Count Molecules with Homoatomic Covalent Bonds

To determine the total number of molecules containing a covalent bond formed between two atoms of the same element (homoatomic covalent bond), we examine the structure of each given species:

1. $\text{B}_2\text{H}_6$ (Diborane):

   • Structure consists of four 2-center-2-electron (2c-2e) terminal $\text{B}-\text{H}$ bonds and two 3-center-2-electron (3c-2e) $\text{B}-\text{H}-\text{B}$ bridge bonds.
   • It contains only $\text{B}-\text{H}$ bonds. There is no $\text{B}-\text{B}$ bond.
   • Homoatomic bond present: No

2. $\text{B}_3\text{N}_3\text{H}_6$ (Borazine):

   • Structure features a six-membered planar ring with alternating boron and nitrogen atoms ($\text{B}-\text{N}-\text{B}-\text{N}-\text{B}-\text{N}$).
   • The bonds present are $\text{B}-\text{N}$, $\text{B}-\text{H}$, and $\text{N}-\text{H}$.
   • It contains no $\text{B}-\text{B}$ or $\text{N}-\text{N}$ bonds.
   • Homoatomic bond present: No

3. $\text{N}_2\text{O}$ (Nitrous oxide):

   • Resonance structures: \text{:N}\equiv\text{N}^{+}-\text{\ddot{O}:}^{-} \leftrightarrow \text{:}\ddot{\text{N}}^{-}=\text{N}^{+}=\ddot{\text{O}}\text{:}
   • It contains a covalent bond between two nitrogen atoms ($\text{N}-\text{N}$).
   • Homoatomic bond present: Yes ($\text{N}-\text{N}$)

4. $\text{N}_2\text{O}_4$ (Dinitrogen tetroxide):

   • Structure: Two $\text{NO}_2$ monomeric units bonded via a nitrogen-nitrogen single bond ($\text{O}_2\text{N}-\text{NO}_2$).
   • It contains a covalent bond between two nitrogen atoms ($\text{N}-\text{N}$).
   • Homoatomic bond present: Yes ($\text{N}-\text{N}$)

5. $\text{H}_2\text{S}_2\text{O}_3$ (Thiosulfuric acid):

   • Structure: Analogous to $\text{H}_2\text{SO}_4$, where one non-protonated oxygen is replaced by a terminal sulfur atom, yielding $\text{S}=\text{S}(\text{OH})_2(=\text{O})$.
   • It contains a sulfur-sulfur bond ($\text{S}=\text{S}$).
   • Homoatomic bond present: Yes ($\text{S}-\text{S}$)

6. $\text{H}_2\text{S}_2\text{O}_8$ (Peroxodisulfuric acid / Marshall's acid):

   • Structure: $\text{HO}-\text{SO}_2-\text{O}-\text{O}-\text{SO}_2-\text{OH}$
   • It contains a peroxide linkage with an oxygen-oxygen single bond ($\text{O}-\text{O}$).
   • Homoatomic bond present: Yes ($\text{O}-\text{O}$)

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Conclusion:

The species containing a homoatomic covalent bond are $\text{N}_2\text{O}$, $\text{N}_2\text{O}_4$, $\text{H}_2\text{S}_2\text{O}_3$, and $\text{H}_2\text{S}_2\text{O}_8$.

Thus, the total count of such molecules is 4.