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: Write down the percentages of each element
- Magnesium (Mg): 21.9%
- Phosphorus (P): 27.8%
- Oxygen (O): 50.3%

### Step 2: Convert percentages to grams
Assuming we have 100 grams of the compound, the mass of each element will be:
- Mg: 21.9 g
- P: 27.8 g
- O: 50.3 g

### Step 3: Convert grams to moles
To convert grams to moles, we will use the molar masses of each element:
- Molar mass of Mg = 24 g/mol
- Molar mass of P = 31 g/mol
- Molar mass of O = 16 g/mol

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

### Step 4: Find the simplest mole ratio
To find the simplest ratio, we divide the number of moles of each element by the smallest number of moles calculated:
- For Mg: 0.9125 / 0.8968 ≈ 1.017
- For P: 0.8968 / 0.8968 = 1
- For O: 3.14375 / 0.8968 ≈ 3.5

### Step 5: Convert to whole numbers
The ratios we have are approximately:
- Mg: 1.017 (approximately 1)
- P: 1
- O: 3.5

Since we cannot have a fraction in the simplest formula, we multiply all ratios by 2 to convert them into whole numbers:
- Mg: 1 × 2 = 2
- P: 1 × 2 = 2
- O: 3.5 × 2 = 7

### Step 6: Write the simplest formula
The simplest formula of the compound is:
\[ \text{Mg}_2\text{P}_2\text{O}_7 \]

### Summary
The simplest formula of the compound containing magnesium, phosphorus, and oxygen is \( \text{Mg}_2\text{P}_2\text{O}_7 \).

---