Question

The copper-containing compound \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{SO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) is a beautiful blue solid. Calculate the molar mass of the compound and the mass percent of each element.

Short answer

The molar mass is 241.76 g/mol. Mass percents: Cu = 26.30%, N = 23.18%, H = 4.18%, S = 13.27%, O = 33.07%.

Step-by-step solution

Identifying Elemental Components

The compound has the chemical formula \( \text{Cu(NH}_3)_4\text{SO}_4 \cdot \text{H}_2\text{O} \). It contains copper (Cu), nitrogen (N), hydrogen (H), sulfur (S), and oxygen (O).

Listing Atomic Weights

The atomic weights are approximately as follows: Cu = 63.55 g/mol, N = 14.01 g/mol, H = 1.01 g/mol, S = 32.07 g/mol, and O = 16.00 g/mol.

Calculating Molar Mass

Calculate the total molar mass by adding the individual contributions: 1 Cu (63.55 g/mol) + 4 N (4 x 14.01 g/mol) + 12 H (12 x 1.01 g/mol) + 1 S (32.07 g/mol) + 5 O (5 x 16.00 g/mol).

Calculation of Individual Contributions

For copper: 63.55 g/mol.For nitrogen: \(4 \times 14.01\) g/mol = 56.04 g/mol.For hydrogen: \(10 \times 1.01\) g/mol = 10.10 g/mol.For sulfur: 32.07 g/mol.For oxygen: \(5 \times 16.00\) g/mol = 80.00 g/mol.

Summing to Find Total Molar Mass

The total molar mass is \(63.55 + 56.04 + 10.10 + 32.07 + 80.00 = 241.76\) g/mol.

Calculating Mass Percentages

To find the mass percent of each element, divide the total mass of each element by the molar mass of the compound, then multiply by 100. For example, for copper, \((63.55 / 241.76) \times 100\%\). Repeat for all elements.

Calculating Each Element's Mass Percentage

Mass percent of Cu: \((63.55 / 241.76) \times 100 \approx 26.30\%\).Mass percent of N: \((56.04 / 241.76) \times 100 \approx 23.18\%\).Mass percent of H: \((10.10 / 241.76) \times 100 \approx 4.18\%\).Mass percent of S: \((32.07 / 241.76) \times 100 \approx 13.27\%\).Mass percent of O: \((80.00 / 241.76) \times 100 \approx 33.07\%\).

Key concepts

Mass Percentage Calculation

Mass percentage is a way to express the concentration of each element within a chemical compound. To calculate it, you need to understand the contribution of each element to the total molar mass. Here's how you can do it:

1. **Find the atomic mass of each element.** You will use the periodic table for this. For example, copper (Cu) has an atomic mass of about 63.55 g/mol.
2. **Calculate the total mass of each element within the compound.** Take into account how many of each element are present. For example, in the compound \(\text{Cu(NH}_3)_4\text{SO}_4 \cdot \text{H}_2\text{O}\), there are four nitrogen (N) atoms, which means you multiply the atomic mass of N by 4.
3. **Sum up the masses of all elements to find the molar mass of the compound.**
4. **Determine the mass percentage.** Divide the total mass of each element by the molar mass of the compound, then multiply by 100 to get a percentage. This gives you a clear picture of how much each element contributes to the overall mass.

Chemical Formulas

Chemical formulas are symbolic representations of compounds. They indicate the types and numbers of atoms involved.

- **Subscripts** in a chemical formula show the number of each atom in the molecule. For example, in \(\text{(NH}_3)_4\), the subscript 4 indicates four ammonia units.
- **Parentheses** are used when a group of atoms appears more than once in the compound. For example, \(\text{(NH}_3)_4\) means the ammonia unit is present four times.
- **Dotted formulas**, like \(\cdot \text{H}_2\text{O}\), represent water of hydration, indicating water molecules associated with the compound.

The chemical formula essentially tells us what elements and how many of each are present in a compound. This information is crucial for calculating both molar mass and mass percentage.

Atomic Weights

Atomic weights are fundamental for understanding the mass contributions of different elements in a compound. They represent the average mass of an atom of an element compared to 1/12th the mass of a carbon-12 atom, which is a common reference.

- Each element's atomic weight is usually listed in units of grams per mole (g/mol).
- In calculations, these atomic weights help determine how much each element weighs when multiplied by the number of atoms in a formula unit of the compound.
- For example, oxygen has an atomic weight of 16.00 g/mol. If a chemical formula includes 5 oxygen atoms, you would multiply 16.00 by 5 to find the total mass contribution of oxygen.

Understanding atomic weights enables chemists to calculate substances' molar masses accurately, which is essential for determining how compounds react or are utilized in processes.