91Ó°ÊÓ

To calculate the molar mass of a compound, you must sum up the atomic masses of all the atoms in its chemical formula. This involves looking at the periodic table to obtain the atomic masses of each element. For example, in the compound \(\mathrm{CuSO}_4\), we must consider the different atoms present:
- Copper (Cu): 63.55 g/mol
- Sulfur (S): 32.07 g/mol
- Oxygen (O): 16.00 g/mol but there are four oxygen atoms, so multiply by 4.
Combine these masses into one calculation: \(63.55 + 32.07 + (4 \times 16.00) = 159.62 \, \mathrm{g/mol}\).

In the case of a hydrated compound like \(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2\mathrm{O}\), you also need to add the mass of the water. One water molecule has a molar mass of \((2 \times 1.01) + 16.00 = 18.02 \, \mathrm{g/mol}\). Since there are five water molecules (_5_ \(\mathrm{H}_2\mathrm{O}\)), the total would be \(5 \times 18.02 = 90.10 \, \mathrm{g/mol}\). The total molar mass of the hydrated \(\mathrm{CuSO}_4\) is then \(159.62 + 90.10 = 249.72 \, \mathrm{g/mol}\).

Percent composition is an important concept in chemistry that tells you how much of each element is present in a compound compared to the total. It is especially useful when dealing with hydrated compounds to find out the portion of water.

To find the percent composition of water in the compound \(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2\mathrm{O}\), divide the total mass of water (in this case from the five water molecules) by the total molar mass of the compound and multiply by 100 for a percentage.

Using the numbers we calculated earlier:

• Mass of water: 90.10 g/mol
• Total molar mass: 249.72 g/mol

\(\text{Percent water} = \frac{90.10}{249.72} \times 100 = 36.08\%.\)So, this compound consists of 36.08% water by mass. This knowledge can help chemists understand the stability and reactions of the compound.

Hydration refers to the process of adding water molecules to a substance, often forming a solid compound known as a hydrate. In our exercise, \(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2\mathrm{O}\) is a hydrated form of copper sulfate, with five water molecules associated with each formula unit of \(\mathrm{CuSO}_4\).

This hydration process changes the properties of the original compound, often influencing both its physical appearance and chemical behavior. In particular, the mass of the hydrated compound is significantly increased due to the added water molecules.

When heat is applied, as in our example, these water molecules can be released as steam, leading to a process known as dehydration. As a result, the compound reverts to its anhydrous form \(\mathrm{CuSO}_4\), losing a fraction of its mass equivalent to the mass of the water driven off.

The fraction of mass lost upon dehydration can be calculated by dividing the mass of water by the total hydrated mass. Using our previous calculations, this is:

• Mass of water: 90.10 g/mol
• Total hydrated mass: 249.72 g/mol

\(\text{Fraction of mass lost} = \frac{90.10}{249.72} = 0.3608\,\)which means approximately 36% of the compound's mass is due to bound water, and thus lost during heating.