The hydrate, CaCl2•xH2O, loses 25% of its mass when heated to constant mass. What is the formula of the hydrate?
To determine the formula of the hydrate, we need to understand the concept of a hydrate and how to calculate its formula.
A hydrate is a compound that contains water molecules within its crystal structure. The formula of a hydrate consists of the formula of the anhydrous compound combined with a specific number of water molecules. The dot (•) is used to separate the anhydrous compound formula from the water molecules formula.
In this case, we are given that the hydrate, CaCl2•xH2O, loses 25% of its mass when heated to constant mass. This means that the water molecules are being removed, leaving behind the anhydrous compound.
To find the formula of the hydrate, we need to determine the value of x, which represents the number of water molecules associated with one formula unit of the anhydrous compound.
To calculate x, we can use the mass loss information provided. The mass loss is due to the removal of water molecules, which have a known molecular weight of 18 g/mol (2 hydrogen atoms of 1 g/mol each and 1 oxygen atom of 16 g/mol).
Given that the mass loss is 25%, we can set up the following equation:
(18 g/mol) * x / (molar mass of CaCl2•xH2O) = 25%
Now we need to determine the molar mass of CaCl2•xH2O. It consists of calcium chloride (CaCl2) and water (H2O). The molar mass of CaCl2 is (40.08 g/mol for calcium + (2 * 35.45 g/mol) for chlorine) = 110.98 g/mol.
Now substituting the values into the equation:
(18 g/mol) * x / (110.98 g/mol + 18 g/mol * x) = 25%
To solve for x, we need to isolate it on one side of the equation. Let's multiply both sides by the denominator to eliminate it:
(18 g/mol) * x = 0.25 * (110.98 g/mol + 18 g/mol * x)
Next, distribute on the right-hand side:
(18 g/mol) * x = 0.25 * 110.98 g/mol + 0.25 * (18 g/mol) * x
Combine like terms:
(18 g/mol) * x = 27.745 g/mol + 4.5 g/mol * x
Move the terms involving x to one side by subtracting 4.5 g/mol * x from both sides:
(18 g/mol) * x - 4.5 g/mol * x = 27.745 g/mol
Simplify:
13.5 g/mol * x = 27.745 g/mol
Now solve for x by dividing both sides by 13.5 g/mol:
x = 27.745 g/mol / 13.5 g/mol
x ≈ 2.055
Since x represents the number of water molecules, it must be a whole number. We can round it to the nearest whole number, which in this case is 2.
Therefore, the formula of the hydrate is CaCl2•2H2O.