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Step-by-Step Explanation
Step 1: Identify Each Compound and Its Structure
The problem asks for the number of P–O–P (phosphorus–oxygen–phosphorus) bonds in three different compounds:
1. $H_{4}P_{2}O_{7}$ (pyrophosphoric acid),
2. $(HPO_{3})_{3}$ (cyclotriphosphoric acid),
3. $P_{4}O_{10}$ (phosphorus pentoxide).
Each compound has a distinct structural arrangement that leads to a specific count of bridging P–O–P bonds.
Step 2: Count the P–O–P Bonds in $H_{4}P_{2}O_{7}$
• Pyrophosphoric acid contains two phosphorus atoms connected by a bridging oxygen atom.
• This single bridging oxygen leads to exactly one P–O–P linkage.
• Hence, $H_{4}P_{2}O_{7}$ has 1 P–O–P bond.
Step 3: Count the P–O–P Bonds in $(HPO_{3})_{3}$
• Cyclotriphosphoric acid forms a cyclic structure with three phosphorus atoms and three bridging oxygens in the ring.
• Each bridging oxygen links two phosphorus atoms, and there are three such bridges in the ring.
• Thus, $(HPO_{3})_{3}$ has 3 P–O–P bonds.
Step 4: Count the P–O–P Bonds in $P_{4}O_{10}$
• Phosphorus pentoxide ($P_{4}O_{10}$) has four phosphorus atoms arranged in a cage-like framework with bridging oxygen atoms.
• There are six bridging oxygens that each link two phosphorus atoms, creating six distinct P–O–P bonds.
• Therefore, $P_{4}O_{10}$ contains 6 P–O–P bonds.
Step 5: Final Answer
Combining the results:
• $H_{4}P_{2}O_{7}$: 1 P–O–P bond
• $(HPO_{3})_{3}$: 3 P–O–P bonds
• $P_{4}O_{10}$: 6 P–O–P bonds
Thus, the correct answer is 1, 3, 6.
