Match the entries of column I with appropriate entries of column II a…

The correct answer is option 3. (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i).

Column I	Column II
(a) Average rate of reaction	(iv) \(\frac{ΔC}{Δt}\)
(b) Instantaneous rate of reaction	(iii) \(\frac{dC}{dt}\)
(c) Active mass	(ii) Molar concentration of substance
(d) Rate law	(i) \(\frac{dx}{dt}\) ∝ [A]a x [b]b

Let us explain the matching in detail:

(a) Average rate of reaction: (iv) \(\frac{ΔC}{Δt}\)

The average rate of reaction measures how the concentration of a reactant or product changes over a specific time interval. It is typically expressed as:

\(\text{Average rate} = \frac{\Delta C}{\Delta t}\)

where \(\Delta C\) is the change in concentration over the time interval \(\Delta t\).

(b) Instantaneous rate of reaction: (iii) \(\frac{dC}{dt}\)

The instantaneous rate of reaction is the rate at a particular moment in time. It is the derivative of the concentration of a reactant or product with respect to time:

\(\text{Instantaneous rate} = \frac{dC}{dt}\)

where \(dC\) is the infinitesimal change in concentration and \(dt\) is the infinitesimal change in time

(c) Active mass: (ii) Molar concentration of substance

Active mass refers to the effective concentration of a substance in a reaction. In most cases, it is simply the molar concentration of the substance. This concept is crucial in the context of the law of mass action.

(d) Rate law: (i) \(\frac{dx}{dt}\) ∝ [A]^a x [b]^b

The rate law expresses the rate of a reaction as a function of the concentrations of reactants raised to specific powers (which are determined experimentally). For a reaction involving reactants \(A\) and \(B\), it can be written as:

\(\text{rate} \propto [A]^a [B]^b\)

Here, \(a\) and \(b\) are the orders of the reaction with respect to \(A\) and \(B\), respectively.

Thus, the correct option is 3. (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)