Consider a reaction $a G+b H ightarrow$ Products. When concentration of both the reactants $G$ and $H$ is…

Consider a reaction $a G+b H ightarrow$ Products. When concentration of both the reactants $G$ and $H$ is doubled, the rate increases by eight times. However, when concentration of $G$ is doubled keeping the concentration of $H$ fixed, the rate is doubled. The overall order of the reaction is
  1. 0
  2. 1
  3. 2
  4. 3

Solution

Overall order $=$ sum of orders w.r.t each reactant.
Let the order be $x$ and $y$ for $\mathrm{G}$ and $\mathrm{H}$ respectively
$\begin{array}{|c|c|c|c|}
\hline \text{Exp.No.} & \text{[G]mole litre} ^{-1} & \text{[H]mole litre} ^{-1} & \text{rate(mole litre} ^{-} \text{ time} ^{-1} ) \\
\hline 1 & a & b & r \\
2 & 2 a & 2 b & 8 r \\
3 & 2 a & b & 2 r \\
\hline
\end{array}$
$\because$ For (1) and (3), the rate is doubled when conc. of G is doubled keeping that of H constant i.e.,
rate $\propto[\mathrm{G}] \therefore x=1$
From (2) and (3), $\mathrm{y}=2$
$\therefore$ Overall order is 3.

Asked in: JEE-TOPICTESTS-CHEMISTRY

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