Understanding the reactions of lime with water and carbon dioxide is important for many chemistry concepts. The solubility characteristics of the products are key to interpreting the given scenario.
The reaction of calcium oxide (CaO) with water forms calcium hydroxide ('A'):
\[ \text{CaO}(s) + \text{H}_2\text{O}(l) \rightarrow \text{Ca(OH)}_2(aq) \]
The product, calcium hydroxide, is known as slaked lime, and its aqueous solution is called lime water.
The reaction of calcium hydroxide with carbon dioxide forms calcium carbonate ('B'):
\[ \text{Ca(OH)}_2(aq) + \text{CO}_2(g) \rightarrow \text{CaCO}_3(s) + \text{H}_2\text{O}(l) \]
The product, calcium carbonate, is insoluble in water.
When calcium carbonate reacts with more water and carbon dioxide, it forms calcium hydrogencarbonate, which is soluble in water:
\[ \text{CaCO}_3(s) + \text{H}_2\text{O}(l) + \text{CO}_2(g) \rightarrow \text{Ca(HCO}_3\text{)}_2(aq) \]
The substance 'A' is calcium hydroxide (slaked lime).
A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol$^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____________ \(\times 10^{-2}\). (nearest integer)
[Given : $K_{b}$ of the solvent = 5.0 K kg mol$^{-1}$]
Assume the solution to be dilute and no association or dissociation of X takes place in solution.
Inductance of a coil with \(10^4\) turns is \(10\,\text{mH}\) and it is connected to a DC source of \(10\,\text{V}\) with internal resistance \(10\,\Omega\). The energy density in the inductor when the current reaches \( \left(\frac{1}{e}\right) \) of its maximum value is \[ \alpha \pi \times \frac{1}{e^2}\ \text{J m}^{-3}. \] The value of \( \alpha \) is _________.
\[ (\mu_0 = 4\pi \times 10^{-7}\ \text{TmA}^{-1}) \]