Answer to Question #968 in Organic Chemistry for bami

Question

& Butadiene (C[sub]4[/sub]H[sub]6[/sub]) reacts with itself at 250 °C to form a dimer with the formula C[sub]8[/sub]H[sub]12[/sub].
2 C[sub]4[/sub]H[sub]6[/sub] (g) ----> C[sub]8[/sub]H[sub]12 [/sub](l)
The reaction is second order in C[sub]4[/sub]H[sub]6[/sub].
(a) What is the rate law for the reaction, and;
(b) if the rate constant is 4.0 x 10[sup]-2[/sup] M[sup]-1[/sup]& s[sup]-1[/sup], and the initial concentration of C[sub]4[/sub]H[sub]6[/sub] is 0.200 M, how long will it take for the concentration of C[sub]4[/sub]H[sub]6[/sub] to reach 0.04 M?

Answer 1

a. The rate law for the reaction:
1/[C₄H₆] - 1/[C₄H₆]₀ = kt
b. The intial concentration is 0.200 M, and the final concentration is 0.200 M. K is 0.84 L/mol min, so

1/0.040 M - 1/0.200 M = 4.0 x 10^-2 M^-1 s^-1 * t
t = 500 s = 8.33 min.