Match List I with List II

Choose the correct answer from the options given below

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

The correct answer is option 2. A-III, B-IV, C-I, D-II.

Let us go through a detailed explanation of how the units of rate constants for reactions of different orders are derived using the general form of rate laws.

Rate Law:

For a reaction:

\(\text{Rate} = k[\text{Reactant}_1]^{x}[\text{Reactant}_2]^{y}...\)

The overall reaction order \( n \) is the sum of the exponents \( x + y + ... \).

Units of the Rate Constant:

The rate of reaction generally has units of concentration per time, i.e., \( \text{mol/L/s} \) or \( \text{mol} \cdot L^{-1} \cdot s^{-1} \).

The units of the rate constant \( k \) can be derived based on the reaction order \( n \), using the formula:

\(k = \frac{\text{rate}}{[\text{concentration}]^n}\)

Where \( n \) is the order of the reaction. This leads to the following general expression for the units of \( k \):

\(\text{Units of } k = \frac{(\text{mol} \cdot L^{-1} \cdot s^{-1})}{(\text{mol} \cdot L^{-1})^n}\)
Simplifying the denominator gives the units for \( k \) for each reaction order.

Let us now look at the order of reaction in the list I of the match:

A. Second Order Reaction :

For a second-order reaction** (\( n = 2 \)):

\(\text{Units of } k = \frac{(\text{mol} \cdot L^{-1} \cdot s^{-1})}{(\text{mol} \cdot L^{-1})^2}\)

Simplifying this gives:

\(k = \text{mol}^{-1} \cdot L \cdot s^{-1}\)

Thus, the units of \( k \) for a second-order reaction are \( \mathbf{mol^{-1} \cdot L \cdot s^{-1}} \) (III).

B. Fourth Order Reaction:

For a fourth-order reaction (\( n = 4 \)):

\(\text{Units of } k = \frac{(\text{mol} \cdot L^{-1} \cdot s^{-1})}{(\text{mol} \cdot L^{-1})^4}\)

Simplifying this gives:

\(k = \text{mol}^{-3} \cdot L^3 \cdot s^{-1}\)

Thus, the units of \( k \) for a fourth-order reaction are \( \mathbf{mol^{-3} \cdot L^3 \cdot s^{-1}} \) (IV).

C. First Order Reaction:

For a first-order reaction (\( n = 1 \)):

\(\text{Units of } k = \frac{(\text{mol} \cdot L^{-1} \cdot s^{-1})}{(\text{mol} \cdot L^{-1})^1}\)

Simplifying this gives:

\(k = s^{-1}\)

Thus, the units of \( k \) for a first-order reaction are \( \mathbf{s^{-1}} \) (I).

D. Third Order Reaction:

For a third-order reaction (\( n = 3 \)):

\(\text{Units of } k = \frac{(\text{mol} \cdot L^{-1} \cdot s^{-1})}{(\text{mol} \cdot L^{-1})^3}\)

Simplifying this gives:

\(k = \text{mol}^{-2} \cdot L^2 \cdot s^{-1}\)

Thus, the units of \( k \) for a third-order reaction are \( \mathbf{mol^{-2} \cdot L^2 \cdot s^{-1}} \) (II).

Thus the correct answer is option 2: A-III, B-IV, C-I, D-II