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.


Electricity is passed through an acidic solution of Cu$^{2+}$ till all the Cu$^{2+}$ was exhausted, leading to the deposition of 300 mg of Cu metal. However, a current of 600 mA was continued to pass through the same solution for another 28 minutes by keeping the total volume of the solution fixed at 200 mL. The total volume of oxygen evolved at STP during the entire process is ___ mL. (Nearest integer)
Given:
$\mathrm{Cu^{2+} + 2e^- \rightarrow Cu(s)}$
$\mathrm{O_2 + 4H^+ + 4e^- \rightarrow 2H_2O}$
Faraday constant = 96500 C mol$^{-1}$
Molar volume at STP = 22.4 L
In the following \(p\text{–}V\) diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where \(a\) is a constant. The total work done in the closed path is: 
Let \( ABC \) be a triangle. Consider four points \( p_1, p_2, p_3, p_4 \) on the side \( AB \), five points \( p_5, p_6, p_7, p_8, p_9 \) on the side \( BC \), and four points \( p_{10}, p_{11}, p_{12}, p_{13} \) on the side \( AC \). None of these points is a vertex of the triangle \( ABC \). Then the total number of pentagons that can be formed by taking all the vertices from the points \( p_1, p_2, \ldots, p_{13} \) is ___________.
Consider the following two reactions A and B: 
The numerical value of [molar mass of $x$ + molar mass of $y$] is ___.