A salt containing water of crystallization gave the following percentage composition :
Mg = 9.76 , S = 13.01 , O = 26.01 and `H_(2)O = 51.22`
Calculate the simplest formula. (At. Mass of Mg = 24)

Explanation

To find the simplest formula of the salt containing water of crystallization, we will follow these steps:

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

### Step 2: Convert Percentages to Grams
Assuming we have 100 grams of the compound, the mass of each component will be equal to its percentage:
- Mg = 9.76 g
- S = 13.01 g
- O = 26.01 g
- H₂O = 51.22 g

### Step 3: Calculate the Number of Moles of Each Element
We will use the molar mass of each element to convert grams to moles.

1. **Moles of Magnesium (Mg)**:
\[ \text{Moles of Mg} = \frac{9.76 \, \text{g}}{24 \, \text{g/mol}} = 0.407 \, \text{moles} \]

2. **Moles of Sulfur (S)**:
\[ \text{Moles of S} = \frac{13.01 \, \text{g}}{32 \, \text{g/mol}} = 0.407 \, \text{moles} \]

3. **Moles of Oxygen (O)**:
\[ \text{Moles of O} = \frac{26.01 \, \text{g}}{16 \, \text{g/mol}} = 1.626 \, \text{moles} \]

4. **Moles of Water (H₂O)**:
\[ \text{Moles of H₂O} = \frac{51.22 \, \text{g}}{18 \, \text{g/mol}} = 2.846 \, \text{moles} \]

### Step 4: Find the Simplest Ratio
Now we will divide the number of moles of each component by the smallest number of moles calculated (which is 0.407 for both Mg and S):

1. **Ratio for Mg**:
\[ \frac{0.407}{0.407} = 1 \]

2. **Ratio for S**:
\[ \frac{0.407}{0.407} = 1 \]

3. **Ratio for O**:
\[ \frac{1.626}{0.407} \approx 4 \]

4. **Ratio for H₂O**:
\[ \frac{2.846}{0.407} \approx 7 \]

### Step 5: Write the Empirical Formula
From the ratios calculated, we can write the empirical formula:
- Mg: 1
- S: 1
- O: 4
- H₂O: 7

Thus, the simplest formula of the salt is:
\[ \text{MgSO}_4 \cdot 7\text{H}_2\text{O} \]