The correct relationship between the boiling point of very dilute solutions of `AiCI_(3)(t_(1))` and `caCI_(2)(t_(2))` having the same molar concentration is:

Options

A. `t_(1) = t_(2)`
B. `t_(1) gt t_(2)`
C. `t_(2) gt t_(1)`
D. `t_(2) ge t_(1)`

Explanation

To solve the problem, we need to analyze the boiling point elevation of very dilute solutions of \( \text{AlCl}_3 \) and \( \text{CaCl}_2 \) with the same molar concentration.

### Step-by-Step Solution:

1. **Understand the Concept of Boiling Point Elevation**:
The boiling point elevation (\( \Delta T_b \)) of a solution is given by the formula:
\[ \Delta T_b = i \cdot m \cdot K_b \]
where:
- \( i \) = van 't Hoff factor (number of particles the solute breaks into)
- \( m \) = molality of the solution (which is the same for both solutions in this case)
- \( K_b \) = ebullioscopic constant of the solvent (also the same for both solutions)

2. **Determine the van 't Hoff Factor (\( i \)) for Each Solute**:
- For \( \text{AlCl}_3 \):
\[ \text{AlCl}_3 \rightarrow \text{Al}^{3+} + 3 \text{Cl}^- \]
This dissociates into 4 ions (1 aluminum ion and 3 chloride ions), so:
\[ i_{\text{AlCl}_3} = 4 \]

- For \( \text{CaCl}_2 \):
\[ \text{CaCl}_2 \rightarrow \text{Ca}^{2+} + 2 \text{Cl}^- \]
This dissociates into 3 ions (1 calcium ion and 2 chloride ions), so:
\[ i_{\text{CaCl}_2} = 3 \]

3. **Compare the Values of \( i \)**:
Since both solutions have the same molality (\( m \)) and the same \( K_b \), the boiling point elevation will depend solely on the van 't Hoff factor (\( i \)):
\[ \Delta T_{b,\text{AlCl}_3} = i_{\text{AlCl}_3} \cdot m \cdot K_b \]
\[ \Delta T_{b,\text{CaCl}_2} = i_{\text{CaCl}_2} \cdot m \cdot K_b \]

- Since \( i_{\text{AlCl}_3} = 4 \) and \( i_{\text{CaCl}_2} = 3 \):
\[ \Delta T_{b,\text{AlCl}_3} > \Delta T_{b,\text{CaCl}_2} \]

4. **Relate the Boiling Points**:
The boiling point of a solution increases with the elevation:
\[ T_{b,\text{AlCl}_3} = T_{b,\text{pure solvent}} + \Delta T_{b,\text{AlCl}_3} \]
\[ T_{b,\text{CaCl}_2} = T_{b,\text{pure solvent}} + \Delta T_{b,\text{CaCl}_2} \]

Since \( \Delta T_{b,\text{AlCl}_3} > \Delta T_{b,\text{CaCl}_2} \), it follows that:
\[ T_{b,\text{AlCl}_3} > T_{b,\text{CaCl}_2} \]

5. **Final Conclusion**:
Therefore, the correct relationship between the boiling points of the two solutions is:
\[ T_1 > T_2 \]
where \( T_1 \) is the boiling point of the \( \text{AlCl}_3 \) solution and \( T_2 \) is the boiling point of the \( \text{CaCl}_2 \) solution.

### Answer:
The correct relationship is \( T_1 > T_2 \).