At 500 degree C, cyclopropane (C3H6) rearranges to propene (CH3CH=CH2): The reac

Question

At 500 degree C, cyclopropane (C3H6) rearranges to propene (CH3CH=CH2): The reaction is first order and the rate constant is 6.7 times 10-4 s-1. 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? Butadiene (C4H6) reacts with itself at 250 degree C to form a dimer with the formula C8H12. 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 times 10-2 M-1 .s-1. and the initial concentration of C_4H_6 is 0.200 M, how long will it take for the concentration of C4H6 to reach 0.04 M? In Q. 2 above what is the half life for the reaction and what is concentration of C_3H_6 after 3 half-lives In Q. 3 above how long are the first and second half-lives?

Explanation / Answer

Since the reaction is first order reaction , the rate law is rate = k[C3H6] ----(1)

For a first order reaction rate constant , k = ( 2.303 /t )x log ( Mo / M)

Where

Mo = initial concentration = 0.10 M

M= concentration after time t = ?

t = time = 20 min = 20 min x 60 s/min = 1200 s

k = rate constant = 6.7x10-4 s-1

Plug the values we get

log ( Mo / M) = (kt) / 2.303

= 0.349

( Mo / M) = 10 0.349 = 2.234

M = Mo / 2.234

= 0.100 / 2.234

= 0.045 M

Therefore the concentration after 20 min is 0.045 M

Simillarly the second one

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