The rate of reaction between two reactants $\mathrm{A}$ and $\mathrm{B}$ decreases by a factor of 4 if the…

The rate of reaction between two reactants $\mathrm{A}$ and $\mathrm{B}$ decreases by a factor of 4 if the concentration of reactant $B$ is doubled. The order of this reaction iwth respect is reactant $\mathrm{B}$ is:
  1. 2
  2. -2
  3. 1
  4. -1

Solution

Rate of reaction $=\mathrm{K}\left[\mathrm{A}_0\right]^\alpha\left[\mathrm{B}_0\right]^\beta$ $\begin{aligned} {[\mathrm{B}] } & =2\left[\mathrm{~B}_0\right] \\ \frac{r_1}{r_2} & =\frac{\mathrm{K}\left[\mathrm{A}_0\right]^\alpha\left[\mathrm{B}_0\right]^\beta}{\left[\mathrm{A}_0\right]^\alpha\left[2 \mathrm{~B}_0\right]^\beta} ; \\ 4 & =\left(\frac{1}{2}\right)^\beta=\beta=-2 . \end{aligned}$

Asked in: NEET 2005

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