Question

What is the percent composition of each of the following compounds? (a) \(\mathrm{SO}_{2}\) (b) \(\mathrm{CuCl}_{2}\) (c) \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) (d) \(\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\)

Short answer

The percent composition of the compounds is as follows: (a) SO2: S: 50.03%, O: 49.97%, (b) CuCl2: Cu: 47.27%, Cl: 52.73%, (c) Na3PO4: Na: 42.01%, P: 18.90%, O: 39.08%, (d) Mg(NO3)2: Mg: 16.38%, N: 18.88%, O: 64.75%.

Step-by-step solution

Calculating the molar mass of each compound

For each compound, determine the molar mass by adding up the molar masses of each atom in the molecule. Molar mass values can be found on a periodic table.

Calculating the percent composition

To find the percent composition, divide the total molar mass of each element by the total molecular mass of the compound and then multiply by 100. Perform these steps for each compound.

SO2

The molar mass of S is 32.07 g/mol and O is 16.00 g/mol. Therefore, the molar mass of SO2 is 32.07 + 2(16.00) = 64.07 g/mol. Then, the percent composition is: S: (32.07/64.07)*100=50.03%; O: (2(16.00)/64.07)*100=49.97%.

CuCl2

The molar mass of Cu is 63.55 g/mol and Cl is 35.45 g/mol. Therefore, the molar mass of CuCl2 is 63.55 + 2(35.45)=134.45 g/mol. The percent composition is: Cu: (63.55/134.45)*100=47.27%; Cl: (2(35.45)/134.45)*100=52.73%.

Na3PO4

The molar mass of Na is 22.99 g/mol, P is 30.97 g/mol, and O is 16.00 g/mol. Therefore, the molar mass of Na3PO4 is 3(22.99) + 30.97 + 4(16.00) = 163.94 g/mol. The percent composition is: Na: (3(22.99)/163.94)*100=42.01%; P: (30.97/163.94)*100=18.90%; O: (4(16.00)/163.94)*100=39.08%.

Mg(NO3)2

The molar mass of Mg is 24.31 g/mol, N is 14.01 g/mol, and O is 16.00 g/mol. Therefore, the molar mass of Mg(NO3)2 is 24.31 + 2(14.01 + 3(16.00)) = 148.33 g/mol. The percent composition is: Mg: (24.31/148.33)*100=16.38%; N: (2(14.01)/148.33)*100=18.88%; O: (2*3(16.00)/148.33)*100=64.75%.

Key concepts

Molar Mass

Molar mass is a crucial concept in chemistry that helps us understand the weight of a chemical compound. It is the sum of the atomic masses of all atoms in a molecule. To find the molar mass, look up the atomic masses on the periodic table and add them together. For example, in

• \(\text{SO}_2\), the molar mass is calculated as: \(32.07 + 2 \times 16.00 = 64.07 \text{ g/mol}\).
• For \(\text{CuCl}_2\), it’s \(63.55 + 2 \times 35.45 = 134.45 \text{ g/mol}\).

Understanding molar mass allows us to convert between grams and moles, which is essential in stoichiometry and balancing chemical equations.

Chemical Compounds

Chemical compounds are substances formed when two or more elements combine in fixed ratios. Each compound has a unique formula that shows the types and numbers of atoms involved. For instance:

• \(\text{SO}_2\) consists of sulfur and oxygen.
• \(\text{CuCl}_2\) consists of copper and chlorine.

These compounds have specific properties different from the individual elements that make them up. Recognizing these formulas helps in understanding and computing the percent composition of each element within the compound, illustrating how elements contribute to the overall mass.

Periodic Table

The periodic table is a tabular arrangement of elements based on their atomic numbers, electron configurations, and recurring chemical properties. Each element has a specific atomic mass, usually listed underneath its symbol. This information is vital when calculating molar mass, as it provides the necessary atomic weights. For example:

• The atomic mass of sulfur (S) is 32.07 g/mol.
• The atomic mass of chlorine (Cl) is 35.45 g/mol.

Using the periodic table effectively allows you to quickly find these atomic masses, which are key to understanding elemental quantities in a compound.

Elemental Composition

Elemental composition refers to the percentage by mass of each element in a compound. To determine it, divide the molar mass of each element by the total molar mass of the compound and multiply by 100. This process helps illustrate how each element contributes to the compound's overall mass. For example:

• In \(\text{Na}_3\text{PO}_4\), the percent sodium is \((3 \times 22.99/163.94) \times 100 = 42.01\%\).
• In \(\text{Mg(NO}_3)_2\), the percent nitrogen is \((2 \times 14.01/148.33) \times 100 = 18.88\%\).

Understanding elemental composition is vital for chemical analysis, allowing chemists to determine the makeup of a compound precisely.