1. Tardigrade
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  3. Chemistry
  4. At 518° C , the rate of decomposition of sample of gaseous acetaldehyde, initially at a pressure of 363 Torr, was 1. 00 Torr s-1 when 5 % had reacted and 0.5 Torr s-1 when 33 % had reacted. The order of the reaction is -

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Q. At $518^{\circ} C$ , the rate of decomposition of sample of gaseous acetaldehyde, initially at a pressure of $363$ Torr, was $1. 00$ Torr $s^{-1}$ when $5\%$ had reacted and $0.5$ Torr $s^{-1}$ when $33\%$ had reacted. The order of the reaction is -

JEE MainJEE Main 2018Chemical Kinetics

Solution:

Assume the order of reaction with respect to acetaldehyde is $x$.

Condition-1 :

Rate $= k\, \left[ CH _{3} CHO \right]^{ x }$

$1= k \,[363 \times 0.95]^{ x }$

$1= k\, [344.85]^{ x }\,\,\,\,\,\,\,\,\,...(i)$

Condition-2 :

$0.5= k\, [363 \times 0.67]^{ x }$

$0.5= k \,[243.21]^{ x }\,\,\,\,\,\,\,...(ii)$

Divide equation (i) by (ii),

$ \frac{1}{0.5}=\left(\frac{344.85}{243.21}\right)^{ x } $

$\Rightarrow 2=(1.414)^{ x } $

$\Rightarrow x =2$