The oxidation number of phosphorus in `PO_(4)^(3-), P_(4)O_(10)`, and `P_(2)O_(7)^(4-)` is

Options

A. `+5`
B. `+3`
C. `-3`
D. `+2`

Explanation

To determine the oxidation number of phosphorus in the compounds \( PO_4^{3-} \), \( P_4O_{10} \), and \( P_2O_7^{4-} \), we will analyze each compound step by step.

### Step 1: Calculate the oxidation number of phosphorus in \( PO_4^{3-} \)

1. Let the oxidation number of phosphorus be \( x \).
2. The oxidation number of oxygen is \(-2\).
3. The compound has 4 oxygen atoms, so the total contribution from oxygen is \( 4 \times (-2) = -8 \).
4. The overall charge of the ion is \(-3\).

Now, we can set up the equation:

\[ x + (-8) = -3 \]

5. Rearranging gives:

\[ x - 8 = -3 \implies x = -3 + 8 \implies x = +5 \]

### Step 2: Calculate the oxidation number of phosphorus in \( P_4O_{10} \)

1. Again, let the oxidation number of phosphorus be \( x \).
2. There are 4 phosphorus atoms, so their total contribution is \( 4x \).
3. The compound has 10 oxygen atoms, contributing \( 10 \times (-2) = -20 \).
4. Since this is a neutral compound, the total charge is 0.

Setting up the equation:

\[ 4x + (-20) = 0 \]

5. Rearranging gives:

\[ 4x - 20 = 0 \implies 4x = 20 \implies x = \frac{20}{4} = +5 \]

### Step 3: Calculate the oxidation number of phosphorus in \( P_2O_7^{4-} \)

1. Let the oxidation number of phosphorus be \( x \).
2. There are 2 phosphorus atoms, so their total contribution is \( 2x \).
3. The compound has 7 oxygen atoms, contributing \( 7 \times (-2) = -14 \).
4. The overall charge of the ion is \(-4\).

Setting up the equation:

\[ 2x + (-14) = -4 \]

5. Rearranging gives:

\[ 2x - 14 = -4 \implies 2x = -4 + 14 \implies 2x = 10 \implies x = \frac{10}{2} = +5 \]

### Conclusion

The oxidation number of phosphorus in all three compounds \( PO_4^{3-} \), \( P_4O_{10} \), and \( P_2O_7^{4-} \) is \( +5 \).