Chemical Kinetics

The rate of a chemical reaction can be expressed in terms of the rate of change of concentration of any reactant or product. According to the given reaction:

$ 2A + 3B \to 3C + 4D $

The rate of this reaction can be expressed as the rate of disappearance of the reactants A or B, or as the rate of appearance of the products C or D. Since A is being consumed, its concentration will decrease over time and because B, C, and D are all involved in the reaction in different stoichiometric ratios, their rates of consumption or production will be proportional to their stoichiometric coefficients.

The general relation between the rate of the reaction and the rate of change of concentration of any species is given by:

$ \text{Rate} = -\frac{1}{\text{stoichiometric coefficient}} \frac{d[\text{reactant}]}{dt} = \frac{1}{\text{stoichiometric coefficient}} \frac{d[\text{product}]}{dt} $

For reactant A with a stoichiometric coefficient of 2:

$ \text{Rate} = -\frac{1}{2} \frac{d[A]}{dt} $

For reactant B with a stoichiometric coefficient of 3:

$ \text{Rate} = -\frac{1}{3} \frac{d[B]}{dt} $

For product C with a stoichiometric coefficient of 3:

$ \text{Rate} = \frac{1}{3} \frac{d[C]}{dt} $

For product D with a stoichiometric coefficient of 4:

$ \text{Rate} = \frac{1}{4} \frac{d[D]}{dt} $

So the correct options that match the expression for the rate of reaction based on the appearance of products C and D are:

Option C: $ {1 \over 3}{{d[C]} \over {dt}} $

Option D: $ {1 \over 4}{{d[D]} \over {dt}} $

Note that when expressing the rate with respect to the reactants (A and B), the rate must include a negative sign because their concentrations decrease as the reaction proceeds. For products (C and D), the rate is positive because their concentrations increase.