1. Idea of bridging oxo group

A bridging oxo group is an oxygen atom connecting two central atoms, i.e. a linkage like: $\text{A}-\text{O}-\text{A}$ Typical examples here are $\text{N}-\text{O}-\text{N}$, $\text{P}-\text{O}-\text{P}$, or $\text{S}-\text{O}-\text{S}$.

We check each compound one by one.

2. Examination of each compound

(i) $N_2O_3$

Dinitrogen trioxide has structure corresponding to nitrous anhydride: $O=N-O-N=O$ Here the middle oxygen bridges the two nitrogen atoms.

So, $N_2O_3$ has a bridging oxo group.

✅ Count = 1

(ii) $N_2O_5$

In gaseous/molecular form, dinitrogen pentoxide has structure: $O_2N-O-NO_2$ There is one oxygen atom bridging the two nitrogen atoms.

So, $N_2O_5$ has a bridging oxo group.

✅ Count = 2

(iii) $P_4O_6$

$P_4O_6$ has a cage structure derived from $P_4$, where the phosphorus atoms are connected through oxygen bridges. All six oxygen atoms are bridging oxygens.

So, $P_4O_6$ has bridging oxo groups.

✅ Count = 3

(iv) $P_4O_7$

This is obtained by partial oxidation of $P_4O_6$. It still retains the cage framework with $P-O-P$ bridges, along with one terminal $P=O$ bond.

So, $P_4O_7$ has bridging oxo groups.

✅ Count = 4

(v) $H_4P_2O_5$

This is pyrophosphorous acid. Its structure contains a $P-O-P$ linkage: $HO-P(H)-O-P(H)-OH$ Hence it contains one bridging oxygen.

So, $H_4P_2O_5$ has a bridging oxo group.

✅ Count = 5

(vi) $H_5P_3O_{10}$

This is triphosphoric acid-type chain compound. It contains phosphorus atoms connected through $P-O-P$ linkages. A chain of three phosphorus atoms requires two bridging oxygens.

So, $H_5P_3O_{10}$ has bridging oxo groups.

✅ Count = 6

(vii) $H_2S_2O_3$

This is thiosulfuric acid. Its structure is analogous to sulfuric acid with one oxygen replaced by sulfur, and it contains an $S-S$ bond, not an $S-O-S$ bridge.

So, $H_2S_2O_3$ does not have a bridging oxo group.

❌ Count remains 6

(viii) $H_2S_2O_5$

This is disulfurous (pyrosulfurous) acid. Its structure contains an $S-O-S$ linkage: $HO-S(=O)-O-S(=O)-OH$ Thus one oxygen bridges the two sulfur atoms.

So, $H_2S_2O_5$ has a bridging oxo group.

✅ Count = 7

3. Total count

Compounds having at least one bridging oxo group are: $N_2O_3,\ N_2O_5,\ P_4O_6,\ P_4O_7,\ H_4P_2O_5,\ H_5P_3O_{10},\ H_2S_2O_5$

Hence total number is: $7$

4. Comparison with stored answer

Stored correct answer = $6$

My derived answer = $7$

I disagree with the stored answer. The likely omitted compound is $H_2S_2O_5$, which does contain an $S-O-S$ bridging oxo group.