Question

Catalytic decomposition of nitrous oxide by gold at ${900}^{0}C$ at an initial pressure of 200 mm was 50 % in 53 min and 73 % in 100 min, the value of velocity constant is :

• A. $1.308\times {10}^{-2}mi{n}^{-1}$
• B. $1.432\times {10}^{-2}mi{n}^{-1}$
• C. $2.318\times {10}^{-2}mi{n}^{-1}$
• D. None of these

Answer 1

The correct option is A $1.308\times {10}^{-2}mi{n}^{-1}$

Case I:
$a\propto 200mm$
$x\propto 200\times \frac{50}{100}$
or $x\propto 100mm.$

$t_{1/2}=53min.$

$k_1=\frac{2.303}{t}log\frac{a}{a-x}$

$k_1=\frac{2.303}{53}log\frac{200}{200-100}=1.308\times {10}^{-2}mi{n}^{-1}$
Case II :
a $\propto$ 200 mm
$x$ $\propto 200\times \frac{73}{100}$
or, $x\propto 146mm$

$t_{73\%}$ = 100 min

$k_2=\frac{2.303}{100}log\left(\frac{200}{200-146}\right)=1.309\times {10}^{-2}mi{n}^{-1}$

(b) $k=\frac{k_1+k_2}{2}=\frac{(1.308+1.309)\times {10}^{-2}}{2}$

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