Match the entries of column I with appropriate entries of column II and choose the correct option out of the four options given.

A-q, B-p, C-s, D-r

The correct answer is option 3. A-q, B-p, C-s, D-r.

Let us explain how the units of the rate constant relate to the order of a reaction:

A. \(\text{mol L}^{-1}s^{-1}\): q. Zero order rate constant

For a zero-order reaction, the rate of the reaction is independent of the concentration of the reactant. The rate law is:

\(\text{Rate} = k\)

where \( k \) is the rate constant.

The rate is measured in units of concentration per time, which is typically \( \text{mol L}^{-1} \text{s}^{-1} \). Therefore, the units of the rate constant for a zero-order reaction must be the same as the units of the rate:

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

B. \(s^{-1}\) : p. First order rate constant

For a first-order reaction, the rate of the reaction is directly proportional to the concentration of one reactant. The rate law is:

\(\text{Rate} = k[\text{A}]\)

where \([\text{A}] \) is the concentration of the reactant.

The rate is in units of \( \text{mol L}^{-1} \text{s}^{-1} \), and concentration \( [\text{A}] \) is in \( \text{mol L}^{-1} \). To maintain the units consistent, the rate constant \( k \) must have units of \( \text{s}^{-1} \):

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

C. \(\text{L mol}^{-1}s^{-1}\) : s. Second order rate constant

For a second-order reaction, the rate can be proportional to the square of the concentration of one reactant or the product of the concentrations of two reactants. The rate law is:

\(\text{Rate} = k[\text{A}]^2 \quad \text{or} \quad \text{Rate} = k[\text{A}][\text{B}]\)

The rate is in \( \text{mol L}^{-1} \text{s}^{-1} \), and concentration squared \( [\text{A}]^2 \) is in \( (\text{mol L}^{-1})^2 \). To balance the units, the rate constant \( k \) must have units of \( \text{L mol}^{-1} \text{s}^{-1} \):

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

D. \(L^2\text{ mol}^{-2} s^{-1}\) : Third order rate constant

For a third-order reaction, the rate can be proportional to the cube of the concentration of one reactant or to the product of the concentrations of three reactants. The rate law is:

\(\text{Rate} = k[\text{A}]^3 \quad \text{or} \quad \text{Rate} = k[\text{A}][\text{B}][\text{C}]\)

The rate is in \( \text{mol L}^{-1} \text{s}^{-1} \), and concentration cubed \( [\text{A}]^3 \) is in \( (\text{mol L}^{-1})^3 \). To balance the units, the rate constant \( k \) must have units of \( \text{L}^2 \text{mol}^{-2} \text{s}^{-1} \):

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