Determine reaction order of Cyclopentadiene


> 
> Reaction: $\ce{2 C5H6 -> C10H12}$
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> For this reaction it is stated that $\pu{0.609 M}$ cyclopentadiene was formed in an ethanol solution. When the solution was heated $(\pu{40 ^\circ C})$ and dicyclopentadiene was formed. The amount of dicyclopentadiene after time/h was:
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> 
> $$
> \begin{array}{lr}
> \hline
> \text{time}/\pu{h} & c/\pu{M} \\
> \hline
> 6 & \pu{0.017} \\
> 24 & \pu{0.059} \\
> 48 & \pu{0.099} \\
> 78 & \pu{0.135} \\
> 143 & \pu{0.18} \\
> 167 & \pu{0.191} \\
> 192 & \pu{0.201} \\
> \hline
> \end{array}
> $$
> 
> 
> 


When given data like this, i.e. the concentration for dicyclopentadiene and not cyclopentadiene, do I have to convert the concentration to the concentration of cyclopentadiene? And in that case, will the concentration of cyclopentadiene at each of given time become:


$$ [\ce{C5H6}] = 0.609 - 2x$$


where $x$ is the concentration of dicyclopentadiene at each of corresponding time?




Yes. You are right. The concentration of cyclopentadiene is equal to $c=0.609−2x$. And afterwards, you should plot the natural logarithm of this concentration c vs. time. If the points are well alined, the order is $1$. If the alinement is not good, plot the inverse $1/c$ versus time. If the points are well alined, the order is $2$. In both cases the slope of the line is the rate constant $k\_1$ or $k\_2$


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