Question

At ${518}^{o}C$, the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of $363Torr$, was $1.00Torr{s}^{-1}$ when $5\%$ had reacted and $0.5Torr{s}^{-1}$ when $33\%$ had reacted. The order of the reaction is:

• A. $1$
• B. $0$
• C. $2$
• D. $3$

Answer 1

The correct option is C $2$

Let $x$ be order of reaction, $C{H}_{3}CHO\to$

$\frac{d\left[C{H}_{3}CHO\right]}{dt}=k[C{H}_{3}CH{]}^x$

$PV=nRT$

$P=CRT$

$\therefore C=\frac{P}{RT}$

$\frac{-1}{RT}\frac{d[C{H}_{3}CHO{]}_p}{dt}=k[C{H}_{3}CHO{]}^x$

Rate $=1Torr{s}^{-1}$ when 5% had reacted

Rate $=0.5Torr{s}^{-1}$ when 33% had reacted

$\therefore \frac{-1}{RT}.1=k[0.95{]}^x$

$\frac{-1}{RT}.0.5=k[0.66{]}^x$

Dividing boh the equation, we get

$2=(1.43{)}^x$

$\therefore x=2$