The gas phase decomposition of acetaldehyde
CH₃CHO(g) → CH₄(g) + CO(g)
at 680 K is observed to follow the rate expression
$rate = \frac{- d [{CH}_{3} CHO]}{dt} = k {[{CH}_{3} CHO]}^{1 / 2}$
If the rate of the decomposition is followed by monitoring the partial pressure of the acetaldehyde, we can express the rate as
$\frac{{dp}_{{CH}_{3} CHO}}{dt} = k {[p_{{CH}_{3} CHO}]}^{3 / 2}$
If the pressure is measured in atmosphere and time in minutes then
(i) What are the units of the rate of reaction?
(ii) What are the units of rate constant k?

Solution

The gas phase decomposition of acetaldehyde

CH₃CHO(g) → CH₄(g) + CO(g)

at 680 K is observed to follow the rate expression
$rate = \frac{- d [{CH}_{3} CHO]}{dt} = k {[{CH}_{3} CHO]}^{1 / 2}$

Thus,

(i) Units of rate of reaction =
$\frac{atmosphere}{minutes} = atm \min^{- 1}$

(ii)
$Units of k = \frac{units of rate}{(units of p_{{CH}_{3} CH})^{3 / 2}} = \frac{atm \min^{- 1}}{atm^{3 / 2}} = \frac{\min^{- 1}}{{atm}^{1 / 2}} = {atm}^{- 1 / 2} \min^{- 1} = {bar}^{- 1 / 2} \min^{- 1} .$

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Chemical Kinetics

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