Chemical Kinetics - Result Question 2

####2. In the following reaction; $x A \rightarrow y B$

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

$A$ and $B$ respectively can be

(2019 Main, 12 April I)

(a) n-butane and iso-butane

(b) $C _2 H _2$ and $C _6 H _6$

(c) $C _2 H _4$ and $C _4 H _8$

(d) $N _2 O _4$ and $NO _2$

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Answer:

Correct Answer: 2. (c)

Solution:

  1. In the given reaction; $x A \longrightarrow y B$

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

Value of $\log 2=0.3010$

Substituting 0.3010 by $\log 2$

$$ \log _{10}\left[-\frac{d[A]}{d t}\right]=\log _{10}\left[\frac{d[B]}{d t}\right]+\log 2 $$

Using logarithm rules,

$$ \left[\frac{-d[A]}{d t}\right]=2 \times\left[\frac{d[B]}{d t}\right] \Rightarrow-\frac{1}{2}\left[\frac{d[A]}{d t}\right]=\left[\frac{d[B]}{d t}\right] $$

Using the rate equation (i) to determine the reaction involved is

$$ 2 A \longrightarrow B $$

Option that fits correct in the above reaction is (c).

$$ 2 C _2 H _4 \longrightarrow C _4 H _8 $$



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