To determine the elevation of the boiling point for the solutions in both vessels, we need to use the concept of boiling point elevation. The boiling point elevation is given by the formula:

$$ \Delta T_b = i \cdot K_b \cdot m $$

Where:

• $$\Delta T_b$$ is the boiling point elevation
• $$i$$ is the van't Hoff factor
• $$K_b$$ is the ebullioscopic constant (which is the same for both solutions since they are dissolved in water)
• $$m$$ is the molality of the solution

We need to compare the boiling point elevations for both solutions in Vessel-1 and Vessel-2.

For Vessel-1, let the boiling point elevation be $$\Delta T_{b1}$$, and for Vessel-2, let it be $$\Delta T_{b2}$$.

Let's denote the molar mass of solute $$Y$$ as $$M_Y$$ g/mol. According to the problem, the molar mass of solute $$X$$ is 80% of that of $$Y$$, i.e.,

$$ M_X = 0.8 \cdot M_Y $$

The van't Hoff factor for $$X$$ is 1.2 times that of $$Y$$, i.e.,

$$ i_X = 1.2 \cdot i_Y $$

The molality $$m$$ of each solution can be calculated using the formula:

$$ m = \dfrac{w_2}{M \cdot w_1} $$

Thus, the molality of $$X$$ and $$Y$$ solutions are:

For solute $$X$$:

$$ m_X = \dfrac{w_2}{M_X \cdot w_1} = \dfrac{w_2}{0.8 \cdot M_Y \cdot w_1} $$

For solute $$Y$$:

$$ m_Y = \dfrac{w_2}{M_Y \cdot w_1} $$

Now, substituting the values into the boiling point elevation formula, we get for Vessel-1:

$$ \Delta T_{b1} = i_X \cdot K_b \cdot m_X = (1.2 \cdot i_Y) \cdot K_b \cdot \left( \dfrac{w_2}{0.8 \cdot M_Y \cdot w_1} \right) $$

For Vessel-2:

$$ \Delta T_{b2} = i_Y \cdot K_b \cdot m_Y = i_Y \cdot K_b \cdot \left( \dfrac{w_2}{M_Y \cdot w_1} \right) $$

To find the ratio of $$\Delta T_{b1}$$ to $$\Delta T_{b2}$$:

$$ \dfrac{\Delta T_{b1}}{\Delta T_{b2}} = \dfrac{(1.2 \cdot i_Y) \cdot K_b \cdot \left( \dfrac{w_2}{0.8 \cdot M_Y \cdot w_1} \right)}{i_Y \cdot K_b \cdot \left( \dfrac{w_2}{M_Y \cdot w_1} \right)} $$

Simplifying the ratio:

$$ \dfrac{\Delta T_{b1}}{\Delta T_{b2}} = \dfrac{1.2}{0.8} = 1.5 $$

This means the elevation of the boiling point for the solution in Vessel-1 is 150% of that in Vessel-2. Thus, the elevation of boiling point for solution in Vessel-1 is 150% of the elevation of the boiling point for the solution in Vessel-2.