Question

Arrange the following rate expressions (of hypothetical reactions) in the increasing arrangement of their order of reaction:
Assume the concentrations of A and B in all the rate expressions is same.
(A) \(\text{Rate} = k [\text{A}]^{1/2} [\text{B}]^{3/2}\)
(B) \(\text{Rate} = k [\text{A}]^{1/2} [\text{B}]^{1/2}\)
(C) \(\text{Rate} = k [\text{A}]^{3/2} [\text{B}]^{-1}\)
(D) \(\text{Rate} = k [\text{A}]^2 [\text{B}]^1\)
Choose the correct answer from the options given below:

• A. (A), (B), (C), (D)
• B. (C), (B), (A), (D)
• C. (B), (A), (D), (C)
• D. (C), (B), (D), (A)

Hint:

When finding the overall reaction order, simply add the powers algebraically:
\(x + y = n\).
Remember to include negative signs when present in the exponent.

Answer 1

The Correct Option is B

Concept:
The overall order of a chemical reaction is defined as the sum of the powers of the concentration terms of the reactants appearing in the empirical rate law expression:
\[ \text{If } \text{Rate} = k [\text{A}]^x [\text{B}]^y, \quad \text{Overall Order } (n) = x + y \] The order of a reaction can be positive, negative, zero, or fractional.

Step 1: Calculating Order for Reaction (A):
For the rate expression:
\[ \text{Rate} = k [\text{A}]^{1/2} [\text{B}]^{3/2} \] The overall order \(n_\text{A}\) is:
\[ n_\text{A} = \frac{1}{2} + \frac{3}{2} = \frac{4}{2} = 2 \]

Step 2: Calculating Order for Reaction (B):
For the rate expression:
\[ \text{Rate} = k [\text{A}]^{1/2} [\text{B}]^{1/2} \] The overall order \(n_\text{B}\) is:
\[ n_\text{B} = \frac{1}{2} + \frac{1}{2} = 1 \]

Step 3: Calculating Order for Reaction (C):
For the rate expression:
\[ \text{Rate} = k [\text{A}]^{3/2} [\text{B}]^{-1} \] The overall order \(n_\text{C}\) is:
\[ n_\text{C} = \frac{3}{2} + (-1) = \frac{3}{2} - 1 = \frac{1}{2} = 0.5 \]

Step 4: Calculating Order for Reaction (D):
For the rate expression:
\[ \text{Rate} = k [\text{A}]^2 [\text{B}]^1 \] The overall order \(n_\text{D}\) is:
\[ n_\text{D} = 2 + 1 = 3 \]

Step 5: Arranging in Increasing Order:
Comparing the calculated values:
\[ n_\text{C} (0.5) < n_\text{B} (1) < n_\text{A} (2) < n_\text{D} (3) \] Therefore, the increasing order of overall reaction order is:
\[ \text{(C)} < \text{(B)} < \text{(A)} < \text{(D)} \] Final Answer:
The correct increasing arrangement is (C), (B), (A), (D), corresponding to option (B).