Question

$A\to B+2C$

At ${100}^{o}C$, in above gaseous reaction, is observed to be of the first order. On starting with pure A, at the end of $14$ minutes, the total pressure found to be $264$ mm of Hg. After a long time, the total pressure of the system was $450$ mm of Hg.

Rate constant of the reaction is:

• A. $6.455\times {10}^{-2}mi{n}^{-1}$
• B. $3.415\times {10}^{-2}mi{n}^{-1}$
• C. $5.575\times {10}^{-2}mi{n}^{-1}$
• D. none of these

Answer 1

Answer: (B)

$3.415\times {10}^{-2}mi{n}^{-1}$

To provide a long time or heating to a reaction mixture means that reaction has gone to completion.

$A\to B+2C$

Mole before dissociation	a	0	0
Mole after dissociation	a-x	x	2x
Mole after complete dissociation	0	a	2a

$\because$ Total mole at a time $\propto$ pressure at that time

$a\propto P_0;t=0$ ......(i)

$a+2X\propto 264;t=14minutes$ ....(ii)

$3a=450;t=\infty$ .....(iii)

$\because$ By Eqs. (i), (ii) and (iii) we get $X=57;a=150.$

$K=\frac{2.303}{14}log\frac{150}{150-57}=3.415\times {10}^{-2}mi{n}^{-1}$

Hence, the correct option is $B$.