1.5g of an organic compound in a quantitative determination of phosphorus gave 2.5090g of `Mg_(2)P_(2)O_(7)`. Calculate the percentage of phosphorus in the compound

Answer

To calculate the percentage of phosphorus in the organic compound based on the provided data, we can follow these steps:

### Step 1: Determine the Molecular Weight of Mg₂P₂O₇
The molecular formula for magnesium pyrophosphate is Mg₂P₂O₇. We need to calculate its molecular weight using the atomic weights of magnesium (Mg), phosphorus (P), and oxygen (O):

- Atomic weight of Mg = 24 g/mol
- Atomic weight of P = 31 g/mol
- Atomic weight of O = 16 g/mol

Now, we can calculate the molecular weight of Mg₂P₂O₇:

\[ \text{Molecular weight of Mg}_2\text{P}_2\text{O}_7 = (2 \times 24) + (2 \times 31) + (7 \times 16) \]

Calculating each component:

- For Mg: \(2 \times 24 = 48\)
- For P: \(2 \times 31 = 62\)
- For O: \(7 \times 16 = 112\)

Now, add them together:

\[ \text{Molecular weight of Mg}_2\text{P}_2\text{O}_7 = 48 + 62 + 112 = 222 \text{ g/mol} \]

### Step 2: Determine the Weight of Phosphorus in Mg₂P₂O₇
Next, we need to find out how much phosphorus is present in the compound Mg₂P₂O₇. Since there are 2 phosphorus atoms in the formula, we can calculate the total weight of phosphorus:

\[ \text{Weight of phosphorus in Mg}_2\text{P}_2\text{O}_7 = 2 \times 31 = 62 \text{ g} \]

### Step 3: Calculate the Weight of Phosphorus in the Sample
We have 2.5090 g of Mg₂P₂O₇. To find out how much phosphorus is in this amount, we set up a ratio:

\[ \text{Weight of phosphorus in 2.5090 g of Mg}_2\text{P}_2\text{O}_7 = \left(\frac{62 \text{ g P}}{222 \text{ g Mg}_2\text{P}_2\text{O}_7}\right) \times 2.5090 \text{ g} \]

Calculating this gives:

\[ \text{Weight of phosphorus} = \left(\frac{62}{222}\right) \times 2.5090 \approx 0.173 \text{ g} \]

### Step 4: Calculate the Percentage of Phosphorus in the Organic Compound
Now, we can calculate the percentage of phosphorus in the original organic compound:

\[ \text{Percentage of phosphorus} = \left(\frac{\text{Weight of phosphorus}}{\text{Weight of organic compound}}\right) \times 100 \]

Substituting the values:

\[ \text{Percentage of phosphorus} = \left(\frac{0.173}{1.5}\right) \times 100 \approx 11.53\% \]

### Final Answer
The percentage of phosphorus in the organic compound is approximately **11.53%**.

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