Question
$$3A \to 2B,$$ rate of reaction $$ + \frac{{d\left[ B \right]}}{{dt}}$$ is equal to
A.
$$ - \frac{3}{2}\frac{{d\left[ A \right]}}{{dt}}$$
B.
$$ - \frac{2}{3}\frac{{d\left[ A \right]}}{{dt}}$$
C.
$$ - \frac{1}{3}\frac{{d\left[ A \right]}}{{dt}}$$
D.
$$ + 2\frac{{d\left[ A \right]}}{{dt}}$$
Answer :
$$ - \frac{2}{3}\frac{{d\left[ A \right]}}{{dt}}$$
Solution :
$$\eqalign{
& {\text{For reaction,}} \cr
& 3A \to 2B \cr} $$
$${\text{Rate}} = - \frac{1}{3}\frac{{d\left[ A \right]}}{{dt}}$$ $${\text{[Rate of disappearance]}}$$
$$\,\,\,\,\,\,\,\,\,\,\,\, = + \frac{1}{2}\frac{{d\left[ B \right]}}{{dt}}$$ $$[{\text{Rate of appearance]}}$$
$$\therefore \,\,{\text{ + }}\frac{{d\left[ B \right]}}{{dt}} = - \frac{2}{3}\frac{{d\left[ A \right]}}{{dt}}$$