For the given reaction $2A + B \rightarrow 3C + D$, the rate of reaction is expressed by dividing the rate of disappearance of reactants or rate of appearance of products by their respective stoichiometric coefficients. Reactants have a negative sign (as their concentration decreases), and products have a positive sign (as their concentration increases). $\text{Rate} = -\frac{1}{2} \frac{d[A]}{dt} = -\frac{d[B]}{dt} = +\frac{1}{3} \frac{d[C]}{dt} = +\frac{d[D]}{dt}$ Since $C$ is a product, the expression should be $+\frac{1}{3} \frac{d[C]}{dt}$. Thus, $-\frac{d[C]}{3dt}$ does not express the correct reaction rate.