Question

Determine the mass percent \(\mathrm{H}_{2} \mathrm{O}\) in the hydrate \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\)

Short answer

After calculating the mass percent of water in the given compound using the equation and observations made in Step 4, write down the obtained value which indicates the mass percent of water in \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} . 9 \mathrm{H}_{2}\mathrm{O}\).

Step-by-step solution

- Find molar masses

First, look up the molar masses of all elements involved. Hydrogen (H) has a molar mass of 1.00794 g/mol, oxygen (O) is 15.9994 g/mol, nitrogen (N) is 14.00674 g/mol, chromium (Cr) is 51.9961 g/mol, and lastly, oxygen (O) is again 15.9994 g/mol. Keep in mind that Nitrate (NO3) has one nitrogen atom and three oxygen atoms.

- Calculate molar mass of the hydrate

Next, calculate the molar mass of the entire hydrate. The formula \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} . 9 \mathrm{H}_{2}\mathrm{O}\) includes 1 atom of chromium, 3 nitrate groups (each containing 1 nitrogen atom and 3 oxygen atoms), and 9 water molecules (each containing 2 hydrogen atoms and 1 oxygen atom). Thus, the molar mass of the entire compound is calculated as follows: \(1 * 51.9961 \, g/mol + 3 * (1 * 14.00674 \, g/mol + 3 * 15.9994 \, g/mol) + 9 * (2 * 1.00794 \, g/mol + 15.9994 \, g/mol)\).

- Calculate molar mass of the water in the hydrate

Now, calculate the molar mass of only the water part in the hydrate. As there are 9 water molecules in the compound, the molar mass of water only is \(9 * (2 * 1.00794 \, g/mol + 15.9994 \, g/mol)\).

- Determine mass percent of water

The mass percent of a component in a compound is the mass of that component divided by the total mass of the compound, all multiplied by 100%. Hence, mass percent of water in the compound is \(\frac{{molar \, mass \, of \, water}}{{total \, molar \, mass \, of \, hydrate}} * 100%\). Calculate this using the values determined in steps 2 and 3.

Key concepts

hydrate

A hydrate is a compound that includes water molecules that are chemically bonded to it.
This means there are water molecules integrated into its solid structure.
In the chemical formula, this is typically represented with a “dot” notation, like in \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\).
Hydrates contain a specific number of water molecules.
For example, in this compound, there are 9 water molecules for each unit of \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}\).
This is critical for understanding the compound's complete chemical identity. When these hydrates are heated, the water can be removed, turning the compound into what we call an "anhydrous" form (without water).
The calculation of the mass percent of water in such compounds involves comparing the mass of the water component to the total mass of the compound.
This is an important concept in chemistry, especially when determining formulas and analyzing the composition of substances.

molar mass calculation

Calculating molar mass is a fundamental skill in chemistry.
It's important because it allows us to relate the mass of a chemical substance to its mole count.
This enables us to predict the proportions of elements in a compound.
To calculate the molar mass of a compound, sum the masses of all the atoms found in the chemical formula.
For example, in the hydrate \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\), you have to add up:

• the molar mass of chromium (Cr),
• three nitrate groups (each containing one nitrogen and three oxygens), and
• the mass of 9 water molecules (each containing 2 hydrogen atoms and 1 oxygen atom).

The molar mass for the entire compound is crucial when determining parameters like mass percent.

chemical formula interpretation

Interpreting a chemical formula involves understanding what each part of it represents.
This step helps in identifying the amounts and types of atoms within the compound.
For example, each symbol stands for a different element, and the subscript numbers indicate the quantity of atoms in that group present in the formula.
In \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\), this tells us there is one chromium atom, three nitrate ions, and nine water molecules.
The dot in the formula indicates the waters of hydration, which are distinct from the other atoms but part of the same crystalline structure.
Understanding this is crucial for calculating things likemolar masses and the composition of compounds.
It also helps in setting up and solving different types of chemical equations.