To determine which electrolyte can be used to obtain \( \text{H}_2\text{S}_2\text{O}_8 \) (peroxydisulfuric acid) by the process of electrolysis, we need to understand the conditions required for its formation:
1. Principle of Electrolysis: Electrolysis involves the decomposition of compounds using an electric current. The electrolyte's nature significantly affects the products formed.
2. Peroxydisulfuric Acid Formation: This compound is specifically formed when concentrated sulfuric acid is electrolyzed. The equation for the formation of \( \text{H}_2\text{S}_2\text{O}_8 \) is as follows:
2 \( \text{HSO}_4^- \) (aq) → \( \text{H}_2\text{S}_2\text{O}_8 \) (aq) + 2 \( e^- \)
3. Options Analysis:
| Option | Suitability |
| Dilute solution of sodium sulphate | Not suitable, lacks sufficient sulfate ions and concentration. |
| Dilute solution of sulphuric acid | Not suitable due to low concentration. |
| Concentrated solution of sulphuric acid | Suitable; provides high concentration of sulfate ions for forming \( \text{H}_2\text{S}_2\text{O}_8 \). |
| Acidified dilute solution of sodium sulphate | Not suitable, lacks adequate concentration of \( \text{HSO}_4^- \) ions. |
The process's efficiency in forming \( \text{H}_2\text{S}_2\text{O}_8 \) increases with the concentration of \( \text{HSO}_4^- \) ions provided by concentrated sulfuric acid, which makes it the correct choice.
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 _________.
\[ (\mu_0 = 4\pi \times 10^{-7}\ \text{TmA}^{-1}) \]