Question

A (aq)$\rightarrow$ B (aq) + C (aq) is a first order reaction.

Time t $\infty$

Moles of reagent n1 n2

Reaction progress is measure with the help of titration of reagent ‘R’. If all A, B and C reacted with reagent and have ‘n’ factors $\left\lbrack nfactors;eq.wt. = \frac{mol.wt}{n} \right\rbrack$in the ratio of 1 : 2 : 3 with the reagent. The k in terms of t, n1 and n2 is :

• A. $k = \frac{1}{t}In\left( \frac{n_{2}}{n_{2} - n_{1}} \right)$
• B. $k = \frac{1}{t}In\left( \frac{2n_{2}}{n_{2} - n_{1}} \right)$
• C. $k = \frac{1}{t}In\left( \frac{4n_{2}}{n_{2} - n_{1}} \right)$
• D. $k = \frac{1}{t}In\left( \frac{4n_{2}}{5\left( n_{2} - n_{1} \right)} \right)$

Answer 1

Answer: (D)

$k = \frac{1}{t}In\left( \frac{4n_{2}}{5\left( n_{2} - n_{1} \right)} \right)$

Answer 2

A (aq) $\longrightarrow$ B (aq) + C (aq)

t=0 a 0 0

t=t a–x x x

t= 0 a a

(a – x) + 2x + 3x $\propto$ n1

a + 4x $\propto$ n1.....(i)

2a + 3a $\propto$ n2

$a \propto \frac{n_{2}}{5}$.....(ii)

$k = \frac{1}{t}In\left\lbrack \frac{a}{a - x} \right\rbrack$