• question_answer $(aq)\xrightarrow{{}}B(aq)+C(aq)$ is a first order reaction. Time t $\infty$ Moles of reagent ${{x}_{1}}$ ${{x}_{2}}$ Reaction progress is measured with the help of titration of reagent P, if all A, B and C reacted with reagent have n factors $\left[ \text{n factor}:n=\frac{mol.wt.}{eq.wt.} \right]$ in the ratio 1 : 2 : 3 with the reagent. The k in terms of t, ${{x}_{1}}$ and ${{x}_{2}}$ is A) $k=\frac{1}{t}\ln \left( \frac{{{x}_{2}}}{{{x}_{2}}-{{x}_{1}}} \right)$  B) $k=\frac{1}{t}\ln \left( \frac{2{{x}_{2}}}{{{x}_{2}}-{{x}_{1}}} \right)$ C) $k=\frac{1}{t}\ln \left( \frac{4{{x}_{2}}}{5({{x}_{2}}-{{x}_{1}})} \right)$ D) $k=\frac{1}{t}\ln \left( \frac{8{{x}_{2}}}{{{x}_{2}}-{{x}_{1}}} \right)$

Solution :

Idea This problem includes conceptual basis of kinetics of chemical reaction while solving this problem, students are advised to follow the steps
 Write the chemical reaction.
 Write the concentration of each species below it.
 Calculate the value of ${{x}_{1}}$ and ${{x}_{2}}$ using information supplied in the question.
 Now, put the values in first order rate equation then come to the correct conclusion.
Let n is the moles of reagent P when P is reacted with A at time t = 0

 $A\xrightarrow{{}}B+C$ t = 0 x 0 0 At $t=t$ $n-x$ $2x$ $3x$ At $t=\infty$ 0 $2n$ $3n$
$5n={{x}_{2}}\Rightarrow n=\frac{{{x}_{2}}}{5}$
$\{n-x+2x+3x\}={{x}_{1}}$
$n+4x={{x}_{1}},\,x=\frac{{{x}_{1}}-n}{4}$
$k=\frac{2303}{t}\log \left( \frac{n}{n-x} \right)$
Put x and n,
So, $k=\frac{1}{t}\ln \left( \frac{4{{x}_{2}}}{5({{x}_{2}}-{{x}_{1}})} \right)$
TEST Edge In JEE Main, these types of questions are included to judge the knowledge of student in rate constant involving quantitative approach of student towards solving such type of problem. Question related to rate constant and ideal gas equation can also be asked.

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