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?

Explanation:

From the rate law:

where

Note the negative sign in front of the right hand side of the equation. Rearrange the rate law expression to separate the two variables,

Implicitly integrate both sides of the expression (with the power rule) to obtain the general expression (i.e., the one with the arbitary constant "") for concentration at given time :

Now, solve for the value of for this particular configuration (i.e., with an initial, concentration , as seen in the question)

Thus, the concentration at time given an initial concentration of would be

where again, the time into the reaction in seconds.

The question is asking for the concentration at

Reference:

Lannah Lua, Ciara Murphy, and Victoria Blanchard, "Second-Order Reactions," Libretext Chemistry