Question

Trans-1,2-dideuterocyclopropane $\left(A\right)$ undergoes a first-order decomposition. The observed rate constant at a certain temperature measured in terms of disappearance of '$A$' has $1.52\times {10}^{-4}{sec}^{-1}$. Analysis of products showed that the reaction followed two parallel paths, one leading to dideuteropropane $\left(B\right)$ and the other to cis-1,2-dideuterocyclopropane $\left(C\right)$. $\left(B\right)$ was found to constitute $11.2$% of the reaction product, independently of the extent of reaction. What is the order of reaction for each path and what is the value of the rate constant for the formation of each of the products?

Answer 1

$B\stackrel{11.2\%}{\leftarrow }A\stackrel{88.8\%}{\to }C$

In case of parallel path reaction,
$k_B=k_A\times$ fractional yield of $B$
$=1.52\times {10}^{-4}\times 0.112=1.7\times {10}^{-5}{sec}^{-1}$
$k_C=k_A\times$ fractional yield of $C$
$=1.52\times {10}^{-4}\times 0.888=1.35\times {10}^{-4}{sec}^{-1}$
The reaction will be first order for each individual path.