Question

2. At 500 °C, cyclopropane (C3H6) rearranges to propene (CH3CH=CH2):   C3H6 (g) ------> CH3CH=CH2 (g)

The reaction is first order and the rate constant is 6.7 x 10-4 s-1. (a) What is the rate law for the reaction, and; (b) if the initial concentration of C3H6 is 0.100 M, what is the concentration of cyclopropane of after 20 min?

3. Butadiene (C4H6) reacts with itself at 250 °C to form a dimer with the formula C8H12.

2 C4H6 (g) ----> C₈H₁₂ (l)

The reaction is second order in C4H6. (a) What is the rate law for the reaction, and; (b) if the rate constant is 4.0 x 10-2 M-1.s-1, and the initial concentration of C₄H₆ is 0.200 M, how long will it take for the concentration of C4H6 to reach 0.04 M?

4.    a) In Q. 2 above what is the half life for the reaction and what is concentration of C₃H₆ after 3 half-lives

  

   b) In Q. 3 above how long are the first and second half-lives?

Answer 1

C3H6 (g) ------> CH3CH=CH2 (g)

rate law

rate = K[C3H6]¹

t     = 20min = 20*60 = 1200sec

K = 2.303/t log[A0]/[A]

6.7*10^-4 = 2.303/1200 log0.1/[A]

log0.1/[A]   = 6.7*10^-4 *1200/2.303

                   = 3491.1*10^-4

log0.1/[A]    = 0.34911

    0.1/[A]    = 10^0.34911

    0.1/[A]    = 2.2341

         [A]    = 0.1/2.2341 = 0.04476M

3. 2 C4H6 (g) ----> C₈H₁₂ (l)

      rate = k[C4H6]²  

K = 1/t [1/[A0] -1/[A]

t   = 1/K [1/[A] -1/[A0] ]

    = 1/4*10^-2 [1/0.04 -1/0.2]

     =25*(25-5)

     = 500sec

4. no of half live = total time/half life time

              3             = 1200/half live time

             half life time = 1200/3 = 400sec

b. 1 = total time /400

   time = 400sec

    2   = total time/400

   time   = 800sec