1.24 g of $$AX_{2}$$ (molar mass 124 g $$mol^{-1}$$) is dissolved in 1 kg of water to form a solution with boiling point of $$100.0156^{\circ}C$$, while $$25.4g^{\circ}$$ of $$AY_{2}$$ (molar mass 250 g $$mol^{-1}$$) in 2 kg of water constitutes a solution with a boiling point of $$100.0260^{\circ}C.K_{b}(H_{2}O)=0.52 K$$ kg $$mol^{-1}$$ Which of the following is correct ?

Using $$\Delta T_b = i \cdot K_b \cdot m$$ with $$K_b = 0.52$$ K kg mol$$^{-1}$$.

For $$AX_2$$: $$\Delta T_b = 0.0156°C$$, molality = $$0.01$$ mol/kg.

$$i = \frac{0.0156}{0.52 \times 0.01} = 3$$

Since $$AX_2 \to A^{2+} + 2X^-$$ gives 3 particles, $$AX_2$$ is fully ionised.

For $$AY_2$$: $$\Delta T_b = 0.0260°C$$, molality = $$\frac{25.4/250}{2} = 0.0508$$ mol/kg.

$$i = \frac{0.0260}{0.52 \times 0.0508} \approx 1$$

Since $$i \approx 1$$, $$AY_2$$ is completely unionised.

The correct answer is Option 1: $$AX_2$$ is fully ionised while $$AY_2$$ is completely unionised.