Question

Calculate the percentage composition of aluminum sulfate, \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\)

Short answer

The percentage composition of aluminum sulfate, \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\), is \(15.76 \%\) aluminum, \(28.12 \%\) sulfur, and \(56.12 \%\) oxygen.

Step-by-step solution

1. Find the molar mass of aluminum sulfate

First, we need to find the molar mass of \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\). To do this, we will add the molar masses of the individual elements multiplied by their subscript in the compound. The molar masses of the elements are: - Aluminum (Al): \(26.98 \,\mathrm{g/mol}\) - Sulfur (S): \(32.07 \,\mathrm{g/mol}\) - Oxygen (O): \(16.00 \,\mathrm{g/mol}\) Molar mass of \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\): \((2 \times 26.98) + (3 \times (1 \times 32.07 + 4 \times 16.00))\)

2. Calculate the molar mass of each element in aluminum sulfate

Now, we will multiply the molar masses of individual elements with their respective subscripts in the compound: - Aluminum (Al): \(2 \times 26.98 = 53.96\,\mathrm{g/mol}\) - Sulfur (S): \(3 \times 32.07 = 96.21\,\mathrm{g/mol}\) - Oxygen (O): \(3 \times 4 \times 16.00 = 192.00\,\mathrm{g/mol}\)

3. Find the total molar mass of aluminum sulfate

Now we will add up the molar masses calculated above to find the total molar mass of \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\): Total molar mass: \(53.96 + 96.21 + 192.00 = 342.17\,\mathrm{g/mol}\)

4. Calculate the percentage composition of each element

Finally, we will calculate the percentage composition of each element by dividing the molar mass of the element by the total molar mass of the compound and multiplying by 100. - Aluminum (Al) percentage: \(\frac{53.96}{342.17} \times 100 = 15.76 \% \) - Sulfur (S) percentage: \(\frac{96.21}{342.17} \times 100 = 28.12 \% \) - Oxygen (O) percentage: \(\frac{192.00}{342.17} \times 100 = 56.12 \% \) Therefore, the percentage composition of aluminum sulfate, \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\), is \(15.76 \%\) aluminum, \(28.12 \%\) sulfur, and \(56.12 \%\) oxygen.

Key concepts

Molar Mass Calculation

Understanding the molar mass of a compound is a fundamental concept in chemistry. It accounts for the mass of one mole of a substance, which is the number of particles equal to Avogadro's number (\(6.022 \times 10^{23}\) particles/mol). For compounds like aluminum sulfate, \(\mathrm{Al}_2(\mathrm{SO}_4)_3\), the molar mass is calculated by summing the masses of each individual element, considering their respective numbers in the compound's formula.

For instance, if you have the molar masses of aluminum (Al), sulfur (S), and oxygen (O) and the compound \(\mathrm{Al}_2(\mathrm{SO}_4)_3\), the calculation involves multiplying the molar mass of each element by its subscript in the chemical formula, then summing these values up. The process aligns with stoichiometry and provides the basis for further calculations, like determining the percentage composition of each element within the compound.

Chemical Formula

A chemical formula, such as \(\mathrm{Al}_2(\mathrm{SO}_4)_3\) for aluminum sulfate, represents the types and numbers of atoms present in a molecule of a chemical compound. This shorthand notation is the cornerstone of chemical equations and allows chemists to convey complex information like the elemental composition and proportionality of elements succinctly.

Each element in a chemical formula is followed by a subscript number, indicating the number of atoms of that element in one molecule of the compound. If no subscript is written, it implies there is one atom of that element. Understanding the chemical formula is crucial for molar mass calculation and stoichiometry and provides an insight into the chemical’s structure.

Stoichiometry

The Role of Ratios

Stoichiometry is a section of chemistry that deals with the quantitative relationships, or ratios, of reactants and products in chemical reactions. Using the coefficients from balanced chemical equations, stoichiometry involves calculations that predict the amount of product that would form in a chemical reaction based on a given quantity of reactants.

This concept extends to determining the composition by mass of a compound as it ties into the relative masses of the constituent elements. The idea is to use the molar mass of individual elements and the stoichiometric coefficients (the subscripts in the chemical formula) to work out the entire equation for the mass percentage of each element.

Elemental Composition

Breaking Down Compounds

The elemental composition of a compound expresses the proportion of each element in the compound. This is usually presented as a percentage by weight (mass). Calculating the elemental composition involves determining the fraction of the total mass of the compound that is attributable to each element.

It's a metric that offers valuable insight into the compound's chemical characteristics and behavior. To calculate the percentage composition, as in our exercise example, you divide the total molar mass of each element (adjusted for the number of atoms of the element in one molecule) by the overall molar mass of the compound and then multiply by 100 to find the percentage. This knowledge not only lays the groundwork for stoichiometry but is also applied in areas like formulation of mixtures, nutritional studies, and material science.