Rate of a reaction decreases with the passage of time as the concentration of reactants decrease. Conversely, rates generally increase when reactant concentrations increase. So, rate of a reaction depends upon the concentration of reactants. 

Consider a general reaction

aA + bB → cC + dD

where a, b, c and d are the stoichiometric coefficients of reactants and products.

The rate expression for this reaction is

Rate ∝ [A]x [B]y

where exponents x and y may or may not be equal to the stoichiometric coefficients (a and b) of the reactants.

Above equation can also be written as Rate = k [A]^x [B]^y

-\(\frac{dR}{dT}\) = k [A]^x [B]^y

This form of equation is known as differential rate equation, where k is a proportionality constant called rate constant.

In the reaction A + 3B → 2C + D. Which of the following expression does not describe changes in the concentration of the various species as a function of time?

\(\frac{d[B]}{dT}\) = -\(\frac{3}{2}\)\(\frac{d[C]}{dT}\)

In the reaction A + 3B → 2C + D

rate = -\(\frac{d[A]}{dT}\) = -\(\frac{1}{3}\)\(\frac{d[B]}{dT}\) = +\(\frac{1}{2}\)\(\frac{d[C]}{dT}\) = +\(\frac{d[D]}{dT}\) 

 -\(\frac{1}{3}\)\(\frac{d[B]}{dT}\) = +\(\frac{1}{2}\)\(\frac{d[C]}{dT}\) 

\(\frac{d[B]}{dT}\) = -\(\frac{3}{2}\)\(\frac{d[C]}{dT}\)