Match the items of List I with List II

Choose the correct answer from the options given below:

A-III, B-IV, C-II, D-I

The correct answer is option 4. A-III, B-IV, C-II, D-I.

Let us explore each term in detail and how they match with the definitions provided:

A. Instantaneous rate: III. short interval of time:

The instantaneous rate of a reaction refers to the rate of the reaction at a specific moment in time. It is measured over a very short time interval to capture the rate at that exact instant. It is given by the derivative of the concentration of a reactant or product with respect to time:

\(\text{Instantaneous Rate} = -\frac{d[A]}{dt}\)

where \([A]\) is the concentration of a reactant and \(t\) is time.

B. Average rate: IV. long direction of time

The average rate of a reaction is calculated over a longer period, typically from the start to the end of the reaction or over a substantial interval. It provides an overall rate over that period. It is calculated as:

\(\text{Average Rate} = \frac{\text{Change in concentration}}{\text{Change in time}}\)

For example:

\(\text{Average Rate} = \frac{[A]_t - [A]_0}{t}\)

where \([A]_t\) is the concentration at time \(t\) and \([A]_0\) is the initial concentration.

C. Mathematical expression for rate of reaction in terms of concentration of reactants: II. rate law

The rate law is an equation that expresses the rate of a chemical reaction in terms of the concentration of reactants. It shows how the reaction rate depends on the concentration of each reactant. The rate law for a reaction is given by:

\(\text{Rate} = k[A]^m[B]^n\)

where \(k\) is the rate constant, \([A]\) and \([B]\) are the concentrations of the reactants, and \(m\) and \(n\) are the reaction orders with respect to each reactant.

D. Rate of reaction for zero order reaction is equal to: I. rate constant

For a zero-order reaction, the rate of the reaction is independent of the concentration of reactants. This means that the rate remains constant as the concentration of reactants changes. The rate for a zero-order reaction is given by:

\(\text{Rate} = k\)

where \(k\) is the rate constant. Since the rate does not depend on the concentration of the reactants, the rate remains equal to the rate constant.

Summary

Instantaneous Rate: Measures the rate at a specific moment and thus is associated with a short interval of time.

Average Rate: Measures the rate over a longer duration and thus is associated with a long duration of time.

Rate Law: The mathematical expression that relates the rate of the reaction to the concentrations of reactants.

Zero-Order Reaction: The rate of reaction is constant and equal to the rate constant.

Thus, the correct answer is option 4. A-III, B-IV, C-II, D-I.