Question

Catalytic decomposition of nitrous oxide by gold at ${900}^{o}C$ at an initial pressure of $200$ mm, was $50$% in $53$ minutes and $73$% in $100$ minutes.

Velocity constant of the reaction is:

[Note: assume decomposition as the first order.]

• A. $1.308\times {10}^{-2}$
• B. $2.317\times {10}^{-2}$
• C. $3.208\times {10}^{-3}$
• D. none of these

Answer 1

The correct option is A $1.308\times {10}^{-2}$

Taking decomposition as first order:

$\because K=\frac{2.303}{t}log\frac{a}{(a-X)}$

Case $I$: $a\propto 200mm$;

$X\propto 200\times \left(50/100\right)mm$ and $t_{1/2}=53minutes$

$\therefore K_1=\frac{2.303}{53}log\frac{200}{200-100}$

$=1.308\times {10}^{-2}mi{n}^{-1}$

Case $II$: $a\propto 200mm;X\propto 200\times \left(73/100\right)\propto 146mm$

$\therefore K_2=\frac{2.303}{100}log\frac{200}{200-146}$

$=1.309\times {10}^{-2}mi{n}^{-1}$

$K=\frac{K_1+K_2}{2}=\frac{(1.308+1.309)\times {10}^{-2}}{2}=1.308\times {10}^{-2}$

Hence, the correct option is $A$