0.5 g of an organic substance containing phosphorus was heated with conc `HNO_(3)` in the carius tube, the phosphoric acid thus formed was precipitated with magnesia mixture `(MgNH_(4)PO_(4))` which on ignition gave a residue to 1.0 g of megnesium pyrophosphate `(Mg_(2)P_(2)O_(7))` The percentage of phosphorous in the organic compound is

Options

A. `55.85%`
B. `29.72%`
C. 19.81%`
D. `20.5%`

Explanation

To find the percentage of phosphorus in the organic compound, we can follow these steps:

### Step 1: Calculate the molar mass of magnesium pyrophosphate (Mg₂P₂O₇).
- The molar mass is calculated as follows:
- Magnesium (Mg): 24 g/mol, and there are 2 magnesium atoms → 2 × 24 = 48 g/mol
- Phosphorus (P): 31 g/mol, and there are 2 phosphorus atoms → 2 × 31 = 62 g/mol
- Oxygen (O): 16 g/mol, and there are 7 oxygen atoms → 7 × 16 = 112 g/mol
- Total molar mass of Mg₂P₂O₇ = 48 + 62 + 112 = **222 g/mol**

### Step 2: Calculate the percentage of phosphorus in magnesium pyrophosphate (Mg₂P₂O₇).
- The percentage of phosphorus is calculated using the formula:
\[ \text{Percentage of P} = \left(\frac{\text{mass of P in Mg}_2\text{P}_2\text{O}_7}{\text{molar mass of Mg}_2\text{P}_2\text{O}_7}\right) \times 100 \]
- Substituting the values:
\[ \text{Percentage of P} = \left(\frac{62}{222}\right) \times 100 \approx 27.93\% \]

### Step 3: Relate the mass of magnesium pyrophosphate to the organic compound.
- The mass of magnesium pyrophosphate obtained is 1.0 g, and the mass of the organic compound is 0.5 g.
- The ratio of the mass of Mg₂P₂O₇ to the mass of the organic compound is:
\[ \text{Ratio} = \frac{\text{mass of Mg}_2\text{P}_2\text{O}_7}{\text{mass of organic compound}} = \frac{1.0 \text{ g}}{0.5 \text{ g}} = 2 \]

### Step 4: Calculate the percentage of phosphorus in the organic compound.
- Since the ratio is 2, the percentage of phosphorus in the organic compound is double that in Mg₂P₂O₇:
\[ \text{Percentage of P in organic compound} = 2 \times \left(\frac{62}{222}\right) \times 100 \]
- Calculating this gives:
\[ \text{Percentage of P in organic compound} = 2 \times 27.93\% \approx 55.85\% \]

### Final Answer:
The percentage of phosphorus in the organic compound is approximately **55.85%**.

---