Answer:
The given equation shows the decomposition of hydrated sodium sulfate to form anhydrous sodium sulfate:
$Na_2SO_{4 \cdot x} \rightarrow Na_2SO_4 + xH_2O$
From the given data, we know that 10.10 g of hydrated sodium sulfate decomposes to form 4.40 g of anhydrous sodium sulfate. Let's first calculate the number of moles of anhydrous sodium sulfate formed:
$Moles\ of\ Na_2SO_4\ =\ \frac{4.40\ g}{142.04\ g/mol} = 0.0310\ mol$
Since one mole of hydrated sodium sulfate produces one mole of anhydrous sodium sulfate, the number of moles of hydrated sodium sulfate present in 10.10 g can be calculated as:
$Moles\ of\ Na_2SO_{4 \cdot x}\ =\ 0.0310\ mol$
The formula mass of the hydrated sodium sulfate can be calculated by adding the molar masses of all its constituent atoms:
$Formula\ mass\ of\ Na_2SO_{4 \cdot x}\ =\ 2\times23.00\ g/mol\ +\ 32.06\ g/mol\ +\ x\times18.02\ g/mol = 142.04\ g/mol$
Solving for x, we get:
$x = \frac{142.04\ g/mol - 46.00\ g/mol - 32.06\ g/mol}{18.02\ g/mol} = 4$
Therefore, the formula of the hydrated sodium sulfate is $Na_2SO_{4 \cdot 4H_2O}$ and its formula mass is 322.20 g/mol.