Question

In which one of the following reactions, rate constant has the unit mol L^-1 s^-1 ?

• A. Acid catalysed hydrolysis of CH₃COOCH₃
• B. CHCl₃ + Cl₂ → CCl₄ + HCl
• C. \(2NO(g)+O_{2_{(g)}}\rightarrow2NO_{2_{(g)}}\)
• D. Decomposition of HI on the surface of Gold

Answer 1

The Correct Option is D

Determine the Reaction with Rate Constant Units of \( \text{mol} \, \text{L}^{-1} \, \text{s}^{-1} \) 

We need to identify which of the following reactions has a rate constant with units of \( \text{mol} \, \text{L}^{-1} \, \text{s}^{-1} \):

Options:

1. (A) Acid catalysed hydrolysis of \( \text{CH}_3\text{COOCH}_3 \)
2. (B) \( \text{CHCl}_3 + \text{Cl}_2 \rightarrow \text{CCl}_4 + \text{HCl} \)
3. (C) \( 2\text{NO}(\text{g}) + \text{O}_2(\text{g}) \rightarrow 2\text{NO}_2(\text{g}) \)
4. (D) Decomposition of \( \text{HI} \) on the surface of Gold

Analysis:

The unit \( \text{mol} \, \text{L}^{-1} \, \text{s}^{-1} \) corresponds to a second-order reaction with respect to concentration.

Option (A):

Typically, acid catalysed hydrolysis reactions are first order with respect to the ester and first order with respect to the acid catalyst. Thus, the rate constant would have units of \( \text{s}^{-1} \) or \( \text{L} \, \text{mol}^{-1} \, \text{s}^{-1} \).

Option (B):

This reaction is a second-order reaction with respect to \( \text{Cl}_2 \). Thus, the rate constant would have units of \( \text{L} \, \text{mol}^{-1} \, \text{s}^{-1} \).

Option (C):

This reaction is a second-order reaction with respect to \( \text{NO} \) and first order with respect to \( \text{O}_2 \). Thus, the rate constant would have units of \( \text{L}^2 \, \text{mol}^{-2} \, \text{s}^{-1} \).

Option (D):

The decomposition of \( \text{HI} \) on a surface is typically a first-order reaction. However, if it occurs on a surface, the rate constant is often expressed in terms of surface area, not concentration. This could potentially lead to a rate constant with units of \( \text{mol} \, \text{L}^{-1} \, \text{s}^{-1} \) if the surface area effects are normalized to concentration units.

Conclusion:

Based on the analysis, the most likely answer is (D) Decomposition of \( \text{HI} \) on the surface of Gold, as it could potentially have a rate constant with units of \( \text{mol} \, \text{L}^{-1} \, \text{s}^{-1} \) under certain conditions.

Answer 2

The unit of the rate constant depends on the order of the reaction. The rate law for a reaction is given by:

Rate = \(k[A]^m[B]^n\)

The unit of the rate constant (k) for a reaction of order (m+n) is:

Unit of k = mol^{(1 - m - n)} L^{m + n - 1} s^-1

Now, let's analyze each reaction:

(A) Acid catalysed hydrolysis of CH₃COOCH₃: This is typically a first-order reaction with respect to ester concentration, and the unit of the rate constant would be s^-1.

(B) CHCl₃ + Cl₂ → CCl₄ + HCl: This is a reaction involving molecular interactions between two reactants, so it is typically a second-order reaction with respect to the reactants, and the unit of the rate constant would be L^-1s^-1.

(C) 2NO_(g) + O_2(g) → 2NO₂_(g): This is a reaction of second order (1st order with respect to NO and 1st order with respect to O₂), so the unit of the rate constant would be mol^-1L s^-1.

(D) Decomposition of HI on the surface of Gold: This is typically a zero-order reaction, and the unit of the rate constant would be mol L^-1 s^-1.

Thus, the rate constant for option (C) has the unit mol^-1 L s^-1.