If the concentration of a reactant is reduced to half, the rate of re…

The correct answer is Option (3) → 2

For a reaction with rate \( = k[\mathrm{A}]^{n} \), the rate depends on the concentration raised to the power n, the order of the reaction. If the concentration changes by a factor, the rate changes by that factor raised to the power n:

    \( \displaystyle \frac{r_2}{r_1} = \left(\frac{[\mathrm{A}]_2}{[\mathrm{A}]_1}\right)^{n} \)

Here the concentration is halved and the rate becomes one-fourth:

    \( \displaystyle \frac{1}{4} = \left(\frac{1}{2}\right)^{n} \)

    \( \displaystyle \left(\frac{1}{2}\right)^{2} = \left(\frac{1}{2}\right)^{n} \Rightarrow n = 2 \)

So the reaction is of second order.