a student takes 4.597g of hydrated barium chloride and heats it in a crucible. The anhydrous material weighed 3.919g. What is the complete formula for this hydrated salt?

g H2O = 4.597 - 3.919 = 0.678

g BaCl2 = 3.919

Convert 0.678 g H2O moles. Moles = grams/molar mass
Convert 3.919 g BaCl2 to moles the same way.
Now fine the whole number ratio between the two. The easy way to do that is to divide the moles BaCl2 by itself (since you want 1.00 mole BaCl2) and this will give you exactly 1.00 mole. Then divide the moles water by the moles BaCl2 to find x in the formula, BaCl2.xH2O.

To determine the complete formula for the hydrated salt, we need to understand the concept of hydrates. Hydrates are compounds that contain a specific number of water molecules attached to their crystal structure. The water molecules are called water of crystallization.

Given that the student heated the hydrated barium chloride and obtained the anhydrous material, we can calculate the number of water molecules lost during the heating process and then find the complete formula for the hydrated salt.

Let's start by finding the mass of water lost during heating:

Mass of hydrated barium chloride (initial): 4.597g
Mass of anhydrous material (final): 3.919g

Mass of water lost = Mass of hydrated barium chloride - Mass of anhydrous material
= 4.597g - 3.919g
= 0.678g

Now, we know that the molar mass of water (H₂O) is approximately 18 g/mol. So, we can calculate the number of moles of water lost:

Moles of water lost = Mass of water lost / Molar mass of water
= 0.678g / 18 g/mol
≈ 0.03767 mol

The mole ratio between the anhydrous salt and the water molecules will give us the complete formula for the hydrated salt. From the data given, we can see that for every 1 mole of anhydrous material, 0.03767 moles of water were lost.

To simplify the formula, we divide each mole ratio by the smallest value to obtain whole-number ratios. In this case, the smallest value is approximately 0.03767, so we will divide both ratios by 0.03767:

Anhydrous material: water = 1 : 0.03767
Approximately: Anhydrous material: water ≈ 26 : 1

From this calculation, we can conclude that the complete formula for the hydrated salt is BaCl₂ · 2H₂O. The "· 2H₂O" indicates that two moles of water are associated with one mole of BaCl₂.