The value of x is ___.

The boiling‐point elevation formula is
$$\Delta T_b = i\,K_b\,m$$
where $$i$$ is the van’t Hoff factor, $$K_b$$ is the ebullioscopic constant and $$m$$ is the molality.

For solution A:
• Solute = $$AgNO_3$$ which dissociates completely as $$AgNO_3 \rightarrow Ag^{+} + NO_3^{-}$$.
• Number of ions produced = 2, so $$i = 2$$.
• Given molality $$m = 0.1\;{\rm mol\,kg^{-1}}$$.
• Given $$K_b = 0.5\;{\rm K\,kg\,mol^{-1}}$$.

Substituting in the formula:
$$\Delta T_b = 2 \times 0.5 \times 0.1 = 0.1\;{\rm K}$$.

The boiling point of pure water is $$100.00^\circ{\rm C}$$, therefore the boiling point of solution A is
$$x = 100.00^\circ{\rm C} + 0.10^\circ{\rm C} = 100.10^\circ{\rm C}$$.

Hence, the value of $$x$$ is 100.10 °C.