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Question 18.1: The decomposition of acetaldehyde is given by the following ...

The decomposition of acetaldehyde is given by the following balanced reaction:

CH_{3}COH\left( g \right)\to CH_{4}\left( g \right)+CO\left( g \right)

Define the rate of reaction with respect to the pressure of the reactant.

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Beginning with Equation (18.2) and focusing on the acetaldehyde reactant, we obtain

n_{i}=n_{i}^{o}+v_{i}\xi          (18.2)

n_{CH_{3}COH}=n_{CH_{3}COH}^{o}-\xi

Using the ideal gas law, the pressure of acetaldehyde is expressed as

P_{CH_{3}COH}=\frac{n_{CH_{3}COH}}{V}RT=\left[ CH_{3}COH \right]RT

Therefore, the pressure is related to the concentration by the quantity RT. Substituting this result into Equation (18.8) with v_{i}=1 yields

R=\frac{Rate}{V}=\frac{1}{V}\left( \frac{1}{v_{i}}\frac{dn_{i}}{gt} \right)=\frac{1}{v_{i}}\frac{d\left[ i \right]}{dt}           (18.8)

R=\frac{Rate}{V}=-\frac{1}{v_{CH_{3}COH}}\frac{d\left[ CH_{3}COH \right]}{dt}

 

=-\frac{1}{RT}\frac{dP_{CH_{3}COH}}{dt}

 

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