Which of the following order is correct?

Options

A. `K^(+)ltCa^(2+)ltP^(3-)ltS^(2-)` Ionic size
B. `Na_(aq.)^(+)gtK_(aq.)^(+)gtRb_(aq.)^(+)gtCs_(aq.)^(+)`: Electrical conductance
C. `Al_(aq.)^(3+)gtMg_(aq.)^(2+)gtNa_(aq.)^(+)`: Hydrated size
D. `I_(aq.)^(-)ltBr_(aq.)^(-)gtCl_(aq.)^(-)gtF_(aq.)^(-)`: Ionic mobility

Explanation

To determine the correct order among the given options, we will analyze each case step by step.

### Step 1: Analyze Ionic Size
We are given the ions S²⁻, P³⁻, Ca²⁺, and K⁺.

- **Ionic Size Trend**: The size of anions increases with an increase in negative charge, while the size of cations decreases with an increase in positive charge.
- **Comparison**:
- P³⁻ has the largest size due to the highest negative charge.
- S²⁻ is next, as it has a lower negative charge than P³⁻.
- K⁺ is larger than Ca²⁺ because K⁺ has a +1 charge while Ca²⁺ has a +2 charge.
- Ca²⁺ is the smallest due to its +2 charge.

**Order**: P³⁻ > S²⁻ > K⁺ > Ca²⁺

### Step 2: Analyze Electrical Conductance
We are given the cations Na⁺, K⁺, Rb⁺, and Cs⁺.

- **Conductance Trend**: Conductance is inversely related to ionic size. Smaller ions have higher conductance due to better mobility.
- **Comparison**:
- Na⁺ is the smallest and has the highest conductance.
- K⁺ is larger than Na⁺ but smaller than Rb⁺.
- Rb⁺ is larger than K⁺ but smaller than Cs⁺.
- Cs⁺ is the largest and has the lowest conductance.

**Order**: Cs⁺ > Rb⁺ > K⁺ > Na⁺ (in terms of conductance, this is reversed)

### Step 3: Analyze Hydrated Size
We are given Al³⁺, Mg²⁺, and Na⁺.

- **Hydrated Size Trend**: The hydrated size is influenced by the charge and size of the cation. Higher charged cations have a smaller ionic radius but can have a larger hydrated radius due to stronger hydration.
- **Comparison**:
- Al³⁺ has the highest charge and will have the largest hydrated radius.
- Mg²⁺ is next, as it has a +2 charge.
- Na⁺ has the lowest charge and thus the smallest hydrated radius.

**Order**: Al³⁺ > Mg²⁺ > Na⁺

### Step 4: Analyze Ionic Mobility
We are given F⁻, Cl⁻, Br⁻, and I⁻.

- **Ionic Mobility Trend**: Ionic mobility increases with increasing ionic size (for ions with the same charge).
- **Comparison**:
- I⁻ is the largest and has the highest mobility.
- Br⁻ is next, followed by Cl⁻.
- F⁻ is the smallest and has the lowest mobility.

**Order**: I⁻ > Br⁻ > Cl⁻ > F⁻

### Conclusion
After analyzing all the orders, we find that the only correct order is the hydrated size order: Al³⁺ > Mg²⁺ > Na⁺.

### Final Answer
The correct order is: **Al³⁺ > Mg²⁺ > Na⁺**.

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