If 3.943 g of anhydrous salt remains after heating 5.00 g of CuCℓ2·xH2O, determine the number of molecules of water of hydration in the original hydrate.

5.00 g = initial mass

-3.943 g after heating
-------
1.057 g = mass H2O driven off in heating

mols H2O = 1.057/18 = about 0.0587
mols CuCl2 = 3.943/134.5 = about 0.0293

Find the ratio and round to whole numbers with the smaller number being 1.00
0.0293/0.0293 = 1.00
0.0587/0.0293 = 2.00
So formula is (CuCl2)1Cl2.2H2O which would be written as CuCl2.2H2O

To determine the number of molecules of water of hydration in the original hydrate, we need to use the given information about the mass of the anhydrous salt and the mass of the initial hydrate.

First, let's calculate the number of moles of CuCl2 in the initial hydrate. We can do this by dividing the mass of CuCl2 by its molar mass. The molar mass of CuCl2 is calculated by adding the atomic masses of copper (Cu) and chlorine (Cl) together. The atomic masses of Cu and Cl are 63.55 g/mol and 35.45 g/mol, respectively.

Molar mass of CuCl2 = 63.55 g/mol + (2 * 35.45 g/mol) = 134.45 g/mol

Number of moles of CuCl2 = 5.00 g / 134.45 g/mol ≈ 0.0372 mol

Next, we need to calculate the number of moles of water in the anhydrous salt. We can do this by subtracting the mass of the anhydrous salt from the initial mass of the hydrate and then dividing that by the molar mass of water (H2O). The molar mass of water is 18.015 g/mol.

Mass of water in anhydrous salt = 5.00 g - 3.943 g = 1.057 g

Number of moles of water = 1.057 g / 18.015 g/mol ≈ 0.0586 mol

Now, we can find the ratio of moles of water to moles of CuCl2 in the hydrate. Dividing the number of moles of water by the number of moles of CuCl2 gives us the subscript (x) in the chemical formula CuCl2·xH2O.

Ratio of moles of water to moles of CuCl2 = 0.0586 mol / 0.0372 mol ≈ 1.58

Therefore, the number of molecules of water of hydration in the original hydrate is approximately 1.58.