The correct order of equivalent conductances at infinite dilution in water at room temperature for `H^(+), K^(+), CH_(3)COO^(-)` and `HO^(-)` ions is-

Options

A. `HO^(-) gt H^(+) gt K^(+) gt CH_(3)COO^(-)`
B. `H^(+) gt HO^(-) gt K^(+) gt CH_(3)COO^(-)`
C. `H^(+) gt K^(+) gt HO^(-) gt CH_(3)OO^(-)`
D. `H^(+) gt K^(+) gt CH_(3)COO^(-) gt HO^(-)`

Explanation

To determine the correct order of equivalent conductances at infinite dilution for the ions \( H^+, K^+, CH_3COO^-, \) and \( OH^- \), we can follow these steps:

### Step 1: Understand Equivalent Conductance
Equivalent conductance (\( \Lambda \)) is a measure of the ability of ions to conduct electricity in solution. It is influenced by the charge of the ions and their sizes. Smaller ions generally have higher equivalent conductance due to less hindrance in movement through the solvent.

### Step 2: Compare the Sizes of the Ions
- **Hydrogen ion (\( H^+ \))**: This is the smallest cation and has a very high mobility due to its small size.
- **Potassium ion (\( K^+ \))**: This is larger than \( H^+ \) and has lower mobility.
- **Acetate ion (\( CH_3COO^- \))**: This is a larger anion compared to \( OH^- \) and has moderate mobility.
- **Hydroxide ion (\( OH^- \))**: This ion is smaller than acetate and has relatively high mobility.

### Step 3: Order the Ions Based on Size and Conductance
From the above comparisons, we can rank the ions based on their equivalent conductance at infinite dilution:
1. **\( H^+ \)**: Highest conductance due to smallest size.
2. **\( OH^- \)**: Second highest conductance, smaller than acetate.
3. **\( K^+ \)**: Lower conductance due to larger size.
4. **\( CH_3COO^- \)**: Lowest conductance due to being the largest among the ions listed.

### Step 4: Write the Final Order
Based on the analysis, the correct order of equivalent conductances at infinite dilution is:
\[ H^+ > OH^- > K^+ > CH_3COO^- \]

### Conclusion
Thus, the correct order of equivalent conductances at infinite dilution in water at room temperature for \( H^+, K^+, CH_3COO^-, \) and \( OH^- \) ions is:
\[ H^+, OH^-, K^+, CH_3COO^- \]