0.3160 g of an organic substance was heated with fuming nitric acid in a carius tube to convert phosphorus present into phosphoric acid. Addition of magnesia mixture formed `MgNH_(4)PO_(4)` which upon heating gave `0.1697 g Mg_(2)P_(2)O_(7)`. Calculate the percentage of phosphorus in the compound.

Explanation

To calculate the percentage of phosphorus in the organic compound, we will follow these steps:

### Step 1: Determine the molar mass of \( \text{Mg}_2\text{P}_2\text{O}_7 \)

1. **Calculate the molar mass of each element in the compound:**
- Magnesium (Mg): \( 24 \, \text{g/mol} \)
- Phosphorus (P): \( 31 \, \text{g/mol} \)
- Oxygen (O): \( 16 \, \text{g/mol} \)

2. **Calculate the total molar mass of \( \text{Mg}_2\text{P}_2\text{O}_7 \):**
\[ \text{Molar mass of } \text{Mg}_2\text{P}_2\text{O}_7 = (2 \times 24) + (2 \times 31) + (7 \times 16) \]
\[ = 48 + 62 + 112 = 222 \, \text{g/mol} \]

### Step 2: Calculate the mass of phosphorus in \( \text{Mg}_2\text{P}_2\text{O}_7 \)

1. **Determine the total mass of phosphorus in the compound:**
\[ \text{Mass of P in } \text{Mg}_2\text{P}_2\text{O}_7 = 2 \times 31 = 62 \, \text{g} \]

### Step 3: Calculate the percentage of phosphorus in the organic compound

1. **Use the formula for percentage of phosphorus:**
\[ \text{Percentage of P} = \left( \frac{\text{Mass of P in } \text{Mg}_2\text{P}_2\text{O}_7}{\text{Molar mass of } \text{Mg}_2\text{P}_2\text{O}_7} \times \text{Mass of } \text{Mg}_2\text{P}_2\text{O}_7 \right) \div \text{Mass of organic compound} \times 100 \]

2. **Substituting the values:**
\[ \text{Percentage of P} = \left( \frac{62}{222} \times 0.1697 \right) \div 0.3160 \times 100 \]

3. **Calculating the values:**
- Calculate the mass of phosphorus in the sample:
\[ \text{Mass of P} = \frac{62}{222} \times 0.1697 \approx 0.0471 \, \text{g} \]
- Now calculate the percentage:
\[ \text{Percentage of P} = \left( \frac{0.0471}{0.3160} \right) \times 100 \approx 14.89\% \]

### Final Answer:
The percentage of phosphorus in the organic compound is approximately **14.89%**.

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