Which amog the following is most soluble in water?

Options

A. `{:("Compound",Delta_H("hydration")(KJ mol^(-1)),Delta H_("lattice")(K)),(A,-400,+500):}`
B. `{:("Compound",Delta_H("hydration")(KJ mol^(-1)),Delta H_("lattice")(K)),(B,-300,+650):}`
C. `{:("Compound",Delta_H("hydration")(KJ mol^(-1)),Delta H_("lattice")(K)),(C,+200,+150):}`
D. `{:("Compound",Delta_H("hydration")(KJ mol^(-1)),Delta H_("lattice")(K)),(D,-100,+250):}`

Answer

To determine which compound is most soluble in water, we need to analyze the enthalpy of hydration and lattice energy for each compound. The solubility of a compound in water can be assessed by calculating the enthalpy of solution, which is the sum of the enthalpy of hydration and the lattice energy.

### Step-by-Step Solution:

1. **Understand the Concept**:
- A compound is soluble in water if the enthalpy of solution (ΔH_solution) is negative. This means that the energy released during hydration is greater than the energy required to break the lattice structure of the solid.

2. **Identify Given Values**:
- We have four compounds (A, B, C, D) with their respective enthalpy of hydration and lattice energy values provided.

3. **Calculate Enthalpy of Solution**:
- For each compound, we calculate the enthalpy of solution using the formula:
\[ \Delta H_{\text{solution}} = \Delta H_{\text{hydration}} + \Delta H_{\text{lattice}} \]
- We will perform this calculation for each compound.

4. **Analyze Each Compound**:
- **Compound A**:
- Assume ΔH_hydration = X and ΔH_lattice = Y.
- Calculation gives ΔH_solution = +100 (not soluble).
- **Compound B**:
- Calculation gives ΔH_solution = +350 (not soluble).
- **Compound C**:
- Calculation gives ΔH_solution = +350 (not soluble).
- **Compound D**:
- Calculation gives ΔH_solution = +150 (not soluble).

5. **Compare Values**:
- All compounds have positive enthalpy of solution values, indicating they are not soluble.
- However, we need to identify the least positive value, which indicates the highest degree of solubility among the given options.

6. **Conclusion**:
- The least positive value is for Compound A (+100), which means it is the most soluble among the given compounds.

### Final Answer:
- The most soluble compound in water is **Compound A**.