The correct order of increasing solubility in water is:

Options

A. `KFltNaFltLiF`
B. `NaHCO_(3)ltKHCO_(3)ltRbHCO_(3)`
C. `K_(2)CO_(3)ltNa_(2)CO_(3)ltLi_(2)CO_(3)`
D. `LiNO_(3)ltNaNO_(3)ltKNO_(3)`

Explanation

To determine the correct order of increasing solubility in water for the given compounds, we will analyze the solubility based on lattice energy and hydration energy. Here’s the step-by-step solution:

### Step 1: Understand the Concepts
- **Lattice Energy**: The energy required to separate one mole of a solid ionic compound into its gaseous ions. Smaller ions tend to have higher lattice energy.
- **Hydration Energy**: The energy released when ions are surrounded by water molecules. Larger ions typically have lower hydration energy.

### Step 2: Analyze the Given Options
We have four options to analyze for their solubility in water:

1. **Kf < NaF < LiF**
2. **NaHCO3 < KHCO3 < RbHCO3**
3. **K2CO3 < Na2CO3 < Li2CO3**
4. **LiNO3 < NaNO3 < KNO3**

### Step 3: Evaluate Each Option
#### Option 1: Kf < NaF < LiF
- For fluoride ions (F-), the lattice energy is highest for LiF due to the small size of Li+. Therefore, the order of solubility will be the inverse of lattice energy:
- **LiF < NaF < Kf** (correct order of solubility)
- **Conclusion**: This option is incorrect.

#### Option 2: NaHCO3 < KHCO3 < RbHCO3
- For bicarbonate ions (HCO3-), we consider lattice energy. The order of lattice energy based on cation size is:
- **Na+ > K+ > Rb+**
- Thus, the order of solubility will be:
- **NaHCO3 < KHCO3 < RbHCO3** (correct order of solubility)
- **Conclusion**: This option is correct.

#### Option 3: K2CO3 < Na2CO3 < Li2CO3
- For carbonate ions (CO3 2-), we again consider lattice energy. The order is:
- **Li+ > Na+ > K+**
- Therefore, the order of solubility will be:
- **Li2CO3 < Na2CO3 < K2CO3** (correct order of solubility)
- **Conclusion**: This option is incorrect.

#### Option 4: LiNO3 < NaNO3 < KNO3
- For nitrate ions (NO3-), we consider hydration energy. The order based on charge density is:
- **Li+ > Na+ > K+**
- Thus, the order of solubility will be:
- **LiNO3 > NaNO3 > KNO3** (correct order of solubility)
- **Conclusion**: This option is incorrect.

### Final Conclusion
The correct order of increasing solubility in water is:
**NaHCO3 < KHCO3 < RbHCO3** (Option 2).

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