Vessel-1 contains w₂ g of a non-volatile solute X dissolved in w1 g of water. Vessel-2 contains w₂ g of another non-volatile solute Y dissolved in w₁ g of water. Both the vessels are at the same temperature and pressure. The molar mass of X is 80% of that of Y. The van’t Hoff factor for X is 1.2 times of that of Y for their respective concentrations. The elevation of boiling point for solution in Vessel-1 is _____ % of the solution in Vessel-2.

The correct answer is 150.

Let us find the elevation of boiling point for both solutions step-by-step.
The elevation in boiling point (${\mathrm{\Delta T}}_b$) is given by the formula:
${\mathrm{\Delta T}}_b=\; i\; *\; K$_b * m
where:
- $i$ is the van't Hoff factor
- $K_b$ is the molal elevation constant of the solvent (water)
- $m$ is the molality of the solution

Molality ($m$) is calculated as:
$m=\frac{w_2}{M*\; w}$₁ (in kg)
where $w_2$ is the mass of the solute, $M$ is the molar mass of the solute, and $w_1$ is the mass of the solvent (water).

Let the parameters for Vessel-1 (containing solute X) and Vessel-2 (containing solute Y) be:
- Molar mass of Y = $M_Y$
- Molar mass of X = $M_X=\; 0.8\; *\; M$_Y (since molar mass of X is 80% of Y)
- van't Hoff factor of Y = $i_Y$
- van't Hoff factor of X = $i_X=\; 1.2\; *\; i$_Y

Since both vessels contain $w_2$ g of solute dissolved in $w_1$ g of water, the molalities are:
For X (Vessel-1): $m_X=\frac{w_2}{M_X*\; w}$₁ = w20.8 * M_Y * w₁
For Y (Vessel-2): $m_Y=\frac{w_2}{M_Y*\; w}$₁

Now, let's write the ratio of the elevation of boiling point of Vessel-1 to Vessel-2:
$\frac{{\mathrm{\Delta T}}_{b1}}{{\mathrm{\Delta T}}_{b2}}=\frac{i_X*\; K}{}$_b * m_XiY * K_b * m_Y
Substituting the values:
$\frac{{\mathrm{\Delta T}}_{b1}}{{\mathrm{\Delta T}}_{b2}}=\frac{1.2*\; i}{}$_Y * w20.8 * M_Y * w₁iYw2MY * w₁
Simplifying the ratio:
$\frac{{\mathrm{\Delta T}}_{b1}}{{\mathrm{\Delta T}}_{b2}}=\frac{1.2}{0.8}=\frac{3}{2}=\; 1.5$

To express this as a percentage:
$\mathrm{Percentage}=\; 1.5\; *\; 100\%\; =\; 150\%$

Therefore, the elevation of boiling point for the solution in Vessel-1 is 150% of the solution in Vessel-2.