1.6 g of an organic compound gave 2.6 g of magnesium pyrophosphate . The percentage of phosphorus is the compound is

Options

A. `45.38%`
B. `54.38`
C. `37.76%`
D. `19.02%`

Answer

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

### Step 1: Identify the mass of the organic compound and magnesium pyrophosphate.
- Mass of the organic compound = 1.6 g
- Mass of magnesium pyrophosphate (Mg2P2O7) = 2.6 g

### Step 2: Calculate the molar mass of magnesium pyrophosphate (Mg2P2O7).
- Molar mass of magnesium (Mg) = 24 g/mol
- Molar mass of phosphorus (P) = 31 g/mol
- Molar mass of oxygen (O) = 16 g/mol

The formula for magnesium pyrophosphate is Mg2P2O7, which contains:
- 2 magnesium atoms
- 2 phosphorus atoms
- 7 oxygen atoms

Calculating the molar mass:
\[ \text{Molar mass of Mg2P2O7} = (2 \times 24) + (2 \times 31) + (7 \times 16) \]
\[ = 48 + 62 + 112 = 222 \text{ g/mol} \]

### Step 3: Determine the total mass of phosphorus in magnesium pyrophosphate.
Since there are 2 phosphorus atoms in the formula Mg2P2O7:
\[ \text{Mass of phosphorus in Mg2P2O7} = 2 \times 31 = 62 \text{ g} \]

### Step 4: Calculate the percentage of phosphorus in magnesium pyrophosphate.
The percentage of phosphorus in magnesium pyrophosphate can be calculated using the formula:
\[ \text{Percentage of phosphorus} = \left( \frac{\text{Mass of phosphorus}}{\text{Molar mass of Mg2P2O7}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage of phosphorus} = \left( \frac{62}{222} \right) \times 100 \approx 27.93\% \]

### Step 5: Calculate the mass of phosphorus in the organic compound.
Using the mass of magnesium pyrophosphate produced (2.6 g):
\[ \text{Mass of phosphorus in the organic compound} = \text{Percentage of phosphorus} \times \text{Mass of Mg2P2O7} \]
\[ = 0.2793 \times 2.6 \approx 0.726 \text{ g} \]

### Step 6: Calculate the percentage of phosphorus in the organic compound.
Finally, we can find the percentage of phosphorus in the organic compound:
\[ \text{Percentage of phosphorus in the organic compound} = \left( \frac{\text{Mass of phosphorus in organic compound}}{\text{Mass of organic compound}} \right) \times 100 \]
\[ = \left( \frac{0.726}{1.6} \right) \times 100 \approx 45.38\% \]

### Final Answer:
The percentage of phosphorus in the organic compound is approximately **45.38%**.

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