Question

Calculate the percent composition by mass of these compounds: (a) \(\mathrm{NaBr}\) (d) \(\mathrm{SiCl}_{4}\) (b) \(\mathrm{KHCO}_{3}\) (e) \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) (c) \(\mathrm{FeCl}_{3}\) (f) \(\mathrm{AgNO}_{3}\)

Short answer

NaBr: 22.34% Na, 77.66% Br. KHCO3: 39.06% K, 1.01% H, 12.00% C, 47.94% O. FeCl3: 34.43% Fe, 65.57% Cl. SiCl4: 16.54% Si, 83.46% Cl. Al2(SO4)3: 15.77% Al, 28.12% S, 56.11% O. AgNO3: 63.51% Ag, 8.25% N, 28.24% O.

Step-by-step solution

- Calculate Molar Mass of Each Compound

Determine the molar mass of each compound by summing the atomic masses of the constituent elements. Refer to the periodic table for atomic masses.

- Molar Mass of \(\mathrm{NaBr}\)

The atomic masses are: Na = 22.99, Br = 79.90. Sum them to get the molar mass of \(\mathrm{NaBr}\): \(22.99 + 79.90 = 102.89\) g/mol.

- Molar Mass of \(\mathrm{KHCO}_{3}\)

The atomic masses are: K = 39.10, H = 1.01, C = 12.01, O (3 atoms) = 3 * 16.00 = 48.00. Sum them to get the molar mass of \(\mathrm{KHCO}_{3}\): \(39.10 + 1.01 + 12.01 + 48.00 = 100.12\) g/mol.

- Molar Mass of \(\mathrm{FeCl}_{3}\)

The atomic masses are: Fe = 55.85, Cl (3 atoms) = 3 * 35.45 = 106.35. Sum them to get the molar mass of \(\mathrm{FeCl}_{3}\): \(55.85 + 106.35 = 162.20\) g/mol.

- Molar Mass of \(\mathrm{SiCl}_{4}\)

The atomic masses are: Si = 28.09, Cl (4 atoms) = 4 * 35.45 = 141.80. Sum them to get the molar mass of \(\mathrm{SiCl}_{4}\): \(28.09 + 141.80 = 169.89\) g/mol.

- Molar Mass of \(\mathrm{Al}_{2}(\mathrm{SO}_{4})_{3}\)

The atomic masses are: Al (2 atoms) = 2 * 26.98 = 53.96, S (3 atoms) = 3 * 32.07 = 96.21, O (12 atoms) = 12 * 16.00 = 192.00. Sum them to get the molar mass of \(\mathrm{Al}_{2}(\mathrm{SO}_{4})_{3}\): \(53.96 + 96.21 + 192.00 = 342.17\) g/mol.

- Molar Mass of \(\mathrm{AgNO}_{3}\)

The atomic masses are: Ag = 107.87, N = 14.01, O (3 atoms) = 3 * 16.00 = 48.00. Sum them to get the molar mass of \(\mathrm{AgNO}_{3}\): \(107.87 + 14.01 + 48.00 = 169.88\) g/mol.

- Calculate Percent Composition by Mass for Each Element

For each element in a compound, divide the element's mass in one mole of the compound by the total molar mass of the compound and multiply by 100 to get the percent composition.

- Percent Composition of \(\mathrm{NaBr}\)

For Na: \(\frac{22.99}{102.89} \times 100 = 22.34\%\). For Br: \(\frac{79.90}{102.89} \times 100 = 77.66\%\).

- Percent Composition of \(\mathrm{KHCO}_{3}\)

For K: \(\frac{39.10}{100.12} \times 100 = 39.06\%\). For H: \(\frac{1.01}{100.12} \times 100 = 1.01\%\). For C: \(\frac{12.01}{100.12} \times 100 = 12.00\%\). For O: \(\frac{48.00}{100.12} \times 100 = 47.94\%\).

- Percent Composition of \(\mathrm{FeCl}_{3}\)

For Fe: \(\frac{55.85}{162.20} \times 100 = 34.43\%\). For Cl: \(\frac{106.35}{162.20} \times 100 = 65.57\%\).

- Percent Composition of \(\mathrm{SiCl}_{4}\)

For Si: \(\frac{28.09}{169.89} \times 100 = 16.54\%\). For Cl: \(\frac{141.80}{169.89} \times 100 = 83.46\%\).

- Percent Composition of \(\mathrm{Al}_{2}(\mathrm{SO}_{4})_{3}\)

For Al: \(\frac{53.96}{342.17} \times 100 = 15.77\%\). For S: \(\frac{96.21}{342.17} \times 100 = 28.12\%\). For O: \(\frac{192.00}{342.17} \times 100 = 56.11\%\).

- Percent Composition of \(\mathrm{AgNO}_{3}\)

For Ag: \(\frac{107.87}{169.88} \times 100 = 63.51\%\). For N: \(\frac{14.01}{169.88} \times 100 = 8.25\%\). For O: \(\frac{48.00}{169.88} \times 100 = 28.24\%\).

Key concepts

Molar Mass Calculation

Understanding molar mass calculation is crucial when working with chemical compounds. The molar mass of a compound is the sum of the atomic masses of its constituent elements, expressed in grams per mole. Each element in the periodic table has a specific atomic mass. To find the molar mass of a compound like \(\mathrm{NaBr}\), you need the atomic masses of sodium (Na) and bromine (Br). Add these values: Na = 22.99 g/mol and Br = 79.90 g/mol. So, the molar mass of \(\mathrm{NaBr}\) is \(22.99 + 79.90 = 102.89\) g/mol.

The same process applies to other compounds. For example:

• \(\mathrm{SiCl}_{4}\): Si = 28.09 g/mol, Cl (4 atoms) = \(4 \times 35.45 = 141.80\) g/mol. Total molar mass = \(28.09 + 141.80 = 169.89\) g/mol.
• \(\mathrm{KHCO}_{3}\): K = 39.10 g/mol, H = 1.01 g/mol, C = 12.01 g/mol, O (3 atoms) = \(3 \times 16.00 = 48.00\) g/mol. Total molar mass = \(39.10 + 1.01 + 12.01 + 48.00 = 100.12\) g/mol.

Getting comfortable with calculating molar masses allows you to correctly determine the percent composition by mass of any compound.

Chemical Compounds

Chemical compounds are substances composed of two or more different elements that are chemically bonded. Each compound has a unique chemical formula that indicates the elements involved and their relative proportions. For example:

• \(\mathrm{NaBr}\) is composed of sodium and bromine.
• \(\mathrm{FeCl}_{3}\) consists of one iron (Fe) atom and three chlorine (Cl) atoms.

Understanding the formula of a compound is essential because it allows you to determine the molar mass and thus calculate the percent composition by mass. Each element's contribution to the overall mass of the compound can be identified, which is useful in various chemical analyses and reactions.

Elemental Composition

Elemental composition refers to the percent by mass of each element in a compound. After calculating the molar mass, you can find the percent composition of each element. This is done by dividing the mass of each element in one mole of the compound by the total molar mass, then multiplying by 100.
For example, for \(\mathrm{NaBr}\):

• Sodium (Na): \(\frac{22.99}{102.89} \times 100 = 22.34\%\).
• Bromine (Br): \(\frac{79.90}{102.89} \times 100 = 77.66\%\).

This process tells you how much of each element is present in the compound. It's a fundamental concept in chemistry that ensures you understand the composition of different substances. Learning to calculate elemental composition will aid in grasping more complex topics in chemical analysis and reaction stoichiometry.