Question
For the reaction, $$3A + 2B + C + D,$$ the differential rate law can be written as :
A.
$$\frac{1}{3}\frac{{d\left[ A \right]}}{{dt}} = \frac{{d\left[ C \right]}}{{dt}} = k{\left[ A \right]^n}{\left[ B \right]^m}$$
B.
$$ - \frac{{d\left[ A \right]}}{{dt}} = \frac{{d\left[ C \right]}}{{dt}} = k{\left[ A \right]^n}{\left[ B \right]^m}$$
C.
$$ + \frac{1}{3}\frac{{d\left[ A \right]}}{{dt}} = - \frac{{d\left[ C \right]}}{{dt}} = k{\left[ A \right]^n}{\left[ B \right]^m}$$
D.
$$ - \frac{1}{3}\frac{{d\left[ A \right]}}{{dt}} = \frac{{d\left[ C \right]}}{{dt}} = k{\left[ A \right]^n}{\left[ B \right]^m}$$
Answer :
$$ - \frac{1}{3}\frac{{d\left[ A \right]}}{{dt}} = \frac{{d\left[ C \right]}}{{dt}} = k{\left[ A \right]^n}{\left[ B \right]^m}$$
Solution :
For the reaction
$$3A + 2B \to C + D$$
Rate of disappearance of $$A=$$ Rate of appearance of $$C$$ reaction
$$\eqalign{
& = - \frac{1}{3}\frac{{d\left[ A \right]}}{{dt}} \cr
& = \frac{{d\left[ C \right]}}{{dt}} \cr
& = k{\left[ A \right]^n}{\left[ B \right]^m} \cr} $$