A compound of magnesium contains 21.9% magnesium, 27.8% phosphorus and 50.3% oxygen. What will be the simplest formula of the compound?

Options

A. `Mg_2P_2O_7`
B. `MgPO_3`
C. `Mg_2P_2O_2`
D. `MgP_2O_4`

Explanation

To find the simplest formula of the compound containing magnesium, phosphorus, and oxygen, we will follow these steps:

### Step 1: Convert the percentages to grams
Assuming we have 100 grams of the compound, we can directly take the percentages as grams:
- Magnesium (Mg): 21.9 g
- Phosphorus (P): 27.8 g
- Oxygen (O): 50.3 g

### Step 2: Convert grams to moles
Next, we will convert the mass of each element to moles using their atomic weights:
- Atomic weight of Magnesium (Mg) = 24 g/mol
- Atomic weight of Phosphorus (P) = 31 g/mol
- Atomic weight of Oxygen (O) = 16 g/mol

Calculating the moles:
- Moles of Mg = 21.9 g / 24 g/mol = 0.9125 mol
- Moles of P = 27.8 g / 31 g/mol = 0.8968 mol
- Moles of O = 50.3 g / 16 g/mol = 3.14375 mol

### Step 3: Divide by the smallest number of moles
Now, we will divide each mole value by the smallest number of moles calculated:
- Smallest number of moles = 0.8968 (for P)

Calculating the ratios:
- Ratio of Mg = 0.9125 mol / 0.8968 mol ≈ 1.018
- Ratio of P = 0.8968 mol / 0.8968 mol = 1
- Ratio of O = 3.14375 mol / 0.8968 mol ≈ 3.5

### Step 4: Convert to whole numbers
To convert the ratios to whole numbers, we can multiply all ratios by 2 (to eliminate the fraction for oxygen):
- Mg: 1.018 × 2 ≈ 2.036 ≈ 2
- P: 1 × 2 = 2
- O: 3.5 × 2 = 7

### Step 5: Write the simplest formula
The simplest formula based on the whole number ratios is:
- Mg₂P₂O₇

### Final Answer
The simplest formula of the compound is **Mg₂P₂O₇**.

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