An inorganic compound on analysis was found to have following composition : Mg = 9.76%, S = 13.01%, O = 26.01%, `H_2O` = 51.22% Calculate the empirical formula of the compound.

Answer

To calculate the empirical formula of the compound based on the given percentage composition, we will follow these steps:

### Step 1: List the Elements and Their Percentages
We have the following elements and their respective percentages:
- Magnesium (Mg) = 9.76%
- Sulfur (S) = 13.01%
- Oxygen (O) = 26.01%
- Water (H₂O) = 51.22%

### Step 2: Convert Percentages to Masses
Assuming we have 100 grams of the compound, the masses of each element will be equal to their percentages:
- Mass of Mg = 9.76 g
- Mass of S = 13.01 g
- Mass of O = 26.01 g
- Mass of H₂O = 51.22 g

### Step 3: Calculate Moles of Each Element
To find the number of moles, we will divide the mass of each element by its molar mass:
- Molar mass of Mg = 24 g/mol
- Molar mass of S = 32 g/mol
- Molar mass of O = 16 g/mol
- Molar mass of H₂O = 18 g/mol

Calculating moles:
- Moles of Mg = 9.76 g / 24 g/mol = 0.4067 mol
- Moles of S = 13.01 g / 32 g/mol = 0.4063 mol
- Moles of O = 26.01 g / 16 g/mol = 1.6256 mol
- Moles of H₂O = 51.22 g / 18 g/mol = 2.8444 mol

### Step 4: Find the Simplest Ratio
To find the simplest ratio, we will divide the number of moles of each element by the smallest number of moles calculated:
- Smallest number of moles = 0.4063 (for S and Mg)

Calculating the ratios:
- Ratio of Mg = 0.4067 / 0.4063 ≈ 1
- Ratio of S = 0.4063 / 0.4063 = 1
- Ratio of O = 1.6256 / 0.4063 ≈ 4
- Ratio of H₂O = 2.8444 / 0.4063 ≈ 7

### Step 5: Write the Empirical Formula
From the simplest ratios, we can write the empirical formula:
- The empirical formula is Mg₁S₁O₄H₇, which can be written as MgSO₄·7H₂O.

### Final Answer
The empirical formula of the compound is **MgSO₄·7H₂O**.