The rate of a chemical reaction for the general equation $aA + bB \rightarrow cC + dD$ is expressed as: $\text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = +\frac{1}{c}\frac{d[C]}{dt} = +\frac{1}{d}\frac{d[D]}{dt}$

For the specific reaction $2A + B \rightarrow 3C + D$:

• Reactants (A, B) disappear, so their rates have a negative sign.
• Products (C, D) appear, so their rates have a positive sign.

The correct rate expressions are: $\text{Rate} = -\frac{1}{2}\frac{d[A]}{dt} = -\frac{d[B]}{dt} = +\frac{1}{3}\frac{d[C]}{dt} = +\frac{d[D]}{dt}$

Option A gives the expression as $-\frac{1}{3}\frac{d[C]}{dt}$. Since C is a product, its rate of formation should be positive. Therefore, this expression implies the disappearance of a product, which is incorrect .