The half-life period of a $second$ order reaction is:

  • A
    Proportional to the initial concentration of reactants
  • B
    Independent of the initial concentration of reactants
  • C
    Inversely proportional to the initial concentration of reactants
  • D
    Inversely proportional to the square of the initial concentration of reactants

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Total order of reaction $X + Y \rightarrow XY$ is $3$. The order of reaction with respect to $X$ is $2$. State the differential rate equation for the reaction.

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Rate law for a reaction between $A$ and $B$ is given by $R=k[A]^{n}[B]^{m}$. If concentration of $A$ is doubled and concentration of $B$ is halved from their initial value,the ratio of new rate of reaction to the initial rate of reaction $\left(\frac{r_2}{r_1}\right)$ is

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