Butadiene, C₄H₆ (used to make synthetic rubber and latex paints), dimerizes to C₈H₁₂ with a rate law of rate = 0.014 L/mol• s [C₄H₆]². What will be the concentration of C₄H₆ after 3.0 hours if the initial concentration is 0.025 M?

Question

Quizplus · Accepted Answer

The rate law can be used to set up a differential equation for the concentration of butadiene as a function of time: $\frac{d[CS_4H_6]}{dt}=-k[CS_4H_6]^2$ Separating variables and integrating: $\int_{[CS_4H_6]_0}^{[CS_4H_6]} \frac{d[CS_4H_6]}{[CS_4H_6]^2}=-\int_0^t kdt$ $-\frac{1}{[CS_4H_6]}+\frac{1}{[CS_4H_6]_0}=kt$ Solving for [C₄H₆] and plugging in the given values: $[CS_4H_6]=\frac{1}{\frac{1}{[CS_4H_6]_0}+kt}$ $[CS_4H_6]=\frac{1}{\frac{1}{0.025 M}+(0.014 L/mol\cdot s)(0.025 M)^2\cdot 10800 s}$ $[CS_4H_6]=0.0052 M$ Therefore, the answer is A, 0.0052 M.

Butadiene, C4H6 (Used to Make Synthetic Rubber and Latex Paints)

Butadiene, C₄H₆ (Used to Make Synthetic Rubber and Latex Paints)