Match the rate law given in column I with the dimensions of rate constants given in column II and mark the appropriate choice.
`{:("Column I","Column II"),((A) "Rate" = k[NH_(3)]^(0),(i) mol L^(-1) s^(-1)),((B)"Rate" = k[H_(2)O_(2)][I^(-)],(ii) L mol^(-1) s^(-1)),((C )"Rate" = k[CH_(3)CHO]^(3//2),(iii) S^(-1)),((D) "Rate" = k [C_(5)H_(5)CI],(iv)L^(1//2) mol^(-1//2) s^(-1)):}`

Options

A. (A) `to` (iv), (B) `to` (iii), (C ) `to` (ii), (D) `to` (i)
B. (A) `to` (i), (B) `to` (ii) (C ) `to` (iv) ,(D) `to` (iii)
C. (A) `to` (iii), (B) `to` (ii) (C ) `to` (i) ,(D) `to` (iv)
D. (A) `to` (ii), (B) `to` (i), (C ) `to` (vi), (D) `to` (iii)

Answer

To solve the problem of matching the rate laws in Column I with the dimensions of rate constants in Column II, we will analyze each rate law expression to determine the overall order of the reaction and then calculate the dimensions of the rate constant \( k \) using the formula for the dimensions of rate constants.

### Step-by-step Solution:

1. **Identify the Rate Law for A:**
- Rate = \( k [NH_3]^0 \)
- The overall order \( n \) = 0 (since the exponent of \( [NH_3] \) is 0).
- Using the formula for the dimensions of \( k \):
\[ \text{Dimensions of } k = \text{mol}^{1-n} \cdot \text{L}^{n-1} \cdot \text{s}^{-1} = \text{mol}^{1-0} \cdot \text{L}^{0-1} \cdot \text{s}^{-1} = \text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \]
- Therefore, the dimensions of \( k \) for A match with (i) mol L\(^{-1}\) s\(^{-1}\).

2. **Identify the Rate Law for B:**
- Rate = \( k [H_2O_2][I^-] \)
- The overall order \( n \) = 1 + 1 = 2.
- Using the formula for the dimensions of \( k \):
\[ \text{Dimensions of } k = \text{mol}^{1-2} \cdot \text{L}^{2-1} \cdot \text{s}^{-1} = \text{mol}^{-1} \cdot \text{L}^{1} \cdot \text{s}^{-1} \]
- Therefore, the dimensions of \( k \) for B match with (ii) L mol\(^{-1}\) s\(^{-1}\).

3. **Identify the Rate Law for C:**
- Rate = \( k [CH_3CHO]^{3/2} \)
- The overall order \( n \) = \( \frac{3}{2} \).
- Using the formula for the dimensions of \( k \):
\[ \text{Dimensions of } k = \text{mol}^{1-\frac{3}{2}} \cdot \text{L}^{\frac{3}{2}-1} \cdot \text{s}^{-1} = \text{mol}^{-\frac{1}{2}} \cdot \text{L}^{\frac{1}{2}} \cdot \text{s}^{-1} \]
- Therefore, the dimensions of \( k \) for C match with (iv) L\(^{1/2}\) mol\(^{-1/2}\) s\(^{-1}\).

4. **Identify the Rate Law for D:**
- Rate = \( k [C_5H_5Cl] \)
- The overall order \( n \) = 1.
- Using the formula for the dimensions of \( k \):
\[ \text{Dimensions of } k = \text{mol}^{1-1} \cdot \text{L}^{1-1} \cdot \text{s}^{-1} = \text{mol}^{0} \cdot \text{L}^{0} \cdot \text{s}^{-1} = \text{s}^{-1} \]
- Therefore, the dimensions of \( k \) for D match with (iii) S\(^{-1}\).

### Final Matching:
- A matches with (i) mol L\(^{-1}\) s\(^{-1}\)
- B matches with (ii) L mol\(^{-1}\) s\(^{-1}\)
- C matches with (iv) L\(^{1/2}\) mol\(^{-1/2}\) s\(^{-1}\)
- D matches with (iii) S\(^{-1}\)

### Summary of Matches:
- A → (i)
- B → (ii)
- C → (iv)
- D → (iii)