To determine the oxidation states of phosphorus in the given compounds, we need to apply the rules for finding oxidation numbers. Let's calculate systematically for each compound:
$H_4P_2O_5$
Let the oxidation state of phosphorus (P) be \(x\).
The oxidation state of hydrogen (H) is +1 and that of oxygen (O) is -2.
There are 4 hydrogens, 2 phosphorus, and 5 oxygens. Thus, the compound is neutral, so we equate the sum of oxidation states to zero:
\(4(+1) + 2(x) + 5(-2) = 0\)
\(4 + 2x - 10 = 0\)
\(2x - 6 = 0\)
\(2x = 6\)
\(x = +3\)
$H_4P_2O_6$
Let the oxidation state of phosphorus (P) be \(x\).
The sum of the oxidation states will also be zero.
\(4(+1) + 2(x) + 6(-2) = 0\)
\(4 + 2x - 12 = 0\)
\(2x - 8 = 0\)
\(2x = 8\)
\(x = +4\)
$H_4P_2O_7$
Again, let the oxidation state of phosphorus (P) be \(x\).
\(4(+1) + 2(x) + 7(-2) = 0\)
\(4 + 2x - 14 = 0\)
\(2x - 10 = 0\)
\(2x = 10\)
\(x = +5\)
Therefore, the oxidation states of phosphorus in $H_4P_2O_5$, $H_4P_2O_6$, and $H_4P_2O_7$ are +3, +4, and +5 respectively. However, the original question specifies the option is an error, suggesting this may be a trick question with the necessity to recognize the lack of a proper option indicative of conceptual understanding. To summarize: