ln[29M]=-k(10min)+ln[50M]2. What is the value of the rate constant for a first order reaction for which half-life is 29.75 minutes?Given: = 29.75 minRequired: kFormula: =Solution: 29.75min=3. A certain first order reaction is 53% complete in 30 min. at 20C. What is its rate constant?Given: [A]o = 100M[A]t = 47Mt = 30 minRequired: kFormula: ln[A]t = -kt + ln[A]oSolution: 4. In a given first-order reaction AB, the initial concentration is 0.385 molar. What will be the concentration after 45 seconds with half-life of 19 seconds?Given: = 19 st = 45 sRequired: [A]tFormula: ln[A]t = -kt + ln[A]oSolution: ln[A]t = -(0.036/s)(45 s+ ln[0.385M]= -2.57[A]t = e-2.57 = 0.08 M5. 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 = 50Mt = 10minRequired: kFormula: ln[A]t = -kt + ln[A]oSolution ln[A]t =-(1.5/s)(3 s)+ln[3 M]=-3.40 [A]t=e-3.40 =0.03M6. 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 = 0.26Mk=0.1x10-3s-1 Required: tFormula: ln[A]t = -kt + ln[A]oSolution: -(0.1x10-3s-1)t

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 = 0.81Mt = 1 sRequired: [A]tFormula: ln[A]t = -kt + ln[A]oSolution 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: = 26.54 hrsRequired: kFormula: =Solution: 26.54 hr=

9. The rate constant at 75C. for the decomposition of its first order is 0.636 per second. Determine the half-life of its reaction.Given: Required: Formula: =Solution: =

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 274C.. It was observed that its half-life is 19s. Determine the amount after 100s.Given: = 19 st = 100 s[A]o=0.397MRequired: [A]tFormula: ln[A]t = -kt + ln[A]oSolution: ln[A]t = -(0.036/s)(100 s+ ln[0.397M]= -4.5[A]t = e-4.5 = 0.01 M

11. The reaction 2AB is first order in A with a rate constant if 4.8x10-2s-1 at 65C. How long will it take for A to decrease from 0.75M to 0.15M?sGiven: [A]o = 0.75M[A]t = 0.15Mk=4.8x10-2s-1Required: tFormula: ln[A]t = -kt + ln[A]oSolution: -(4.8x10-2s-1)t

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 = 0.75Mt = 25 sRequired: [A]tFormula: ln[A]t = -kt + ln[A]oSolution 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 500C. if the initial concentration of reaction was 0.38M. What is the concentration after 150 seconds?Given: k= 5.3x10-4s-1[A]o = 0.38Mt = 150 sRequired: [A]tFormula: ln[A]t = -kt + ln[A]oSolution 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 = 17Mt = 15min = 900sRequired: kFormula: ln[A]t = -kt + ln[A]oSolution: ln[17M]=-k(900 s)+ln[45 M] =-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: = 32.5 min Required: kFormula: =Solution: 32.5 min =

16. In a given first-order reaction AB, 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 Mt = 30 sRequired: [A]tFormula: ln[A]t = -kt + ln[A]oSolution 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 65C for the decomposition at its first order is 2.42x10-2s-1. Determine the half-life of its reaction?Given: = 2.42x10-2s-1Required: Formula: =Solution: =

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 = 0.75Mk=1.2x10-3s-1Required: tFormula: ln[A]t = -kt + ln[A]oSolution: -(1.2x10-3s-1)t

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 Mt = 5.6 minRequired: [A]tFormula: ln[A]t = -kt + ln[A]oSolution 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: = 34.5 min Required: kFormula: =Solution: 34.5 min =

16. Given: 150s ; 0.010 M0s ; 0.026 M Required: average rateFormula: Solution: =1.07x10-4 M/s 11. Given: 800s ; 0.031 M0s ; 0.184 M Required: average rateFormula: Solution: =1.9x10-4 M/s

20. Given: 50s ; 0.020 M200s ; 0.008 M Required: average rateFormula: Solution: =8x10-5 M/s 14. Given: 200s ; 0.129 M1200s ; 0.019 M Required: average rateFormula: Solution: =1.1x10-4 M/s19. Given: 150s ; 0.010 M250s ; 0.006 M Required: average rateFormula: Solution: =4x10-5 M/s 15. Given: 800s ; 0.031 M1500s ; 0.016 M Required: average rateFormula: Solution: =2.14x10-5 M/s18. Given: 100s ; 0.014 M200s ; 0.008 M Required: average rateFormula: Solution: =6x10-5 M/s13. Given: 500s ; 0.069 M1500s ; 0.016 M Required: average rateFormula: Solution: =5.3x10-5 M/s12. Given: 200s ; 0.129 M800s ; 0.031 M Required: average rateFormula: Solution: =1.63x10-4 M/s17. Given: 50s ; 0.020 M150s ; 0.010 M Required: average rateFormula: Solution: =1x10-4 M/s

1. A certain second order reaction, AB, when performed at 25C, 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/Ms. 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/Ms at 1000C. 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/Ms. 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/Ms?6. A certain second order reaction has a rate constant if 3.2x10-2/Ms at 23C. 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/Ms.8. The reaction rate constant fir a particular second order reaction is 0.47/Ms. 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/Ms.11. The reaction AB 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/Ms. 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/Ms. 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 AB 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/Ms?18. Find the rate constant of the decomposition at 70C 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/Ms.

Key to Correction:1. A certain second order reaction, AB, when performed at 25C is 53 % complete 63 minutes. What is the rate constant of this reaction?Given: [A]o = 1.00 M[A]t = 0.47 Mt = 63 min =3750 sRequired: kFormula:

Solution: k=5.6x10-4s-12. 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 = 0.56Mk = 7.8x10-2/Mst = 3.2 min =192 sRequired: kFormula:

Solution: [A]t =0.06 M3. The decomposition of Carbon Sulfide, CS2, to Carbon Monosulfide, CS, and sulfur is second-order with k= 2.9x10-2/Ms at 1000C. If the initial concentration was 0.324M, calculate the concentration after 5.90 min.Given: [A]o = 0.324Mk = 2.9x10-2/Mst = 5.90 min = 354sRequired: kFormula:

Solution: [A]t =0.08 M4. At a given temperature, a first-order reactionhas a rate constant of 2.5x10-3/Ms. Calculate the time required (in seconds) for the reaction to be 63% complete.Given: [A]o = 1.00 MRequired: t[A]t = 0.37 Mk= 2.5x10-3/MsFormula:

Solution: t=2724s5. The half-life for a second order reaction is 48s. What was the original concentration if its rate constant is 5.19x10-2/Ms.Given: =48sRequired: [A]ok= 5.19x10-2/Ms Formula:Solution: [A]o=0.40M6. A certain second order reaction has a rate constant if 3.2x10-2/Ms at 23C. If the initial concentration was 0.032M, calculate the concentration after 3 minutes.Given: [A]o = 0.032Mk = 3.2x10-2/Mst = 3 min = 180sRequired: kFormula:

Solution: [A]t =0.03 M7. Calculate the half-life of a certain reaction if its initial concentration is 0.54M and is 0.45/Ms.Given: [A]o=0.54Mk= 4.5x109/MsRequired: Formula:Solution: =4.12x10-2s8. The reaction rate constant fir a particular second order reaction is 0.47/Ms. 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 = 0.13Mk= 0.47/MsRequired: tFormula:

Solution: t=12.35s9. 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: =10.9 min =654s[A]o = 0.36MRequired: kFormula:Solution: k=4.25x10-3/Ms10. 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/MsGiven: =6.5 min=390sk= 2.56x10-3/Ms Required: [A]oFormula:Solution: [A]o=1.00M

11. The reaction AB 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 = 0.73Mt = 35s Required: kFormula:

Solution: k=0.03/Ms12. In a second-order reaction, if the rate constant is 1.9x10-3/Ms. How long will it take the concentration to fall from 2.8M to 0.8M?Given: [A]o = 2.8M[A]t = 0.8M Mk= 1.9x10-3/MsRequired: tFormula:

Solution: t=470 s13. 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 = 1.36Mk = 0.7M-1s-1t = 3sRequired: kFormula:

Solution: [A]t =0.35 M14. If the reaction of ethyl chloride is second order with a constant rate of 0.845/Ms. What is the concentration of the sample that will remain after 100s if the initial concentration is 0.32M?Given: [A]o = 0.32Mk = 0.845/Mst = 100sRequired: kFormula:

Solution: [A]t =0.011 M15. 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: =15 s[A]o = 0.578MRequired: kFormula:Solution: k=0.115/Ms16. 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=0.65Mt=14 minRequired: Formula:Solution: k=0.07/Mmin =8.66 min17. In a second-order reaction of AB 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/Ms?Given: [A]o = 0.4 M[A]t = 0.02Mk= 0.1/MsRequired: tFormula:

Solution: t=475s18. Find the rate constant of the decomposition at 70C if the initial concentration is 1.78M and its half-life is 15s.Given: =15 s[A]o = 1.78MRequired: kFormula:Solution: k=0.04/Ms19. 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 = 0.4Mt = 10s Required: kFormula:

Solution: k=0.167/Ms20. Calculate the half-life of a certain reaction if its initial concentration is 0.25M and is 3.5x109/Ms.Given: [A]o=0.25Mk= 0.35/MsRequired: Formula:Solution: =11.43