Answer:
4
Explanation:
Let's start by assuming that the initial mass of the hydrate CoCl2 x XH2O is 100 grams. This means that the mass of the anhydrous compound CoCl2 after decomposition is 53.9 grams (since it is 53.9% of the hydrate mass).
The mass of water lost during the decomposition is therefore:
Mass of water lost = Initial mass of hydrate - Mass of anhydrous compound
Mass of water lost = 100 g - 53.9 g
Mass of water lost = 46.1 g
The molar mass of CoCl2 is 129.8 g/mol, and the molar mass of H2O is 18.0 g/mol. Therefore, the molar mass of the hydrate CoCl2 x XH2O is:
Molar mass of hydrate = Molar mass of CoCl2 + Molar mass of H2O × X
Molar mass of hydrate = 129.8 g/mol + 18.0 g/mol × X
We can set up a proportion to solve for X:
Mass of water lost / Molar mass of water = X / Molar mass of hydrate
Plugging in the values we found:
46.1 g / 18.0 g/mol = X / (129.8 g/mol + 18.0 g/mol × X)
Solving for X:
46.1 g / 18.0 g/mol = X / (129.8 g/mol + 18.0 g/mol × X)
2.56 mol = X / (129.8 g/mol + 18.0 g/mol × X)
2.56 mol × (129.8 g/mol + 18.0 g/mol × X) = X
331.968 g/mol × X + 46.368 g/mol × X = X
378.336 g/mol × X = X
X = 4
Therefore, the value of X in the hydrate formula CoCl2 x XH2O is 4, and the formula of the hydrate is CoCl2 x 4H2O.