At 500 C, cyclopropane (C3H6) rearranges to propene (CH3CH=CH2). The reaction is

Question

At 500 C, cyclopropane (C3H6) rearranges to propene (CH3CH=CH2). The reaction is first order, and the rate constant is 6.7×104s1. If the initial concentration of C3H6 is 4.50×102 M . What is the molarity of C3H6 after 30 min ?

Plutonium-239 has a decay constant of 2.88×105year1. After 2.30×104 years?

Butadiene (C4H6) reacts with itself to form a dimer with the formula (C8H12). The reaction is second order in C4H6. If the rate constant at a particular temperature is 4.0×102M1s1. What is the half-life (in minutes) of this reaction when the initial C4H6 concentration is 1.60×102 M? How many minutes does it take for the concentration of C4H6 to drop from 1.20×102 M to 6.00×103 M ?

Explanation / Answer

part 1 ) for first order reaction

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

K = 6.7 x 10-4 s-1

[A0] = 4.50 x 10-2 M , [A] = ?

t = 30 min = 1800 s

6.7 x 10-4 = (2.303 / 1800) log [4.50 x 10-2] / [A]

0.524 = - 1.35 - log [A]

log [A] = - 1.874

[A] = 1.34 x 10-2 M

part 3 ) for second order reaction

t1/2 = 1 / K [A0]

t1/2 = 1 / 4.0 x 10-2 [1.60 x 10-2]

t1/2 = 1 / 0.00064

t1/2 = 1562.5 s

t1/2 = 26.04 min

for second order kinetics

1 / [A] = Kt + 1/[A0]

1 / [6.00 x 10-3] = 4.0 x 10-2 x t + 1/ [1.20 x 10-2]

166.7 = 4.0 x 10-2 x t + 83.3

4.0 x 10-2 x t = 83.4

t = 2085 s

t = 34.75 min

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