Sum of $\pi$-bonds present in peroxodisulphuric acid and pyrosulphuric acid is___________

Question

Statement-I: An element ‘X’ of P-block forms a hydride H–X, which has the longest bond length, then element ‘X’ will have the shortest covalent radius.
Statement-II: An element ‘E’ of Group 15 forms hydride EH$_3$, that has least B.P. The maximum covalency of E is 4.

Answer 1

To solve the problem of finding the total number of $\pi$-bonds in peroxodisulphuric acid and pyrosulphuric acid, let's analyze the structure of each compound:

1. Peroxodisulphuric acid ($H_2S_2O_8$):

In peroxodisulphuric acid, the structure involves two sulfate ($SO_4^{-}$) groups linked by a peroxide bond ($O-O$). Each sulfur atom is bonded to four oxygen atoms: one via a single ($O-H$), two via double bonds ($S=O$), and one via an $O-O$ linkage or $O-S$. Therefore, each sulfur has two $\pi$-bonds from the $S=O$ double bonds.

Total $\pi$-bonds in peroxodisulphuric acid: $4$ (2 from each sulfate group).

2. Pyrosulphuric acid ($H_2S_2O_7$):

In pyrosulphuric acid, the structure comprises two sulfate ($SO_4^{-}$) units sharing an oxygen atom (resembling two sulfuric acid units minus one water molecule). Each sulfur atom is bonded to four oxygen atoms: one with a hydroxyl group ($O-H$) and three others ($S=O$) joined via an oxygen ($O$-linkage).

Each sulfur atom in pyrosulphuric acid contains two $\pi$-bonds due to the $S=O$ linkages.

Total $\pi$-bonds in pyrosulphuric acid: $4$ (2 per sulfur within $(SO_4^{-})$ units, shared oxygen does not contribute additional $\pi$-bonds).

Thus, the total number of $\pi$-bonds in both acids is:
$4\: (\text{from}\: H_2S_2O_8)\: +\: 4\: (\text{from}\: H_2S_2O_7)\: =\: 8$.

The sum of $\pi$-bonds is $8$, fitting the expected range of 8 to 8.

Sum of \(\pi\)-bonds present in peroxodisulphuric acid and pyrosulphuric acid is___________

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Correct Answer: 8

Solution and Explanation

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