In the following reaction
Question:

In the following reaction $: x \mathrm{~A} \rightarrow y \mathrm{~B}$

$\log _{10}\left[-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}\right]=\log _{10}\left[\frac{\mathrm{d}[\mathrm{B}]}{\mathrm{dt}}\right]+0.3010$

‘A’ and ‘B’ respectively can be:

  1. $n$-Butane and Iso-butane

  2. $\mathrm{C}_{2} \mathrm{H}_{2}$ and $\mathrm{C}_{6} \mathrm{H}_{6}$

  3. $\mathrm{C}_{2} \mathrm{H}_{4}$ and $\mathrm{C}_{4} \mathrm{H}_{8}$

  4. $\mathrm{N}_{2} \mathrm{O}_{4}$ and $\mathrm{NO}_{2}$


Correct Option: , 3

Solution:

$x A \rightarrow y B$

$\therefore \quad \frac{-\mathrm{d} \mathrm{A}}{\mathrm{xdt}}=\frac{1}{\mathrm{y}} \frac{\mathrm{dB}}{\mathrm{dt}}$

$\frac{-\mathrm{d} \mathrm{A}}{\mathrm{dt}}=\frac{\mathrm{dB}}{\mathrm{dt}} \times \frac{\mathrm{x}}{\mathrm{y}}$

$\log \left[\frac{-\mathrm{d} \mathrm{A}}{\mathrm{dt}}\right]=\log \left[\frac{\mathrm{dB}}{\mathrm{dt}}\right]+\log \left(\frac{\mathrm{x}}{\mathrm{y}}\right)$

Comparing this equation with the equation given in question. We get,

$\log \frac{x}{y}=0.3010$ or $\log \frac{x}{y}=\log 2$

$\therefore \quad \frac{x}{y}=2$

$\therefore$ The reaction is of type $2 \mathrm{~A} \rightarrow \mathrm{B}$.

Hence, option (3) is correct.

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