For the reaction $\mathrm{A}+\mathrm{B} \longrightarrow$ products, it is observed that: (1) On doubling the…

For the reaction $\mathrm{A}+\mathrm{B} \longrightarrow$ products, it is observed that:
(1) On doubling the initial concentration of $\mathrm{A}$ only, the rate of reaction is also doubled and
(2) On doubling the initial concentrations of both A and B, there is a change by a factor of 8 in the rate of the reaction. The rate of this reaction is given by:
  1. rate $=\mathrm{k}[\mathrm{A}][\mathrm{B}]^{2}$
  2. rate $=\mathrm{k}[\mathrm{A}]^{2}[\mathrm{~B}]^{2}$
  3. rate $=\mathrm{k}[\mathrm{A}][\mathrm{B}]$
  4. rate $=\mathrm{k}[\mathrm{A}]^{2}[\mathrm{~B}]$

Solution

When concentration of $\mathrm{A}$ is doubled, rate is doubled. Hence order with respect to $\mathrm{A}$ is one. When concentrations of both $\mathrm{A}$ and $\mathrm{B}$ are doubled, rate increases by 8 times hence order with respect to $\mathrm{B}$ is 2 .
$\therefore$ rate $=\mathrm{k}[\mathrm{A}]^{1}[\mathrm{~B}]^{2}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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