what will be the butadiene concentration after 71.0 min?

Question

Butadiene reacts to form a dimer according to the equation 2C₄H₆(g) → C₈H₁₂(g) The reaction obeys the second order rate law, Rate = k[C₄H₆]², with a rate constant k = 3.68 M⁻¹min⁻¹ at a certain temperature. Starting with an initial concentration of [C₄H₆] = 0.0500 M, what will be the butadiene concentration after 71.0 min?

Answer 1

2C4H6(g) ==> C8H12(g)

Rate = k[C4H6]² ... k = 3.68 M^-1min^-1

[C4H6]_o = 0.0500 M

?[C4H6] after 71.0 min

Integrated rate law for a 2nd order reaction is 1/[A] = 1/[A]_o + kt

Solving for [A], we have ...

1/[A] = 1/0.05 M + (3.68 M^-1min^-1)(71.0 min)

1/[A] = 20 + 261 = 281

[A] = 0.00356 M