Question

The unsaturated hydrocarbon butadiene (C4H6) dimerizes to 4-vinylcyclohexene (C8H12). When data collected in studies of the kinetics of this reaction were plotted against reaction time, plots of [C4H6] or ln[C4H6] produced curved lines, but the plot of 1/[C4H6] was linear.
a) What is the rate law for the reaction?

Answer 1

Answer:

The dimerization of butadiene to 4-vinylcyclohexene folows second order kinetics and its rate law will be given by :

$R=k[C_4H_6]^2$

Explanation:

$2C_4H_6\rightarrow C_8H_{12}$

The rate of the reaction ;

$R=k[C_4H_6]^x$

As given in the question , that graph of time verses $\frac{1}{[C_4H_6]}$ was linear but plots of $[C_4H_6]$ or $\ln[C_4H_6]$  was curved.

Generally:

Graph of time verses $[concentration]$ for zero order reaction is linear with negative slope.

Graph of time verses $\ln [concentration]$ for secon order reaction is linear with negative slope.

Graph of time verses $\frac{1}{[concentration]}$ for secon order reaction is linear with positive slope.

So, the dimerization of butadiene to 4-vinylcyclohexene folows second order kinetics and its rate law will be given by :

$R=k[C_4H_6]^2$