How many moles of `H_3 PO_4` are obtained on hydrolysis of one mole of `P_4 O_8`.

Explanation

To determine how many moles of \( H_3PO_4 \) (phosphoric acid) are obtained from the hydrolysis of one mole of \( P_4O_8 \) (tetraphosphorus octoxide), we can follow these steps:

### Step 1: Write the Hydrolysis Reaction
The hydrolysis of tetraphosphorus octoxide can be represented by the following equation:
\[ P_4O_8 + H_2O \rightarrow H_3PO_3 + H_3PO_4 \]
This indicates that \( P_4O_8 \) reacts with water to produce phosphorous acid (\( H_3PO_3 \)) and phosphoric acid (\( H_3PO_4 \)).

### Step 2: Balance the Reaction
Next, we need to balance the reaction. We start by counting the number of phosphorus atoms, hydrogen atoms, and oxygen atoms on both sides of the equation.

1. **Phosphorus (P)**: There are 4 phosphorus atoms in \( P_4O_8 \). Thus, we can write:
\[ P_4O_8 + H_2O \rightarrow 2 H_3PO_3 + 2 H_3PO_4 \]
This means we need 2 moles of \( H_3PO_3 \) and 2 moles of \( H_3PO_4 \) to balance the phosphorus.

2. **Hydrogen (H)**: The total hydrogen from the products is \( 2 \times 3 + 2 \times 3 = 6 + 6 = 12 \) hydrogen atoms. Therefore, we need 6 water molecules:
\[ P_4O_8 + 6 H_2O \rightarrow 2 H_3PO_3 + 2 H_3PO_4 \]

3. **Oxygen (O)**: Now we check the oxygen. On the left side, we have 8 from \( P_4O_8 \) and 6 from water, totaling 14 oxygen atoms. On the right side, we have:
\[ 2 \times 3 + 2 \times 4 = 6 + 8 = 14 \]
Thus, the equation is balanced.

### Step 3: Determine Moles of \( H_3PO_4 \)
From the balanced equation, we see that for every mole of \( P_4O_8 \) that undergoes hydrolysis, we produce 2 moles of \( H_3PO_4 \).

### Final Answer
Therefore, the number of moles of \( H_3PO_4 \) obtained from the hydrolysis of one mole of \( P_4O_8 \) is:
\[ \text{2 moles of } H_3PO_4 \]

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