$$2$$ g of a non-volatile non-electrolyte solute is dissolved in $$200$$ g of two different solvents A and B whose ebullioscopic constants are in the ratio of $$1 : 8$$. The elevation in boiling points of A and B are in the ratio $$\frac{x}{y}$$ ($$x : y$$). The value of $$y$$ is ______ (Nearest Integer)

The elevation in boiling point is given by:

$$\Delta T_b = K_b \times m$$

where $$K_b$$ is the ebullioscopic constant and $$m$$ is the molality.

Molality is given by:

$$m = \frac{n_{\text{solute}}}{W_{\text{solvent (kg)}}}$$

Since the same solute (2 g of non-volatile non-electrolyte) is dissolved in the same mass of solvent (200 g) for both solvents A and B:

$$m_A = m_B = m = \frac{n}{0.2}$$

The molality is the same for both solutions.

Therefore:

$$\Delta T_{b,A} = K_{b,A} \times m$$

$$\Delta T_{b,B} = K_{b,B} \times m$$

Taking the ratio:

$$\frac{\Delta T_{b,A}}{\Delta T_{b,B}} = \frac{K_{b,A}}{K_{b,B}}$$

Given that $$K_{b,A} : K_{b,B} = 1 : 8$$:

$$\frac{\Delta T_{b,A}}{\Delta T_{b,B}} = \frac{1}{8} = \frac{x}{y}$$

So $$x = 1$$ and $$y = 8$$.

Hence, the value of $$y$$ is 8.