Quantitative estimatin of `C,H` and extra elements (e.g., N.S.P., and halogens) is carried out by Liebig's combustion, Carius, Dumas, and Kjeldahl's method.
Q. In the quantitative estimation of phosphorous by using magnesia mixture, the formula used is: Where W is the mass of `Mg_2P_2O_7` and w is the mass of the compound.

Options

A. Percentage of `P=(62)/(222)xx(Wxx100)/(w)`
B. Percentage of `P=(31)/(222)xx(Wxx100)/(w)`
C. Percentage of `P=(62)/(222)xx(wxx100)/(W)`
D. Percentage of `P=(31)/(222)xx(wxx100)/(W)`

Answer

To determine the percentage of phosphorus in a compound using the magnesium mixture method, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: The formula used for the quantitative estimation of phosphorus in a compound is given as:
\[ \text{Percentage of Phosphorus} = \left( \frac{62}{222} \right) \times \frac{W_{Mg_2P_2O_7}}{w} \times 100 \]
where:
- \( W_{Mg_2P_2O_7} \) is the mass of magnesium pyrophosphate (Mg2P2O7).
- \( w \) is the mass of the compound being analyzed.

2. **Identify the Constants**: In the formula:
- \( 62 \) is the mass of phosphorus in one mole of magnesium pyrophosphate (Mg2P2O7).
- \( 222 \) is the molar mass of magnesium pyrophosphate (Mg2P2O7), calculated as follows:
- Magnesium (Mg): 24.31 g/mol (2 moles)
- Phosphorus (P): 30.97 g/mol (2 moles)
- Oxygen (O): 16.00 g/mol (7 moles)
- Total = \( 2 \times 24.31 + 2 \times 30.97 + 7 \times 16.00 = 222 \) g/mol.

3. **Substitute Values**: If you have the mass of magnesium pyrophosphate (\( W_{Mg_2P_2O_7} \)) and the mass of the compound (\( w \)), substitute these values into the formula.

4. **Calculate the Percentage**: Perform the calculation to find the percentage of phosphorus in the compound.

### Example Calculation:
Suppose \( W_{Mg_2P_2O_7} = 1.5 \, \text{g} \) and \( w = 10 \, \text{g} \):
\[ \text{Percentage of Phosphorus} = \left( \frac{62}{222} \right) \times \frac{1.5}{10} \times 100 \]
\[ = \left( 0.279 \right) \times 0.15 \times 100 \]
\[ = 4.19\% \]

### Final Answer:
The percentage of phosphorus in the compound is approximately \( 4.19\% \).