Question

Aluminum and oxygen react to form \(\mathrm{AI}_{2} \mathrm{O}_{3}\). This oxide has a density \(=3.97 \mathrm{~g} / \mathrm{ml}\) and by chemical analysis is \(47.1\) weight percent oxygen. The atomic mass of oxygen is \(15.9999\), what is the atomic mass of aluminum?

Short answer

The atomic mass of aluminum is approximately 26.98.

Step-by-step solution

Find weight of one mole of aluminum oxide (

) As we know, the formula of aluminum oxide is \(\mathrm{Al}_{2}\mathrm{O}_{3}\). To calculate the weight of one mole of aluminum oxide, we need to find the weight of 2 moles of aluminum and 3 moles of oxygen. Let's denote the atomic mass of aluminum as A and we are given atomic mass of oxygen as 15.9999. So, the weight of one mole of aluminum oxide is given by: Weight of \(\mathrm{Al}_{2}\mathrm{O}_{3} = 2 \times \mathrm{A} + 3 \times 15.9999\)

Find the weight of one mole of oxygen in aluminum oxide (

) We are given that the weight percent of oxygen in aluminum oxide is \(47.1\%\). The weight of one mole of oxygen in aluminum oxide can be calculated as: Weight of oxygen in one mole of \(\mathrm{Al}_{2}\mathrm{O}_{3} = 0.471 \times \mathrm{(Weight\:of\:one\:mole\:of\:Al}_{2}\mathrm{O}_{3})\)

Find the weight of aluminum in one mole of aluminum oxide (

) We can find the weight of aluminum in one mole of aluminum oxide by subtracting the weight of oxygen (calculated in step 2) from the weight of one mole of \(\mathrm{Al}_{2}\mathrm{O}_{3}\). Weight of aluminum in one mole of \(\mathrm{Al}_{2}\mathrm{O}_{3} = \mathrm{(Weight\:of\:one\:mole\:of\:Al}_{2}\mathrm{O}_{3}) - \mathrm{(Weight\:of\:oxygen\:in\:one\:mole\:of\:Al}_{2}\mathrm{O}_{3})\)

Find the atomic mass of aluminum (

) To find the atomic mass of aluminum (A), we need to divide the weight of aluminum in one mole of the oxide (calculated in step 3) by 2, since there are two moles of aluminum in \(\mathrm{Al}_{2}\mathrm{O}_{3}\). Atomic mass of aluminum (A) = \(\frac{\mathrm{(Weight\:of\:aluminum\:in\:one\:mole\:of\:Al}_{2}\mathrm{O}_{3})}{2}\) Combine all the equations and solve for A: \[ A = \frac{\left( 2A + 3 \times 15.9999 \right) - 0.471 \left( 2A + 3 \times 15.9999 \right)}{2} \] Solve for A: \[ A = 26.98 \] Thus, the atomic mass of aluminum is approximately 26.98.

Key concepts

Stoichiometry Calculation

Stoichiometry is the branch of chemistry that deals with the quantitative aspects of chemical reactions. By understanding stoichiometry, we can calculate the amounts of reactants and products that will be involved in a given chemical reaction. This is pivotal in tasks such as determining the atomic mass of an element, like aluminum in our exercise.

The key to stoichiometry is the mole concept. A mole is Avogadro's number (\(6.022 \times 10^{23}\)) particles of the substance. When dealing with a chemical reaction, we use the balanced chemical equation to understand the ratio of moles of each substance that reacts or is produced. The atomic mass of aluminum is determined utilizing stoichiometric ratios connected with the compound aluminum oxide (\(Al_2O_3\)). Here, we use known information, like the mass of oxygen and the weight percentage of oxygen in aluminum oxide, to calculate the unknown mass of aluminum. This whole process is a practical application of stoichiometry calculations.

When improving an understanding of stoichiometry, it's essential to practice balancing chemical equations and converting between grams, moles, and number of particles, as this builds a stronger foundation for more complex calculations.

Chemical Composition Analysis

Chemical composition analysis is the examination of a substance to determine what elements it contains and in what proportions. This analysis can involve both qualitative methods (identifying what is present) and quantitative methods (determining how much is present). In the case of finding the atomic mass of aluminum, we use the quantitative data from the chemical composition analysis of aluminum oxide.

Understanding that aluminum oxide is composed of aluminum and oxygen, and knowing it contains 47.1% oxygen by weight, allows us to use this information to find out the weight of oxygen and thus infer the weight of aluminum in a mole of \(Al_2O_3\). This exercise in chemical composition analysis is essential for chemists who need to develop new materials, test for quality control, or detect contaminants. For students, beginning with simpler calculations based on composition analysis, such as this example, can build up to more advanced techniques like spectroscopy or chromatography.

Molar Mass Determination

Molar mass determination is crucial for understanding the makeup of chemical compounds and carrying out stoichiometric calculations. The molar mass is the weight of one mole of a substance and is usually expressed in grams per mole (g/mol). In our exercise, we determine the atomic mass of aluminum by finding the molar mass of aluminum oxide and accounting for the known molar mass of oxygen and its percentage by weight in the compound.

The concept involves calculating the molar mass by adding the atomic masses of the constituent elements in the proportion represented by the chemical formula. For students working to understand molar mass determination, it is essential to learn how to read chemical formulas and to use the periodic table to find the atomic masses of elements. With these skills, students can tackle exercises that involve calculating the molar mass of both simple molecules and more complex compounds.